Adams Tire Mdr3 Help-152

Welcome to Adams/Tire

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Introducing Adams/TireAdams/Tire software is a module you use with Adams/Car, Adams/Chassis, Adams/Solver, or Adams/View to add tires to your mechanical model and to simulate maneuvers such as braking, steering, acceleration, free-rolling, or skidding. Adams/Tire lets you model the forces and torques that act on a tire as it moves over roadways or irregular terrain.

Adams/Tire is a set of shared object libraries that Adams/Solver calls through the Adams DIFSUB, GFOSUB, GSESUB subroutines. These subroutines calculate the forces and moments that tires exert on a vehicle as a result of the interaction between the tires and road surface.

You can use Adams/Tire to model tires for either vehicle-handling, ride and comfort, and vehicle-durability analyses.

• Handling analyses are useful for studying vehicle dynamic responses to steering, braking, and throttle inputs. For example, you can analyze the lateral accelerations produced for a given steering input at a given vehicle speed.

• Ride and comfort analyses are useful for assessing the vehicle's vibrations due to uneven roads with short wavelength obstacles (shorter than tire circumference), such as level crossings, grooves, or brick roads.

• 3D contact analyses are useful for generating road load histories and stress and fatigue studies that require component force and acceleration calculation. These studies can help you calculate the effects of road profiles, such as pothole, curb, or Belgian block.

Adams/Tire ModulesAdams/Tire has a line of tire modules that you can use with Adams/View, Adams/Solver, Adams/Car, and Adams/Chassis. The modules let you model the rubber tires found on many kinds of vehicles, such as cars, trucks, and planes. More specifically, the modules let you model the force and torque that tires produce to accelerate, brake, and steer vehicles. The five modules available in Adams/Tire are:

• Adams/Tire Handling Module

• Adams/Tire 3D Spline Road Module

• Adams/Tire 3D Shell Road Module

• Specific Tire Models

• Features in Adams/Tire Modules

Adams/Tire Handling ModuleAdams/Tire Handling incorporates the following tire models for use in vehicle dynamic studies:

• Using the PAC2002Tire Model*• Using the PAC-TIME Tire Model

• Using Pacejka '89 and '94 Models*• Using the Fiala Handling Force Model

• Using the UA-Tire Model

13Welcome to Adams/Tire

• 521-Tire Model

Adams/Tire Handling uses a point-follower method to calculate tire normal force. Standard Adams/Tire is limited to two-dimensional roads, but can be extended with the three-dimensional capabilities of Adams/Tire 3D Spline Road.

*The formulae used in the Pacejka tire models are derived from publications, and are commonly referred to as the Pacejka method in the automotive industry. Dr. Pacejka himself is not personally associated with the development of these tire models, nor does he endorse them in any way.

Adams/Tire 3D Spline Road ModuleAdams/3D Spline Road lets you define an arbitrary three-dimensional smooth road surface. In addition, you can place three-dimensional road obstacles, such as a curb, pothole, ramp, or road crown, on top of the underlying smooth road surface. You can use the 3D Spline Road Module with any of the tire models in Adams/Tire. Use the smooth road part in combination with any of the handling tire models, or use the more advanced FTire to deal with road obstacles for ride and comfort and durability analysis.

Adams/Tire 3D Shell Road ModuleAdams/Tire 3D Shell Road uses a three-dimensional equivalent-volume method to calculate tire normal force on three-dimensional roads for use in predicting vehicle loads for durability studies. You can use the Pacejka 2002, Pacejka TIME, Pacejka '89, Pacejka '94, or Fiala models to calculate the tire handling forces and moments (lateral force, longitudinal force, aligning torque, and so on).

Specific Tire ModelsIn addition to the tire models in the Adams/Tire Handling Module, Adams/Tire supplies specific tire models:

• Pacejka Motorcycle Tire Model A Pacejka tire model suitable for motorcycle handling analysis. It describes the tire-road interaction forces with tire-road inclination angles up to 60 degrees.

• Adams/Tire FTire Module FTire can describe the 3D tire dynamic response up to 120 Hz and beyond, due to its flexible ring approach for the tire belt. It can handle any road obstacle.

All tire models support the Adams/Linear functionality.

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Features in Adams/Tire ModulesThe table below lists the features available in Adams/Tire modules.

Which Tire Model Should You Use?Each tire model is valid in a specific area. Using a tire model outside this area can result in non-realistic analysis results. The next table indicates the tire model(s) that are the best to use for a number of applications.

In general, the Adams/Tire Handling models are valid on rather smooth roads only: the wavelength of road obstacles should not be smaller than the tire circumference. If the wavelengths are shorter, you should use the FTire model to cope with the non-linear tire enveloping effects.

Some of the Handling Tire models can describe the first-order response of a tire, but do not take the eigenfrequencies of the tire itself into account. Therefore, the Handling Tire models are valid up to approximately 8 Hz. The PAC2002 uses a contact mass method that enables it to describe tire behavior up to 15 Hz. Beyond that, a tire model should be used, including modeling the tire belt, as FTire does.

Typical Applications for Each Tire Model

Adams/Tire modules: Features: Requirements:Adams/Tire Handling Fiala Tire Model

Pacejka '89* Tire ModelPacejka '94* Tire ModelPacejka 2002 Tire ModelPacejka TIME Tire ModelUA-Tire Tire Model2D Road Models-----------------------------------5.2.1 Tire 5.2.1 Tire Methods:- Equation Method- Interpolation Method5.2.1 Road Methods:- Point Follower- Equivalent Plane

Full Simulation Package

Adams/Tire 3D Spline Road Fiala Tire Model3D Smooth Road and Road pertubations


Adams/Tire FTire 2D FTire Model3D FTire Model2D Road Models


Adams/Tire Motorcycle Tire Pacejka Motorcycle Tire Model2D Road Models


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Learning Adams/Tire Basics

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Use and Understanding of Adams/Tire

How to Use Adams/TireThe Tire Basic help section provides overview material for using Adams/Tire to add tires to a mechanical system model. It assumes that you know how to run Adams/Car, Adams/Solver, Adams/View, or Adams/Chassis. It also assumes that you have a moderate level of tire-modeling proficiency

You use Adams/Tire to simulate tires according to your analysis requirements. You can create your own tire models or you can use the tire models that come with Adams/Tire.

Adams/Tire Steps

13Learning Adams/Tire Basics

To use Adams/Tire:1. Define tires. How you define tires depends on the product you are using (Adams/Chassis,

Adams/Car, or Adams/Solver). For more information on defining tires, see Defining Tires. Regardless of the product you use, the product creates an Adams dataset (.adm), which contains the necessary statements that represent the tires in your Adams model, as well as other elements of the vehicle, such as the wheel, suspension, and landing gear strut. The primary statement for each tire is a GFORCE that applies the tire force to the wheel in your suspension.

2. Reference an existing tire property file from:

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• Adams/Tire (/install_dir/solver/atire)• Tire manufacturers or testing companies.• Files that you create. For example, you can create your own tire property file for simple kinds

of tire models, such as the Fiala model.You can find examples of tire property files for all tire models in the Adams installation directory at:install_dir/solver/atirewhere install_dir/ is the path to the installation directory for Adams/Tire.

3. Reference an existing road property file. You can find an example road property file for a flat road in the Adams installation directory:install_dir/solver/atire/mdi_2d_flat.rdfwhere install_dir/ is the path to the installation directory for Adams/Tire.

4. Run a simulation of your model. You can run a simulation using Adams/Car’s version of Adams/Solver (you do not need an Adams/Car license) or you can create an Adams/Solver user library and then run your simulation using this library and Adams/Solver. For more information, see Performing Simulations.

5. View the results of the simulation in a postprocessor, such as Adams/PostProcessor.

Understanding Adams/Tire ProcessesWhen you add tires to your Adams model, three processes occur:

• Adams/Solver invokes Adams/Tire.• Adams/Tire determines the tire and road model to use.• Adams/Tire performs any calculations the tire model requires.

Flow of Information in Adams/Tire


Invoking Adams/Tire• When you perform an analysis, Adams/Solver investigates your .adm file to find elements that

represent a tire. For example, it looks for a GFORCE with the necessary parameters to define the force to the wheel in your suspension. When it finds these parameters, it invokes Adams/Tire.

• Adams/Solver obtains the names of the tire property file (.tir) and road property file (.rdf) from the STRING statements in the .adm file.

Determining Tire and Road Model to UseInside Adams/Tire, the Tire Object Manager examines the tire property file to determine the tire model (for example, Fiala or Pacejka ‘89) to use and examines the road property file to determine the road model (for example, 2D or 3D) to use.

Performing Calculations• The Tire Object Manager calls the selected tire model to calculate the tire forces and moments.• The tire model reads the tire property file to obtain data for calculating the tire forces and

moments. It then calls the road model to evaluate where the road is in relation to the tire.• The road model reads the road property file to obtain data about the road.

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• The tire model returns the forces and moments to Adams/Solver.• Adams/Solver applies the forces and moments to the wheel part.


Defining Tires If you use Adams/Car or Adams/Chassis, typically the models you work with will already include tires (for example, the statements necessary to invoke Adams/Tire). Therefore, you do not need to add tires to your model. If you work with Adams/View, however, you will need to define the tires, and for Adams/Solver, add statements to your Adams model using Adams/View or a text editor. Learn how to work with:

• Adams/View

• Adams/Car

• Adams/Chassis

• Adams/Solver

• Defining Wheel Inertia

Defining Tires in Adams/CarAdams/Car includes a wheel-tire subsystem and template that you can use in any full-vehicle assembly. The wheel-tire subsystem includes all the elements necessary to start Adams/Tire. You can modify the wheel inertia and change the property files.

To modify tires in a subsystem:1. Select the wheel/tire on the screen, right-click, and then select Modify.

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The Modify Wheel dialog box appears with options that allow you to modify the tire property file and wheel inertia..

2. Change the values as desired, and then select OK. Learn about entering values in Create/Modify Wheel.

Defining Tires in Adams/ChassisAdams/Chassis includes wheels and tires in all body-tire subsystems.

To modify tires in Adams/Chassis:1. In Build mode, in the treeview, select the wheel subsystem.2. In the property editor, select the Tires tab.

The property editor displays options for changing the wheels and tires as shown below.Tires Tab in Adams/Chassis

Note: You can also use the Display Tire Property File tool to display the tire property file in an Information window. You cannot, however, specify or display the road property file from this dialog box. In Adams/Car, you specify the road property file when you submit a full-vehicle analysis

../../../dbox_help/dbox_tem_whe.html

../../../dbox_help/dbox_tem_whe.html


3. Edit the wheels and tires, such as edit the tire property files and change the scaling coefficients. Learn about tire subsystems in ADAMS/Chassis.

Defining Tires in Adams/SolverIf you use Adams/Solver, you must add a set of statements to your Adams model for each tire as described in the table, Statements Needed for Adding Tires to Your Model. Once you have added these statements to your model, you change the tire or road property file by entering new file names in the STRING statements holding the file names. You can do this in your Adams dataset (.adm) or from an Adams/Solver command file (.acf) using a STRING command. In an .acf file, the STRING command must appear before any simulation commands. For example:

test_rig.admmytestSTRING/99, STRING=/usr/mdi/solver/atire/mdi_fiala01.tirSIMULATE/STATICSIMULATE/DYNAMIC, DURATION=1.0,STEPS=50STOP

• Statements Needed for Defining Tires• Example Dataset

Statements Needed for Defining TiresFor each tire you want to add to your model, you must create a set of statements in your model. This can be done using the dialog box in Adams/View (see Defining Tires in Adams/View) or manually using a text editor. For a car with four tires, you need four sets of statements. The table below describes the sets of statements. The table, MARKER Locations and Orientations, describes how to locate and orient the three MARKERs.

../../../build/250_tire.html

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Statements Needed for Adding Tires to Your Model

Statement types: Purpose in dataset:MARKER (3) • Wheel center marker - Identify the wheel part, the wheel center

location and orientation, and the location for applying tire force movements. Use as the GFORCE I marker.

• Road floating marker - Identify the road part to the GFORCE for applying reaction forces. Use as the GFORCE JFLOAT marker.

• Road reference marker - Identify the origin and orientation of the road. Use as the GFORCE RM marker.

You must locate and orient the MARKER statements as described in MARKER Locations and Orientations.

GFORCE (1) Apply the tire force and moments to the wheel part.DIFF (2) Integrate internal tire states for lag effects.REQUEST (Up to 11) Output tire kinematics and forces (longitudinal slip, slip angle, camber angle,

contact patch forces, and moments). For more information, see Performing Simulations and Viewing Results.

STRING (5) Identify the tire property file, road property file, and other miscellaneous information.

Note: The STRING for "contact type" is required for Adams to correctly create the STI tire, but it does not change the contact method, which is based entirely on the road model.

ARRAY (1) Holds the IDs of the GFORCE, DIFF, and STRING statements.


MARKER Locations and Orientations

Example DatasetThis section gives you an example dataset fragment that includes a complete set of statements for a single tire. The example is based on the following assumptions:

• PART/21 is the wheel and PART/99 is ground.• The orientations assume that the ground part's x-axis points towards the rear of the vehicle, the

y-axis points towards the right side of the vehicle, and the z-axis points upward.! adams_view_name='wheel_center_marker'MARKER/1, PART=21, QP = 0,0,0, REU = 180D, 0D, 0D !

adams_view_name='road_floating_marker'MARKER/2, PART = 99

Marker statements required in dataset: Location and orientation:

Wheel center marker Because the tire applies forces to the wheel center marker, you must define the wheel center so that it belongs to the wheel part and is located at the wheel center. You orient the wheel center as follows:

• x-axis lies in the wheel plane and points in the forward direction of the wheel.

• y-axis lies along the wheel's spin axis and points towards the left side of the vehicle.

• z-axis lies in the wheel plane and points upward.Road floating marker The tire applies the reaction forces to the road floating marker. The road

floating marker must belong to the road part, usually ground, and must be defined as FLOATING. Because the marker floats, you do not enter a location or orientation.

Road reference marker The road reference marker gives the location and orientation of the road. You define the road reference marker so that it belongs to the road part, usually ground. In addition, the road reference marker’s z-axis must be directed upward, meaning the z-axis is parallel to, but points in the opposite direction of, the gravity vector.

Locations of the points on the road contained in the road property file are given relative to this marker. Generally, the road reference marker should be located on the road surface and below the wheel center by approximately the static loaded radius of the tire.

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, FLOATING !

adams_view_name='road_reference_marker'MARKER/3, PART = 99 ! adams_view_name='tire_forces'GFORCE/1, I = 1, JFLOAT = 2, RM = 3, FUNCTION = USER(900,1,100)/, ROUTINE=abgTire::gfo900 !

adams_view_name='tire_force_dif1'DIFF/2, IC = 0, FUNCTION = USER(900,1,100)/, ROUTINE=abgTire::dif900 !

adams_view_name='tire_force_dif2'DIFF/3, IC = 0, FUNCTION = USER(900,1,100)/, ROUTINE=abgTire::dif900 !Map for GFORCE/DIFF USER Functions:!-----------------------------------!par(1): dispatcher branch for tire request (always 900).!par(2): tire GFORCE statement id.!par(3): tire ARRAY statement id. !

adams_view_name='tire_input_array'ARRAY/100,IC,SIZE=9,NUM= 2, 3, 1, 99, 100, 101, 102, 103, 0!array[ 1] : 1st DIFF statement id!array[ 2] : 2nd DIFF statement id!array[ 3] : side flag (0 left, 1 right)!array[ 4] : tire_minor_role STRING id!array[ 5] : tire_property_file STRING id!array[ 6] : simulation_type STRING id!array[ 7] : road_property_file STRING id!array[ 8] : road_contact_type STRING id!array[ 9] : RIGID_WHEEL Radius (SUSPENSION analysis tire only) !

adams_view_name='tire_rolling_states'REQUEST/1,, FUNCTION = USER(902,1,1) !

adams_view_name='tire_kinematic_states_ISO'REQUEST/2,, FUNCTION = USER(902,2,1)!adams_view_name='tire_forces_contact_patch_ISO'


REQUEST/3,, FUNCTION = USER(902,3,1) !Map for REQUEST USER Functions:!-------------------------------!par(1) = branch for tire request (always 902).!par(2) = reqtyp = {1,2,3,4,5,6,7.8.9.10,11}!par(3) = tire GFORCE statement id.!String Statements Description of use:!------------------!! adams_view_name='tire_minor_role'! Used by Adams/Car to determine minor role (for example, FRONT or REAR).STRING/99,S=front

! adams_view_name='tire_property_file'! Used by TYRxxx routines. Name of tire property file including

full path that! contains tire data or 'RIGID_WHEEL' for use in a suspension

analysis.STRING/100,S=mdi_tire01.tir

!adams_view_name='simulation_type'

! Used by Adams/Car to determine analysis to be performed one of'VEHICLE_HANDLING_DYNAMIC'or 'SUSPENSION'STRING/101,S=VEHICLE_HANDLING_DYNAMIC

!adams_view_name='road_property_file'

! Used by ARCxxx routines. Name of road property file including full path that

! contains road data or 'BEDPLATE' for a flat, rigid road used! with suspension analysis.

STRING/102,S=example_2d_flat.rdf ! adams_view_name='road_contact_type'! handling/durability !STRING/103, STRING =handling

Defining Tires in Adams/ViewAdams/View provides a dialog box that introduces a tire-wheel assembly in your model. You can also use the dialog box to create a road.

• Creating a Tire-Wheel Assembly

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• Creating a Road

Creating a Tire-Wheel Assembly

To create a tire-wheel assembly in Adams/View:1. Do one of the following:

• From the Forces tool stack or palette, select the Tire tool.• From the Build menu, point to Forces, and then select Special Force: Tire.

The Create Wheel and Tire dialog box appears with options that allow you to introduce the wheel inertia, tire property file, and side of the vehicle.

../../view_help/connector_panel.htm

../../view_help/connector_panel.htm


2. Enter the values as desired to define the tire, and then select OK.

Creating a RoadIf your model includes tires, you must specify a road because each tire must reference a road. The road determines the surface friction, bumps, and other inputs to tires.

To create the road:1. Display the Create Wheel and Tire dialog box as explained in step 1 above.

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2. Right-click the Road text box, point to vpg_road, and then select Create.The Create Road dialog box appears.

3. Enter the values as desired, and then select OK..

Defining Wheel InertiaThe input values for the wheel part inertia are different depending on the tire model you are using. There are differences among the tire models in the Adams/Tire Handling Module, including Adams/Tire Motorcycle Tire, and FTire, as explained in the next sections:

• Adams/Tire Handling and Motorcycle Modules

• Adams/Tire FTire

Adams/Tire Handling and Motorcycle ModulesFor tire models in the Adams/Tire Handling Module and the Pacejka Motorcycle Tire model, the inertia given for the wheel part must be equal to the total inertia of the tire and the rim.

Note: This dialog box generates a tire interface based on the general-state equation subroutine. A more simple interface is shown in Defining Tires Using Adams/Solver.


Adams/Tire FTire In FTire, a part of the tire can move with respect to the rim. Therefore, the tire mass and moments of inertia have to be split into two parts: a part that is moving with the rim (wheel part) and a part that is moving with the tire itself. This subdivision is performed during preprocessing of the tire property (.tir) file. When a simulation begins with FTire, the following lines appear in the .msg file:

CTI: add the following mass properties to the rim in your MBS modelCTI: (the 'rim-fixed' tire parts which are not accounted for in FTire):

The inertia data printed after this message has to be added to the rim inertia and used to defined the wheel part inertia. Modification of the wheel part is not done automatically.

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Simulations and Results

Performing SimulationsOnce you have incorporated the required statements for modeling a tire into your dataset, you can submit the dataset for simulation. If you have Adams/Car installed, you can submit your dataset to the Adams/Car version of Adams/Solver, or you can create an Adams/Solver user library and then run your simulation using this library and standard Adams/Solver.

To submit your dataset to the Adams/Car version of Adams/Solver, do one of the following:In a command window, submit your dataset for simulation using the following commands:

• For UNIX, enter: mdi -c acar ru-solver

• For Windows, enter: mdi acar ru-solver

• On Windows, from the Start menu, point to Programs, point to MSC.Software, point to MD R2 Adams, point to ACar, and then select Adams - Car (solver).

• On UNIX, from the Adams Toolbar, right-click the Adams/Car tool, and then select Adams/Car - Solver.

To create an Adams/Solver user library: 1. Copy the file install_dir/solver/atire/atire.f to your local directory. 2. Using atire.f, create a user Adams/Solver library:

a. In a command window, enter the command, where mysol.dll is the name of the library: • For UNIX, enter:

mdi -c cr-user n atire.f -n mysol.dll exit• For Windows, enter:

mdi cr-user n atire.f -n mysol.dll exitb. On Windows, from the Start button, point to Programs, point to MSC.Software, point to

MD R2 Adams, point to ASolver, and then select Create Custom Solver. Follow the menu selections to create a private or site library.

Note: You can also set the Adams/Car tool on the Adams Toolbar to automatically run Adams/Car with Adams/Solver.


c. On UNIX, from the Adams Toolbar, right-click the Adams/Solver tool, point to New, and then select Adams/Solver User Library. Enter the parameters to define how to create the library. .

To submit your dataset to Adams/Solver using your Adams/Solver user library:

• In a command window, submit your dataset for simulation using the following command (assuming your library was mysol): a. For UNIX, enter:

mdi -c ru-user i mysol .b. For Windows, enter:

mdi -c ru-user i mysol .• On Windows, from the Start menu, point to Programs, point to MSC.Software, point to MD

R2 Adams, point to ASolver, and then select Run Custom Solver. Enter the name of the library you want to run.

• On UNIX, from the Adams Toolbar, right-click the Adams/Solver tool, point to Select Library, and then select a library, such as mysol.

Outputting ResultsIf you combine requests with a USER function, you can output tire results to the request (.req) and results (.res) files. The form of the request statement is:

REQUEST/id, FUNCTION = USER(902, REQTYP, TIR_ID)/, ROUTINE = abgTire::req902

where:

• 902 - Branch flag for tire request subroutine.• REQTYP - Integer code fixing the information output to the request file. Valid values are

{1,2,3,4,5,6,7,8,9,10,11}. The output for each value of REQTYP is described in the table, Tire Outputs.

• TIR_ID - Tire GFORCE statement ID.

For information on the axis systems and sign conventions for these outputs, see About Axis Systems and Sign Conventions.

Example of a request in a dataset.

Note: On Windows, you can now enter the FORTRAN file directly without first compiling it.

Note: You can also set the AdamsAdams/Solver tool on the Adams Toolbar to automatically run with your user library.

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Tire Outputs

Output:REQTYP Request: Component definitions:

Tire rolling states 1 x = rolling radius

y = (rad/sec)

z = free (rad/sec)

is the actual angular velocity about the wheel's axis, while free is the velocity of the wheel's axle center divided by

the radius to the instantaneous center of rotation. The difference between the two is, therefore, a measure of the slip when the vehicle is accelerating or decelerating.

Tire kinematic properties in TYDEX-W axis (ISO) system.

2 x = longitudinal slip (%)

y = lateral slip angle (degrees)

z = inclination angle (degrees)Tire contact patch forces in TYDEX-W axis (ISO) system

3 x = longitudinal force (model units)

y = lateral force (model units)

z = vertical force (model units)

r1 = residual overturning moment (model units)

r2 = rolling resistance moment (model units)

r3 = aligning moment (model units)Tire contact patch forces in SAE axis system




r1 = residual overturning moment (model units)


r3 = aligning moment (model units)Tire kinematic properties in SAE axis system

5 x = longitudinal slip (%)

y = lateral slip angle (radians)

z = inclination angle (radians)

ω

ω

ωω


Forces at hub, in TYDEX-C axis system




r1 = overturning moment (model units)


r3 = aligning moment (model units)Miscellaneous tire states #1

7 x = longitudinal lag (du/dt)*

y = lateral lag (du/dt)*

z = longitudinal coefficient of friction

r1 = lateral coefficient of friction

r2 = FXMAX = DX + SVX (peak from Pacejka + vertical shift)

r3 = FYMAX = DY + SVY (peak from Pacejka + vertical shift)

Miscellaneous tire states #2

8 x = pneumatic trail *

y = residual aligning moment at contact patch in ISO

z = FX moment arm*

r1= longitudinal relaxation length*

r2 = lateral relaxation length*

r3 = gyroscopic moment*Miscellaneous tire states #3

9 x = inclination angle induced side force*

y = surface friction


μ

μ

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Miscellaneous tire states #4

14 x = distance traveled*

y = effective plane height*

z = effective plane angle*

r1= effective plane curvature*

r2 = contact length*Contact patch locations (the contact patch location along the plane of the tire in the GFORCE reference marker’s coordinate system.)

10 x = road contact point X location

y = road contact point Y location

z = road contact point Z location

r1 = tire radial penetration into the road surface

r2 = tire radial penetration velocity into the road surfaceHub and wheel velocities 11 x = hub longitudinal velocity in wheel carrier (TYDEX-C)

axis system

y = tire longitudinal velocity at the contact patch in the contact patch axis system

z = tire lateral velocity at the contact patch in the contact patch axis system



About Axis Systems and Sign ConventionsThe following sections describe the tire axis systems and the sign conventions for tire kinematic and force outputs.

• Tire Axis Systems

• About Tire Kinematic and Force Outputs

• Sign Conventions for Tire Outputs

Tire Axis SystemsThe following sections describe the ISO coordinate systems to which Adams/Tire conforms. The ISO coordinates are shown as follows:

• ISO-C (TYDEX C) Axis System

• ISO-W (TYDEX W) Contact-Patch Axis System

• Road Reference Marker Axis System

ISO-C (TYDEX C) Axis SystemThe TYDEX STI specifies the use of the ISO-C axis system for calculating translational and rotational velocities, and for outputting the force and torque at the tire hub.

The properties of the ISO-C axis system are:

• The origin of the ISO-C axis system lies at the wheel center.• The + x-axis is parallel to the road and lies in the wheel plane.• The + y-axis is normal to the wheel plane and, therefore, parallel to the wheel’s spin axis.• The + z-axis lies in the wheel plane and is perpendicular to x and y (such as z = x x y).

TYDEX-C Axis System Used in Adams/Tire

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ISO-W (TYDEX W) Contact-Patch Axis System

The properties of the ISO-W (TYDEX W) axis system are:

• The origin of the ISO-W contact-patch system lies in the local road plane at the tire contact point.

• The + x-axis lies in the local road plane along the intersection of the wheel plane and the local road plane.

• The + z-axis is perpendicular (normal) to the local road plane and points upward.• The + y-axis lies in the local road plane and is perpendicular to the + x-axis and + z-axis (such as

y = z x x).

TYDEX W-Axis System Used in Adams/Tire


Road Reference Marker Axis System

The road reference marker axis system is the underlying coordinate system that Adams/Tire uses internally. For example, the tire translational displacement and local road normal for a three-dimensional road are expressed in the axis system of the road reference marker.

The properties of the reference marker axis system are:

• The GFORCE reference marker defines the axis system.• The + z-axis points upward.

About Tire Kinematic and Force OutputsAdams/Tire calculates the kinematic quantities of slip angle, inclination angle, and longitudinal slip. These are based on the location, orientation, and velocity of the tire relative to the road. In turn, Adams/Tire calculates the forces and moments of the tire using the tire kinematics as inputs to the tire mode you select.

Sign Conventions for Tire OutputsThe table below, Conventions for Naming Variables, and the figure, ISO Coordinate System, show the sign conventions for tire kinematic and force outputs.

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Conventions for Naming Variables

Variable name and abbreviation: Description:

Slip angle The angle formed between the direction of travel (velocity) of the center of the tire contact patch and the ISO-W: x-axis. If the wheel-travel direction has a component in the ISO-W: +y direction, a is positive. This produces a negative lateral force (Fy). Note that the steer angle, or the vehicle attitude angle, plays no part in defining the slip angle.

Inclination angle

The angle formed between the ISO-W: x-z plane and the wheel plane. If the wheel plane has a component lying in the direction of ISO-W, the inclination angle is positive.

Longitudinal slip (Wactual-

Wfree)/Wfree

The ratio of the longitudinal-slip velocity of the contact patch to the longitudinal velocity of the wheel. The longitudinal slip is positive during acceleration of a moving tire and negative during braking. Longitudinal slip is limited to the range -1 to +1.

Longitudinal force at contact patch

Fx The x-component of the force exerted by the road or tire.

Lateral force at contact patch

Fy The y-component of the force exerted by the road or tire. Lateral force may be produced by one or any combination of the following: slip angle, inclination angle, conicity, or plysteer.

Normal force at contact patch

Fz The z-component of the force exerted by the road or tire. The direction of this force is up.

Overturning moment at contact patch

Mx The moment of the forces at the contact patch acting on the tire by the road with respect to the ISO-W: x-axis.

Rolling resistance moment

My The moment of the forces at the contact patch acting on the tire by the road with respect to the y-axis.

Aligning moment

Mz The moment of the forces at the contact patch acting on the tire by the road with respect to the z-axis.

Spin axis Spin Axis The axis about which the wheel rotates. Perpendicular to the wheel plane, not necessarily about the ISO-C: y-axis (only if inclination angle is zero).

The central plane of the tire and wheel

Wheel plane The wheel plane is normal to the wheel spin axis.

α

γ

κ


ISO Coordinate System

Wheel heading along road

ISO W:X This is not the same as the direction in which the wheel is traveling. If the tire reverses its direction, the axis system flips 180 degrees about the z'-axis.

Direction to the left along the road

ISO W:Y The direction to the left along ground as viewed from behind a forward rolling tire. Expressed as right-hand orthogonal to the definitions of x' and z' (such as y = Z x X).

Z-coordinate ISO W:Z Perpendicular to the road in the neighborhood of the origin of the tire axis system in a positive (downward) direction. (If the road is flat and in the x-y plane, this is negative global z.)

Variable name and abbreviation: Description:

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Units Supported in Tire Property FilesThe following tables list the valid choices for the parameters in the UNITS section of a tire property file. Note the following:

• You must enter the choices in single quotes, such as 'METER' for meter. • The choices are case-insensitive. Therefore, 'MeTeR,' 'meter,' and 'METER' are all equivalent. • The strings are limited to 12 characters and the minimum abbreviation is shown in the tables. So,

for example, 'millisecond' is valid and is interpreted as 'MILLI.’

Length Units

Time Units

Angle Units

Note: For some tire models, the [UNITS] section is not applied consistently to all tire parameters. The exceptions are the Magic Formula coefficients for the Pacejka ‘89 and ‘94 model and spline data for the 521 model, where the unit conversion factors have to be defined explicitly.

The unit: Can be abbreviated:Kilometers 'KM' Meters 'METER' Centimeters 'CM' Millimeters 'MM'Miles 'MILE' Feet 'FOOT' Inches 'IN'

The unit: Can be abbreviated:Milliseconds 'MILLI'Seconds 'SEC'Minutes 'MIN'Hours 'HOUR'

The units: Can be abbreviated:Degrees 'DEG' Radians 'RAD'


Mass Units

Force Units

The unit: Can be abbreviated:Kilograms 'KG'Grams 'GRAM' Pound-Mass 'POUND_MASS' Kilo-Pound-Mass 'KPOUND_MASS' Slugs 'SLUG' Ounce-mass OUNCE_MASS'

The unit: Can be abbreviated:Kilograms-Force ‘KG_FORCE' Newtons 'NEWTON' or 'N'Kilo-Newtons 'KNEWTON' or 'KN' Pounds-force 'POUND_FORCE'Kilo-Pound-Force 'KPOUND_FORCE' Dynes (gram-cm/sec2) ‘DYNE' Ounce-force 'OUNCE_FORCE'

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Tire Models

Adams/Tire

12

Using the Fiala Handling Force ModelThis section of the help provides detailed technical reference material for defining tires on a mechanical system model using Adams/Tire. It assumes that you know how to run Adams/Car, Adams/Solver, or Adams/Chassis. It also assumes that you have a moderate level of tire-modeling proficiency.

The Fiala tire model is the standard tire model that comes with all Adams/Tire modules. This chapter contains information for using the Fiala tire model:

• Assumptions

• Inputs

• Tire Slip Quantities and Transient Tire Behavior

• Force Evaluation

• Tire Carcass Shape

• Property File Format Example

• Contact Methods

Fiala Tire AssumptionsThe background of the Fiala tire model is a physical tire model, where the carcass is modeled as a beam on an elastic foundation in the lateral direction. Elastic brush elements provide the contact between carcass and road. Under these assumptions, analytical expressions for the steady-state slip characteristics can be derived, which are the basis for the calculation of the longitudinal and lateral forces in Adams.

• Rectangular contact patch or footprint.• Pressure distribution uniform across contact patch.• No tire relaxation effects are considered.• Camber angle has no effect on tire forces.

Fiala Tire InputsThe inputs to the Fiala tire model come from two sources:

• Input parameters from the tire property file (.tir), such as tire undeflected radius, that the tire references.

• Tire kinematic states, such as slip angle ( ), which Adams/Tire calculates.

The following table summarizes the input that the Fiala tire model uses to calculate force.

α

13Tire Models

Input for Calculating Tire Forces

Quantity: Description: Use by Fiala: Source:Mt Mass of tire • Damping

• Vertical force (Fz)

Alpha Slip angle Lateral force (Fy) Tire kinematic state from Adams/Solver

Ss Longitudinal slip ratio Longitudinal force (Fx) Tire kinematic state from Adams/Solver

pen Penetration (tire deflection) Vertical force (Fz) Tire kinematic state from Adams/Solver

Vpen d/dt (penetration) Vertical force (Fz) Tire kinematic state from Adams/Solver

Vertical_damping

Vertical damping coefficient

• Damping• Vertical force (Fz)

Tire property file (.tir)

Vertical_stiffness Vertical tire stiffness Vertical force (Fz) Tire property file (.tir)CSLIP Partial derivative of

longitudinal force (Fx) with respect to longitudinal slip ratio (S) at zero longitudinal slip

Longitudinal force (Fx) Tire property file (.tir)

CALPHA Partial derivative of lateral force (Fy) with respect to slip angle ( ) at zero slip angle

Lateral force (Fy) Tire property file (.tir)

UMIN Coefficient of friction with full slip (slip ratio = 1)

Fx, Fy, Tz Tire property file (.tir)

UMAX Coefficient of friction at zero slip

Fx, Fy, Tz Tire property file (.tir)

Rolling_resistance

Rolling resistance coefficient

Rolling resistance moment (Ty)

Tire property file (.tir)

α

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Tire Slip Quantities and Transient Tire Behavior

Definition of Tire Slip QuantitiesSlip Quantities at combined cornering and braking/traction

The longitudinal slip velocity Vsx in the SAE-axis system is defined using the longitudinal speed Vx, the

wheel rotational velocity , and the loaded rolling radius Rl:

The lateral slip velocity is equal to the lateral speed in the contact point with respect to the road plane:

The practical slip quantities (longitudinal slip) and (slip angle) are calculated with these slip velocities in the contact point:

and

Note that for realistic tire forces the slip angle is limited to 900 and the longitudinal slip in between -1 (locked wheel) and 1.

Lagged longitudinal and lateral slip quantities (transient tire behavior)In general, the tire rotational speed and lateral slip will change continuously because of the changing interaction forces in between the tire and the road. Often the tire dynamic response will have an important role on the overall vehicle response. For modeling this so-called transient tire behavior, a first-order system is used both for the longitudinal slip ? as the side slip angle, ?. Considering the tire belt as a stretched string, which is supported to the rim with lateral springs, the lateral deflection of the belt can be estimated (see also reference [1]). The figure below shows a top-view of the string model.

Ω Vsx Vx ΩRl–=

Vsy Vy=

κ α

κVsxVx--------–= αtan

VsyVx---------=

α κ

15Tire Models

Stretched String Model for Transient Tire behavior

When rolling, the first point having contact with the road adheres to the road (no sliding assumed). Therefore, a lateral deflection of the string will arise that depends on the slip angle size and the history of the lateral deflection of previous points having contact with the road.

For calculating the lateral deflection v1 of the string in the first point of contact with the road, the

following differential equation is valid during braking slip:

with the relaxation length in the lateral direction. The turnslip can be neglected at radii larger than

10 m. This differential equation cannot be used at zero speed, but when multiplying with Vx, the equation

can be transformed to:

When the tire is rolling, the lateral deflection depends on the lateral slip speed; at standstill, the deflection depends on the relaxation length, which is a measure for the lateral stiffness of the tire. Therefore, with this approach, the tire is responding to a slip speed when rolling and behaving like a spring at standstill.

A similar approach yields the following for the deflection of the string in longitudinal

direction:

1Vx------

dv1dt

--------v1σα------+ αtan aφ+=

σα φ

σαdv1dt

-------- Vx v1+ σαVsy=

σκdu1dt

-------- Vx u1+ σ– κVsx=

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Now the practical slip quantities, and , are defined based on the tire

deformation:

These practical slip quantities and are used instead of the usual and definitions for steady-state tire behavior.

The longitudinal and lateral relaxation length are read from the tire property file, see Fiala Tire Property File Format Example

Fiala Tire Force EvaluationTypes of force evaluation:

• Normal Force of Road on Tire

• Longitudinal Force

• Lateral Force

• Rolling Resistance Moment

• Aligning Moment

• Smoothing

Normal Force of Road on TireThe normal force of a road on a tire at the contact patch in the SAE coordinates (+Z downward) is always negative (directed upward). The normal force is:

Fz = min (0.0, {Fzk + Fzc})where:

• Fzk is the normal force due to tire vertical stiffness

• Fzc is the normal force due to tire vertical damping

• Fzk = - vertical_stiffness × pen

• Fzc = - vertical_damping × Vpen

Instead of the linear vertical tire stiffness, also an arbitrary tire deflection - load curve can be defined in the tire property file in the section [DEFLECTION_LOAD_CURVE] (see the Property File Format Example). If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection datap oints with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify VERTICAL_STIFFNESS in the tire property file, but it does not play any role.

κ' α'

κ'u1σκ------ Vx( )sgn=

α'v1σα------⎝ ⎠⎛ ⎞atan=

κ' α' κ α

17Tire Models

Longitudinal ForceThe longitudinal force depends on the vertical force (Fz), the current coefficient of friction (U), the longitudinal slip ratio (Ss), and the slip angle (Alpha). The current coefficient of friction depends on the static (UMAX) and dynamic (UMIN) friction coefficients and the comprehensive slip ratio (SsAlpha).

UMAX specifies the tire/road coefficient of friction at zero slip and represents the static friction coefficient. This is the y-intercept on the friction coefficient versus slip graph. Note that this value is an unobtainable maximum friction value, because there is always slip within a footprint. This value is used in conjunction with UMIN to define a linear friction versus slip relation. UMAX will normally be larger than UMIN.

UMIN specifies the tire/road coefficient of friction for the full slip case and represents the sliding friction coefficient. This is the friction coefficient at 100% slip, or pure sliding. This value is used in conjunction with UMAZ to define a linear friction versus slip relationship.

The comprehensive slip ( ):

The current value coefficient of friction (U):

Fiala defines a critical longitudinal slip ( ):

This is the value of longitudinal slip beyond which the tire is sliding.

Case 1. Elastic Deformation State: |Ss| S_critical

Fx = -CSLIP × Ss

Case 2. Complete Sliding State: |Ss| S_critical

Fx = -sign(Ss)(Fx1- Fx2)

where:

Ssα

Ssα Ss2 tan2 α( )+=

U Umax Umax Umin–( ) Ssα⋅( )–=

Scritical

ScriticalU Fz⋅

2 CSLIP⋅-------------------------=

<

>

Fx1 U Fz⋅=

Fx2U Fz⋅( )2

4 Ss CSLIP⋅ ⋅--------------------------------------=

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Lateral ForceLike the longitudinal force, the lateral force depends on the vertical force (Fz) and the current coefficient of friction (U). And similar to the longitudinal force calculation, Fiala defines a critical lateral slip ( ):

The lateral force peaks at a value equal to U × |Fz| when the slip angle (Alpha) equals the critical slip

angle ( ).

Case 1. Elastic Deformation State: |Alpha|

Fy = - U × |Fz|× (1-H3) × sign(Alpha)

where:

Case 2. Sliding State: |Alpha| Alpha_critical

Fy = -U|Fz|sign(Alpha)

Rolling Resistance MomentWhen the tire is rolling forward: Ty = -rolling_resistance * Fz

When the tire is rolling backward: Ty = rolling_resistance * Fz

Aligning Moment

Case 1. Elastic Deformation State: |Alpha|

Mz = U × |Fz|× WIDTH × (1-H) × H3 × sign(Alpha)

where:

Case 2. Complete Sliding State: |Alpha|

Mz= 0.0

αcritical

αcritical3 U Fz⋅ ⋅

CALPHA-------------------------⎝ ⎠⎛ ⎞atan=

αcritical

αcritical≤

H 1 CALPHA α( )tan⋅3 U Fz⋅ ⋅

--------------------------------------------------–=

αcritical≤

H 1 CALPHA α( )tan⋅3 U Fz⋅ ⋅

--------------------------------------------------–=

αcritical>

19Tire Models

SmoothingAdams/Tire can smooth initial transients in the tire force over the first 0.1 seconds of simulation. The longitudinal force, lateral force, and aligning torque are multiplied by a cubic step function of time. (See STEP in the Adams/Solver online help).

Longitudinal Force FLon = S*FLon

Lateral Force FLat = S*FLat

Aligning Torque Mz = S*Mz

The USE_MODE parameter in the tire property file allows you to switch smoothing on or off:

• USE_MODE = 1, smoothing is off• USE_MODE = 2, smoothing is on

Fiala Tire Carcass ShapeUsing Fiala tire, you can optionally supply a tire carcass cross-sectional shape in the tire property file in the [SHAPE] block. The 3D-durability, tire-to-road contact algorithm uses this information when calculating the tire-to-road volume of interference. To learn more about this topic, see Applying the Tire Carcass Shape. If you omit the [SHAPE] block from a tire property file, the tire carcass cross-section defaults to the rectangle that the tire radius and width define.

You specify the tire carcass shape by entering points in fractions of the tire radius and width. Because Adams/Tire assumes that the tire cross-section is symmetrical about the wheel plane, you only specify points for half the width of the tire. The following apply:

• For width, a value of zero (0) lies in the wheel center plane.• For width, a value of one (1) lies in the plane of the side wall.• For radius, a value of one (1) lies on the tread.

For example, suppose your tire has a radius of 300 mm and a width of 185 mm and that the tread is joined to the side wall with a fillet of 12.5 mm radius. The tread then begins to curve to meet the side wall at +/- 80 mm from the wheel center plane. If you define the shape table using six points with four points along the fillet, the resulting table might look like the shape block that is at the end of the following property format example.

Fiala Tire Property File Format Example$---------------------------------------------------------MDI_HEADER[MDI_HEADER] FILE_TYPE = 'tir' FILE_VERSION = 2.0 FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'Tire - XXXXXX'

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'Pressure - XXXXXX''Test Date - XXXXXX''Test tire''New File Format v2.1'$---------------------------------------------------------------units[UNITS] LENGTH = 'mm' FORCE = 'newton' ANGLE = 'degree' MASS = 'kg' TIME = 'sec'$--------------------------------------------------------------model[MODEL]! use mode 12 11 12 ! -------------------------------------------- ! smoothingX X! transient X X! PROPERTY_FILE_FORMAT = 'FIALA' USE_MODE = 2.0$----------------------------------------------------------dimension[DIMENSION] UNLOADED_RADIUS = 309.9 WIDTH = 235.0 ASPECT_RATIO = 0.45$----------------------------------------------------------parameter[PARAMETER] VERTICAL_STIFFNESS = 310.0 VERTICAL_DAMPING = 3.1 ROLLING_RESISTANCE = 0.0 CSLIP = 1000.0 CALPHA = 800.0 UMIN = 0.9 UMAX = 1.0 RELAX_LENGTH_X = 0.05 RELAX_LENGTH_Y = 0.15$---------------------------------------------carcass shape[SHAPE]{radius width}1.0000 0.00001.0000 0.50001.0000 0.86490.9944 0.92350.9792 0.98190.9583 1.0000$------------------------------------------------load_curve$ Maximum of 100 points (optional)[DEFLECTION_LOAD_CURVE]{pen fz}0 0.01 212.02 428.03 648.05 1100.0

21Tire Models

10 2300.020 5000.030 8100.0

Fiala Tire Contact MethodsThe Fiala tire model supports the following roads:

• 2D Roads, see Using the 2D Road Model.• 3D Spline Roads, see Adams/3D Spline Road Model

• 3D Shell Roads, see Adams/Tire 3D Shell Road Model

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Using the PAC2002Tire ModelThe PAC2002 Magic-Formula tire model has been developed by MSC.Software according to Tyre and Vehicle Dynamics by Pacejka [1]. PAC2002 is latest version of a Magic-Formula model available in Adams/Tire.

• Learn about:• When to Use PAC2002

• Modeling of Tire-Road Interaction Forces

• Axis Systems and Slip Definitions

• Contact Point and Normal Load Calculation

• Basics of Magic Formula

• Steady-State: Magic Formula

• Transient Behavior

• Gyroscopic Couple

• Left and Right Side Tires

• USE_MODES OF PAC2002: from Simple to Complex

• Quality Checks for Tire Model Parameters

• Contact Methods

• Standard Tire Interface (STI)

• Definitions

• References

• Example of PAC2002 Tire Property File

• Contact Methods

When to Use PAC2002Magic-Formula (MF) tire models are considered the state-of-the-art for modeling tire-road interaction forces in vehicle dynamics applications. Since 1987, Pacejka and others have published several versions of this type of tire model. The PAC2002 contains the latest developments that have been published in Tyre and Vehicle Dynamics by Pacejka [1].

In general, a MF tire model describes the tire behavior for rather smooth roads (road obstacle wavelengths longer than the tire radius) up to frequencies of 8 Hz. This makes the tire model applicable for all generic vehicle handling and stability simulations, including:

• Steady-state cornering• Single- or double-lane change• Braking or power-off in a turn

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12

• Split-mu braking tests• J-turn or other turning maneuvers• ABS braking, when stopping distance is important (not for tuning ABS control strategies)• Other common vehicle dynamics maneuvers on rather smooth roads (wavelength of road

obstacles must be longer than the tire radius)

For modeling roll-over of a vehicle, you must pay special attention to the overturning moment characteristics of the tire (Mx) and the loaded radius modeling. The last item may not be sufficiently accurate in this model.

The PAC2002 model has proven to be applicable for car, truck, and aircraft tires with camber (inclination) angles to the road not exceeding 15 degrees.

PAC2002 and Previous Magic Formula ModelsCompared to previous versions, PAC2002 is backward compatible with all previous versions of PAC2002, MF-Tyre 5.x tire models, and related tire property files.

New FeaturesThe enhancements for PAC2002 in Adams/Tire 2005 r2 are:

• More advanced tire-transient modeling using a contact mass in the contact point with the road. This results in more realistic dynamic tire model response at large slip, low speed, and standstill (usemode > 20).

• Parking torque and turn-slip have been introduced: the torque around the vertical axis due to turning at standstill or at low speed (no need for extra parameters).

• Extended loaded radius modeling (see Contact Point and Normal Load Calculation) are suitable for driving under extreme conditions like roll-over events and racing applications.

• The option to use a nonlinear spline for the vertical tire load-deflection instead of a linear tire stiffness. See Contact Point and Normal Load Calculation.

• Modeling of bottoming of the tire to the road by using another spline for defining the bottoming forces. Learn more about wheel bottoming.

• Online scaling of the tire properties during a simulation; the scaling factors of the PAC2002 can now be changed as a function of time, position, or any other variable in your model dataset. See Online Scaling of Tire Properties.

Modeling of Tire-Road Interaction ForcesFor vehicle dynamics applications, an accurate knowledge of tire-road interaction forces is inevitable because the movements of a vehicle primarily depend on the road forces on the tires. These interaction forces depend on both road and tire properties, and the motion of the tire with respect to the road.

In the radial direction, the MF tire models consider the tire to behave as a parallel linear spring and linear damper with one point of contact with the road surface. The contact point is determined by considering the tire and wheel as a rigid disc. In the contact point between the tire and the road, the contact forces in

13

longitudinal and lateral direction strongly depend on the slip between the tire patch elements and the road.

The figure, Input and Output Variables of the Magic Formula Tire Model, presents the input and output vectors of the PAC2002 tire model. The tire model subroutine is linked to the Adams/Solver through the Standard Tire Interface (STI) [3]. The input through the STI consists of:

• Position and velocities of the wheel center• Orientation of the wheel• Tire model (MF) parameters• Road parameters

The tire model routine calculates the vertical load and slip quantities based on the position and speed of the wheel with respect to the road. The input for the Magic Formula consists of the wheel load (Fz), the

longitudinal and lateral slip ( , ), and inclination angle ( ) with the road. The output is the forces (Fx, Fy) and moments (Mx, My, Mz) in the contact point between the tire and the road. For calculating these forces, the MF equations use a set of MF parameters, which are derived from tire testing data.

The forces and moments out of the Magic Formula are transferred to the wheel center and returned to Adams/Solver through STI.

Input and Output Variables of the Magic Formula Tire Model

Axis Systems and Slip Definitions• Axis Systems

κ α γ

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• Units

• Definition of Tire Slip Quantities

Axis SystemsThe PAC2002 model is linked to Adams/Solver using the TYDEX STI conventions, as described in the TYDEX-Format [2] and the STI [3].

The STI interface between the PAC2002 model and Adams/Solver mainly passes information to the tire model in the C-axis coordinate system. In the tire model itself, a conversion is made to the W-axis system because all the modeling of the tire behavior as described in this help assumes to deal with the slip quantities, orientation, forces, and moments in the contact point with the TYDEX W-axis system. Both axis systems have the ISO orientation but have different origin as can be seen in the figure below.

TYDEX C- and W-Axis Systems Used in PAC2002, Source [2]

The C-axis system is fixed to the wheel carrier with the longitudinal xc-axis parallel to the road and in the wheel plane (xc-zc-plane). The origin of the C-axis system is the wheel center.

The origin of the W-axis system is the road contact-point defined by the intersection of the wheel plane, the plane through the wheel carrier, and the road tangent plane.

The forces and moments calculated by PAC2002 using the MF equations in this guide are in the W-axis system. A transformation is made in the source code to return the forces and moments through the STI to Adams/Solver.

The inclination angle is defined as the angle between the wheel plane and the normal to the road tangent plane (xw-yw-plane).

UnitsThe units of information transferred through the STI between Adams/Solver and PAC2002 are according to the SI unit system. Also, the equations for PAC2002 described in this guide have been developed for

15

use with SI units, although you can easily switch to another unit system in your tire property file. Because of the non-dimensional parameters, only a few parameters have to be changed.

However, the parameters in the tire property file must always be valid for the TYDEX W-axis system (ISO oriented). The basic SI units are listed in the table below.

SI Units Used in PAC2002

Definition of Tire Slip QuantitiesThe longitudinal slip velocity Vsx in the contact point (W-axis system, see Slip Quantities at Combined Cornering and Braking/Traction) is defined using the longitudinal speed Vx, the wheel rotational velocity

, and the effective rolling radius Re:

(1)

Slip Quantities at Combined Cornering and Braking/Traction

Variable type: Name: Abbreviation: Unit:Angle Slip angle

Inclination angle

Radians

Force Longitudinal force

Lateral force

Vertical load

Fx

Fy

Fz

Newton

Moment Overturning moment


Self-aligning moment

Mx

My

Mz

Newton.meter

Speed Longitudinal speed

Lateral speed

Longitudinal slip speed

Lateral slip speed

Vx

Vy

Vsx

Vsy

Meters per second

Rotational speed Tire rolling speed Radians per second

α

γ

ω

ω

Vsx Vx ΩRe–=

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16


(2)

The practical slip quantities (longitudinal slip) and (slip angle) are calculated with these slip velocities in the contact point with:

(3)

(4)

The rolling speed Vr is determined using the effective rolling radius Re:

(5)

Turn-slip is one of the two components that form the spin of the tire. Turn-slip is calculated using the

tire yaw velocity :

(6)

The total tire spin is calculated using:

(7)

The total tire spin has contributions of turn-slip and camber. denotes the camber reduction factor for the camber to become comparable with turn-slip.

Vsy Vy=

κ α

κVsxVx--------–=

αtanVsyVx---------=

Vr ReΩ=

φψ·

Wtψ·

Vx------=

ϕ

ψ11

Vx------ ψ· 1 εγ–( )Ω γsin–{ }=

ε

17

Contact Point and Normal Load Calculation• Contact Point

• Loaded and Effective Tire Rolling Radius

• Wheel Bottoming

Contact PointIn the vertical direction, the tire is modeled as a parallel linear spring and damper having one point of contact (C) with the road. This is valid for road obstacles with a wavelength larger than the tire radius (for example, for car tires 1m).

For calculating the kinematics of the tire relative to the road, the road is approximated by its tangent plane at the road point right below the wheel center (see the figure below).

Contact Point C: Intersection between Road Tangent Plane, Spin Axis Plane, and Wheel Plane

The contact point is determined by the line of intersection of the wheel center-plane with the road tangent (ground) plane and the line of intersection of the wheel center-plane with the plane through the wheel

spin axis. The normal load Fz of the tire is calculated with the tire deflection as follows:ρ

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18

(8)

Using this formula, the vertical tire stiffness increases due to increasing rotational speed and decreases by longitudinal and lateral tire forces. If qFz1 is zero, qFz1 will be CzR0/Fz0.

When you do not provide the coefficients qV2, qFcx, qFcy, qFz1, qFz2 and qFc in the tire property file, the normal load calculation is compatible with previous versions of PAC2002, because, in that case, the normal load is calculated using the linear vertical tire stiffness Cz and tire damping Kz according to:

(9)

Instead of the linear vertical tire stiffness Cz (= qFz1Fz0/R0), you can define an arbitrary tire deflection - load curve in the tire property file in the section [DEFLECTION_LOAD_CURVE] (see the Example of PAC2002 Tire Property File). If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection data points with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify Cz in the tire property file, but it does not play any role.

Loaded and Effective Tire Rolling RadiusWith the loaded tire radius Rl defined as the distance of the wheel center to the contact point of the tire with the road, the tire deflection can be calculated using the free tire radius R0 and a correction for the

tire radius growth due to the rotational tire speed :

(10)

The effective rolling radius Re (at free rolling of the tire), which is used to calculate the rotational speed of the tire, is defined by:

(11)

For radial tires, the effective rolling radius is rather independent of load in its load range of operation because of the high stiffness of the tire belt circumference. Only at low loads does the effective tire radius decrease with increasing vertical load due to the tire tread thickness. See the figure below.

Fz 1 qV2 ΩRoVo------ qFcxl

FxFz0--------⎝ ⎠

⎛ ⎞2

– qFcylFyFz0--------⎝ ⎠

⎛ ⎞2

– qFcylγ2+ +

⎩ ⎭⎨ ⎬⎧ ⎫

qFzlρ

R0------ qFz2

ρR0------⎝ ⎠⎛ ⎞ 2

+ Fz0 Kz ρ·•+

=

ω

γ

Fz CzρλCz Kzρ·+=

ω

ρ R0 R1– qV1R0 ΩR0V0------⎝ ⎠

⎛ ⎞2

+=

ReVxΩ------=

19

Effective Rolling Radius and Longitudinal Slip

To represent the effective rolling radius Re, a MF-type of equation is used:

(12)

in which Fz0 is the nominal tire deflection:

Rf R0 qV1R0ΩR0V0

-----------⎝ ⎠⎛ ⎞

2RFz0 DPeffarc BReffρ

d( ) FReffρd+tan[ ]–+=

ρ

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20

(13)

and is called the dimensionless radial tire deflection, defined by:

(14)

Example of Loaded and Effective Tire Rolling Radius as Function of Vertical Load

Normal Load and Rolling Radius Parameters

Name:Name Used in Tire Property

File: Explanation:Fz0 FNOMIN Nominal wheel loadRo UNLOADED_RADIUS Free tire radiusB BREFF Low load stiffness effective rolling radiusD DREFF Peak value of effective rolling radiusF FREFF High load stiffness effective rolling radiusCz VERTICAL_STIFFNESS Tire vertical stiffness (if qFz1=0)Kz VERTICAL_DAMPING Tire vertical damping

ρFz0Fz0

CzλCz----------------=

ρ

ρd ρρFz0

---------=

21

Wheel Bottoming You can optionally supply a wheel-bottoming deflection, that is, a load curve in the tire property file in the [BOTTOMING_CURVE] block. If the deflection of the wheel is so large that the rim will be hit (defined by the BOTTOMING_RADIUS parameter in the [DIMENSION] section of the tire property file), the tire vertical load will be increased according to the load curve defined in this section.

Note that the rim-to-road contact algorithm is a simple penetration method (such as the 2D contact) based on the tire-to-road contact calculation, which is strictly valid for only rather smooth road surfaces (the length of obstacles should have a wavelength longer than the tire circumference). The rim-to-road contact algorithm is not based on the 3D-volume penetration method, but can be used in combination with the 3D Contact, which takes into account the volume penetration of the tire itself. If you omit the [BOTTOMING_CURVE] block from a tire property file, no force due to rim road contact is added to the tire vertical force.

You can choose a BOTTOMING_RADIUS larger than the rim radius to account for the tire's material remaining in between the rim and the road, while you can adjust the bottoming load-deflection curve for the change in stiffness.

qFz1 QFZ1 Tire vertical stiffness coefficient (linear)qFz2 QFZ2 Tire vertical stiffness coefficient

(quadratic)qFcx1 QFCX1 Tire stiffness interaction with FxqFcy1 QFCY1 Tire stiffness interaction with FyqFc 1 QFCG1 Tire stiffness interaction with camberqV1 QV1 Tire radius growth coefficientqV2 QV2 Tire stiffness variation coefficient with

speed

Name:Name Used in Tire Property

File: Explanation:

γ

Adams/Tire

22

If (Pentire - (Rtire - Rbottom) - ½·width ·| tan(g) |) < 0, the left or right side of the rim has contact with the road. Then, the rim deflection Penrim can be calculated using:

= max(0 , ½·width ·| tan( ) | ) + Pentire- (Rtire - Rbottom)

Penrim= 2/(2 · width ·| tan( ) |)

δ γ

δ γ

23

Srim= ½·width - max(width , /| tan( ) |)/3

with Srim, the lateral offset of the force with respect to the wheel plane.

If the full rim has contact with the road, the rim deflection is:

Penrim = Pentire - (Rtire - Rbottom)

Srim = width2 · | tan( ) | · /(12 · Penrim)

Using the load - deflection curve defined in the [BOTTOMING_CURVE] section of the tire property file, the additional vertical force due to the bottoming is calculated, while Srim multiplied by the sign of

the inclination is used to calculate the contribution of the bottoming force to the overturning moment. Further, the increase of the total wheel load Fz due to the bottoming (Fzrim) will not be taken into account in the calculation for Fx, Fy, My, and Mz. Fzrim will only contribute to the overturning moment Mx using the Fzrim·Srim.

Basics of the Magic Formula in PAC2002The Magic Formula is a mathematical formula that is capable of describing the basic tire characteristics for the interaction forces between the tire and the road under several steady-state operating conditions. We distinguish:

• Pure cornering slip conditions: cornering with a free rolling tire• Pure longitudinal slip conditions: braking or driving the tire without cornering• Combined slip conditions: cornering and longitudinal slip simultaneously

For pure slip conditions, the lateral force Fy as a function of the lateral slip , respectively, and the

longitudinal force Fx as a function of longitudinal slip , have a similar shape (see the figure, Characteristic Curves for Fx and Fy Under Pure Slip Conditions). Because of the sine - arctangent combination, the basic Magic Formula equation is capable of describing this shape:

(15)

where Y(x) is either Fx with x the longitudinal slip , or Fy and x the lateral slip .

δ γ

γ

γ

Note: Rtire is equal to the unloaded tire radius R0; Pentire is similar to effpen (= ).ρ

ακ

Y x( ) D Carc Bx E Bx arc Bx( )tan–( )–{ }tan[ ]cos=

κ α

Adams/Tire

24

Characteristic Curves for Fx and Fy Under Pure Slip Conditions

The self-aligning moment Mz is calculated as a product of the lateral force Fy and the pneumatic trail t added with the residual moment Mzr. In fact, the aligning moment is due to the offset of lateral force Fy, called pneumatic trail t, from the contact point. Because the pneumatic trail t as a function of the lateral slip α has a cosine shape, a cosine version the Magic Formula is used:

(16)

in which Y(x) is the pneumatic trail t as function of slip angle .

The figure, The Magic Formula and the Meaning of Its Parameters, illustrates the functionality of the B, C, D, and E factor in the Magic Formula:

• D-factor determines the peak of the characteristic, and is called the peak factor.• C-factor determines the part used of the sine and, therefore, mainly influences the shape of the

curve (shape factor).• B-factor stretches the curve and is called the stiffness factor.• E-factor can modify the characteristic around the peak of the curve (curvature factor).


α

25

The Magic Formula and the Meaning of Its Parameters

In combined slip conditions, the lateral force Fy will decrease due to longitudinal slip or the opposite, the longitudinal force Fx will decrease due to lateral slip. The forces and moments in combined slip conditions are based on the pure slip characteristics multiplied by the so-called weighing functions. Again, these weighting functions have a cosine-shaped MF equation.

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26

The Magic Formula itself only describes steady-state tire behavior. For transient tire behavior (up to 8 Hz), the MF output is used in a stretched string model that considers tire belt deflections instead of slip velocities to cope with standstill situations (zero speed).

Input VariablesThe input variables to the Magic Formula are:

Output Variables

The output variables are defined in the W-axis system of TYDEX.

Basic Tire ParametersAll tire model parameters of the model are without dimension. The reference parameters for the model are:

As a measure for the vertical load, the normalized vertical load increment dfz is used:

(17)

with the possibly adapted nominal load (using the user-scaling factor, ):

Longitudinal slip [-]

Slip angle [rad]

Inclination angle [rad]

Normal wheel load Fz [N]

Longitudinal force Fx [N]Lateral force Fy [N]Overturning couple Mx [Nm]Rolling resistance moment

My [Nm]

Aligning moment Mz [Nm]

Nominal (rated) load Fz0 [N]Unloaded tire radius R0 [m]Tire belt mass mbelt [kg]

κ

α

γ

fzdFz F'z0–

F'z0--------------------=

γΦz0

27

(18)

Nomenclature of the Tire Model ParametersIn the subsequent sections, formulas are given with non-dimensional parameters aijk with the following logic:

Tire Model Parameters

User Scaling FactorsA set of scaling factors is available to easily examine the influence of changing tire properties without the need to change one of the real Magic Formula coefficients. The default value of these factors is 1. You can change the factors in the tire property file. The peak friction scaling factors, and , are

also used for the position-dependent friction in 3D Road Contact and 3D Road. An overview of all scaling factors is shown in the following tables.

Parameter: Definition:a = p Force at pure slip

q Moment at pure slipr Force at combined slips Moment at combined slip

i = B Stiffness factorC Shape factorD Peak valueE Curvature factorK Slip stiffness = BCDH Horizontal shiftV Vertical shifts Moment at combined slipt Transient tire behavior

j = x Along the longitudinal axisy Along the lateral axisz About the vertical axis

k = 1, 2, ...

F'z0 Fz0 λFz0•=

λμξ λμψ

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28

Scaling Factor Coefficients for Pure Slip

Name:Name used in tire

property file: Explanation:

FzoLFZO Scale factor of nominal (rated) load

CzLCZ Scale factor of vertical tire stiffness

CxLCX Scale factor of Fx shape factor

xLMUX Scale factor of Fx peak friction coefficient

ExLEX Scale factor of Fx curvature factor

KxLKX Scale factor of Fx slip stiffness

HxLHX Scale factor of Fx horizontal shift

VxLVX Scale factor of Fx vertical shift

xLGAX Scale factor of inclination for Fx

CyLCY Scale factor of Fy shape factor

yLMUY Scale factor of Fy peak friction coefficient

EyLEY Scale factor of Fy curvature factor

KyLKY Scale factor of Fy cornering stiffness

HyLHY Scale factor of Fy horizontal shift

VyLVY Scale factor of Fy vertical shift

gyLGAY Scale factor of inclination for Fy

tLTR Scale factor of peak of pneumatic trail

MrLRES Scale factor for offset of residual moment

LGAZ Scale factor of inclination for Mz

MxLMX Scale factor of overturning couple

VMxLVMX Scale factor of Mx vertical shift

MyLMY Scale factor of rolling resistance moment

λ

λ

λ

λμ

λ

λ

λ

λ

λγ

λ

λμ

λ

λ

λ

λ

λ

λ

λ

λγz

λ

λ

λ

29

Scaling Factor Coefficients for Combined Slip

Scaling Factor Coefficients for Transient Response

Note that the scaling factors change during the simulation according to any user-introduced function. See the next section, Online Scaling of Tire Properties.

Online Scaling of Tire PropertiesPAC2002 can provide online scaling of tire properties. For each scaling factor, a variable should be introduced in the Adams .adm dataset. For example:

!lfz0 scaling! adams_view_name='TR_Front_Tires until wheel_lfz0_var'VARIABLE/53, IC = 1, FUNCTION = 1.0

This lets you change the scaling factor during a simulation as a function of time or any other variable in your model. Therefore, tire properties can change because of inflation pressure, road friction, road temperature, and so on.

You can also use the scaling factors in co-simulations in MATLAB/Simulink.

For more detailed information, see Knowledge Base Article 12732.


property file: Explanation:LXAL Scale factor of alpha influence on Fx

LYKA Scale factor of alpha influence on Fx

LVYKA Scale factor of kappa-induced Fy

LS Scale factor of moment arm of Fx



σκLSGKP Scale factor of relaxation length of Fx

σαLSGAL Scale factor of relaxation length of Fy

gyrLGYR Scale factor of gyroscopic moment

λxα

λyκ

λVyκ

λs

λ

λ

λ

http://support.adams.com/kb/faq.asp?ID=kb12732.html

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Steady-State: Magic Formula in PAC2002• Steady-State Pure Slip

• Steady-State Combined Slip

Steady-State Pure Slip• Longitudinal Force at Pure Slip

• Lateral Force at Pure Slip

• Aligning Moment at Pure Slip

• Turn-slip and Parking

Formulas for the Longitudinal Force at Pure SlipFor the tire rolling on a straight line with no slip angle, the formulas are:

(19)

(20)

(21)

(22)

with following coefficients:

(23)

(24)

(25)

(26)

the longitudinal slip stiffness:

(27)

(28)

(29)

Fx Fx0 κ Fz γ, ,( )=

Fx0 Dx Cxarc Bxκx Ex Bxκx arc Bxκx( )tan–( )–{ }tan[ ] SVx+( )sin=

κx κ SHx+=

γx γ λγx⋅=

Cx pCx1 λCx⋅=

Dx μx Fz ζ1⋅ ⋅=

μx pDx1 pDx2 fzd+( ) 1 pDx3 γ2⋅–( )λμx⋅=

Ex pEx1 pEx2 fz2d+( ) 1 pEx4 κx( )sgn–{ } λEx with Ex 1≤⋅ ⋅=

Kx Fz pKx1 pKx2 fzd+( ) pKx3 fzd( ) λKx⋅exp⋅ ⋅=

Kx BxCxDx κx∂∂Fx0at κ 0= = =

Bx Kx CxDx( )⁄=

SHx pHx1 pHx2 dfz⋅+( )λHx=

31

(30)

Longitudinal Force Coefficients at Pure Slip

Formulas for the Lateral Force at Pure Slip

(31)

(32)

(33)

The scaled inclination angle:

(34)

with coefficients:

(35)

(36)


property file: Explanation:pCx1 PCX1 Shape factor Cfx for longitudinal forcepDx1 PDX1 Longitudinal friction Mux at FznompDx2 PDX2 Variation of friction Mux with loadpDx3 PDX3 Variation of friction Mux with inclinationpEx1 PEX1 Longitudinal curvature Efx at FznompEx2 PEX2 Variation of curvature Efx with loadpEx3 PEX3 Variation of curvature Efx with load squaredpEx4 PEX4 Factor in curvature Efx while drivingpKx1 PKX1 Longitudinal slip stiffness Kfx/Fz at FznompKx2 PKX2 Variation of slip stiffness Kfx/Fz with loadpKx3 PKX3 Exponent in slip stiffness Kfx/Fz with loadpHx1 PHX1 Horizontal shift Shx at FznompHx2 PHX2 Variation of shift Shx with loadpVx1 PVX1 Vertical shift Svx/Fz at FznompVx2 PVX2 Variation of shift Svx/Fz with load

SVx Fz pHx1 pHx2 dfz⋅+( )λVx λHμx ζ1⋅ ⋅⋅=

Fy Fy0 α γ Fz, ,( )=

Fy0 Dy Cyarc Byαy Ey Byαy arc Byαy( )tan–( )–{ }tan[ ] SVy+sin=

αy α SHy+=

γy γ λγy⋅=

Cy pCy1 λCy⋅=

Dy μy Fz ζ2⋅ ⋅=

Adams/Tire

32

(37)

(38)

The cornering stiffness:

(39)

(40)

(41)

(42)

(43)

The camber stiffness is given by:

(44)

Lateral Force Coefficients at Pure Slip


property file: Explanation:pCy1 PCY1 Shape factor Cfy for lateral forcespDy1 PDY1 Lateral friction MuypDy2 PDY2 Variation of friction Muy with loadpDy3 PDY3 Variation of friction Muy with squared inclinationpEy1 PEY1 Lateral curvature Efy at FznompEy2 PEY2 Variation of curvature Efy with loadpEy3 PEY3 Inclination dependency of curvature EfypEy4 PEY4 Variation of curvature Efy with inclinationpKy1 PKY1 Maximum value of stiffness Kfy/FznompKy2 PKY2 Load at which Kfy reaches maximum valuepKy3 PKY3 Variation of Kfy/Fznom with inclinationpHy1 PHY1 Horizontal shift Shy at FznompHy2 PHY2 Variation of shift Shy with load

μy pDy1 pDy2dfz+( ) 1 pDy3γy2–( ) λμy⋅ ⋅=

Ey pEy1 pEy2dfz+( ) 1 pEy3 pEy4γy+( ) αy( )sgn–{ } γEy with Ey 1≤⋅ ⋅=

Ky0 PKy1 Fz0 2acFz

PKy2F0λFz0

---------------------------⎩ ⎭⎨ ⎬⎧ ⎫

tan λFz0λKy⋅ ⋅

⎝ ⎠⎜ ⎟⎛ ⎞

sin⋅ ⋅=

Ky Ky0 1 pKy3 γy–( ) ζ3⋅ ⋅=

By Ky CyDy( )⁄=

SHy pHy1 pHy2dfz+( ) λHy pHy3γy ζ0 ζ4 1–+⋅+⋅=

SVy Fz pVy1 pVy2dfz+( ) λVy pVy3 pVy4dfz+( ) γy⋅+⋅{ } λμy ζ4⋅ ⋅ ⋅=

Kyγ0 PHy3Ky0 Fz pνy3 pνy4dfz+( )+=

33

Formulas for the Aligning Moment at Pure Slip

(45)

with the pneumatic trail t:

(46)

(47)

and the residual moment Mzr:

(48)

(49)

(50)


(51)

with coefficients:

(52)

(53)

(54)

pHy3 PHY3 Variation of shift Shy with inclinationpVy1 PVY1 Vertical shift in Svy/Fz at FznompVy2 PVY2 Variation of shift Svy/Fz with loadpVy3 PVY3 Variation of shift Svy/Fz with inclinationpVy4 PVY4 Variation of shift Svy/Fz with inclination and load



M'z Mz0 α γ Fz, ,( )=

Mz0 t Fy0 Mzr+⋅–=

t αt( ) Dt Ctarc Btαt Et Btαt arc Btαt( )tan–( )–{ }tan[ ] α( )coscos=

αt α SHt+=

Mzr αr( ) Dr Crarc Brαr( )tan[ ] α( )cos⋅cos=

αr α SHf+=

SHf SHy SVy Ky⁄+=

γz γ λγz⋅=

Bt qBz1 qBz2dfz qBz3dfz2+ +( ) 1 qBz4γz qBz5 γz+ +( ) λKy λμy⁄⋅ ⋅=

Ct qCz1=

Dt Fz qDz1 qDz2dfz+( ) 1 qDz3γz qDz4γz2+ +( )

R0Fz0-------- λt ζ5⋅ ⋅ ⋅ ⋅ ⋅=

Adams/Tire

34

(55)

(56)

(57)

(58)

An approximation for the aligning moment stiffness reads:

(59)

Aligning Moment Coefficients at Pure Slip


property file: Explanation:qBz1 QBZ1 Trail slope factor for trail Bpt at FznomqBz2 QBZ2 Variation of slope Bpt with loadqBz3 QBZ3 Variation of slope Bpt with load squaredqBz4 QBZ4 Variation of slope Bpt with inclinationqBz5 QBZ5 Variation of slope Bpt with absolute inclinationqBz9 QBZ9 Slope factor Br of residual moment MzrqBz10 QBZ10 Slope factor Br of residual moment MzrqCz1 QCZ1 Shape factor Cpt for pneumatic trailqDz1 QDZ1 Peak trail Dpt = Dpt*(Fz/Fznom*R0)qDz2 QDZ2 Variation of peak Dpt with loadqDz3 QDZ3 Variation of peak Dpt with inclinationqDz4 QDZ4 Variation of peak Dpt with inclination squared.qDz6 QDZ6 Peak residual moment Dmr = Dmr/ (Fz*R0)qDz7 QDZ7 Variation of peak factor Dmr with loadqDz8 QDZ8 Variation of peak factor Dmr with inclination

Et qEz1 qEz2dfz qEz3dfz2+ +( )=

1 qEz1 qEz2γz+( ) 2π---⎝ ⎠⎛ ⎞ arc Bt Ct αt⋅ ⋅( )tan⋅⎝ ⎠⎛ ⎞+

⎩ ⎭⎨ ⎬⎧ ⎫

w ith Et 1≤( )

SHt qHz1 qHz2dfz qHz3 qHz4 dfz⋅+( )γz+ +=

Br qBz9λKyλμy--------- qBz10 By Cy⋅ ⋅+⋅⎝ ⎠

⎛ ⎞ ζ6⋅=

Cr ζ7=

Dr Fz qDz6 qDz7dfz+( ) γr⋅ qDz8 qDz9dfz+( ) γz⋅+[ ] Ro λμγ ζ8 1–+⋅ ⋅ ⋅=

Kz t Ky α∂∂– Mz at α≈⎝ ⎠

⎛ ⎞⋅– 0 )= =

35

Turn-slip and Parking

For situations where turn-slip may be neglected and camber remains small, the reduction factors that

appear in the equations for steady-state pure slip, are to be set to 1:

For larger values of spin, the reduction factors are given below.

The weighting function is used to let the longitudinal force diminish with increasing spin, according

to:

with:

The peak side force reduction factor reads:

with:

The cornering stiffness reduction factor is given by:

qDz9 QDZ9 Variation of Dmr with inclination and loadqEz1 QEZ1 Trail curvature Ept at FznomqEz2 QEZ2 Variation of curvature Ept with loadqEz3 QEZ3 Variation of curvature Ept with load squaredqEz4 QEZ4 Variation of curvature Ept with sign of Alpha-tqEz5 QEZ5 Variation of Ept with inclination and sign Alpha-tqHz1 QHZ1 Trail horizontal shift Sht at FznomqHz2 QHZ2 Variation of shift Sht with loadqHz3 QHZ3 Variation of shift Sht with inclinationqHz4 QHZ4 Variation of shift Sht with inclination and load



ζi

ζi 1= i 0.= 1.…8

ζ1

ζi arc BxϕR0ϕ( )tan[ ]cos=

Bxϕ pDxϕ1 1 pDxϕ2dfz+( ) arc pDxϕ3κ( )tan[ ]cos=

ζ2

ζ2 arc Byϕ R0 ϕ pDyϕ4 R0 ϕ+( ){ }tan[ ]cos=

Byϕ pDxϕ1 1 pDxϕ2dfz+( ) arc pDxϕ3 αtan( )tan[ ]cos=

ζ3

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36

The horizontal shift of the lateral force due to spin is given by:

The factors are defined by:

The spin force stiffness KyRϕ0 is related to the camber stiffness Kyy0:

in which the camber reduction factor is given by:

The reduction factors and for the vertical shift of the lateral force are given by:

The reduction factor for the residual moment reads:

The peak spin torque Dr is given by:

The maximum value is given by:

ζ3 arc pKyϕ1R02ϕ2( )tan[ ]cos=

SHyϕ DHyϕ CHyϕarc BHyϕRoϕ EHyϕ BHyϕ arc BHyϕR0ϕ( )tan–( )–{ }tan[ ]sin=

CHyϕ pHyϕ1

DHyϕ pHyϕ2 pHyϕ3dfz+( ) Vx( )

EHyϕ

sin⋅

PHyϕ4

BHyϕKyRϕ0

CyDyKy0-----------------------

=

=

=

=

KyRϕ0Kyγ01 εγ–-------------=

εγ pεγϕ1 1 pεγϕ2dfz+( )=

ζ0 ζ4

ζ0 0

ζ4 1 SHyϕ SVyγ Ky⁄–+

=

=

ζ8 1 Drϕ+=

ϕ

Drϕ DDrϕ e CDrϕarc BDrϕR0ϕ EDrϕ BDrϕR0ϕ arc BDrϕR0ϕ( )tan–( )–{ }tan[ ]sin=

37

The moment at vanishing wheel speed at constant turning is given by:

The shape factors are given by:

in which:

The reduction factor reads:

The spin moment at 90º slip angle is given by:

The spin moment at 90º slip angle is multiplied by the weighing function to account for the action

of the longitudinal slip (see steady-state combined slip equations).

The reduction factor is given by:

DDrϕMzϕ∞

π2---CDrϕ⎝ ⎠⎛ ⎞sin

-----------------------------=

Mzϕ∞ qCrϕ1μyR0Fz Fz Fz0⁄=

CDrϕ qDrϕ1

EDrϕ qDrϕ2

BDrϕKzγr0

CDrϕDDrϕ 1 εy–( )--------------------------------------------

=

=

=

Kzγr0 FzR0 qDz8 qDz9dfz+( )=

ζ6

ζ6 arc qBrϕ1R0ϕ( )tan[ ]cos=

Mzϕ90 Mzϕ∞2π--- arc qCrϕ2R0ϕ( ) Gyx κ( )⋅tan⋅ ⋅=

Gyκ

ζ7

ζ72π--- arc Mzϕ90 DDrϕ⁄[ ]cos⋅=

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38

Turn-Slip and Parking Parameters

The tire model parameters for turn-slip and parking are estimated automatically. In addition, you can specify each parameter individually in the tire property file (see example).

Steady-State Combined SlipPAC2002 has two methods for calculating the combined slip forces and moments. If the user supplies the coefficients for the combined slip cosine 'weighing' functions, the combined slip is calculated according to Combined slip with cosine 'weighing' functions (standard method). If no coefficients are supplied, the

Name:Name used in

tire property file: Explanation:p 1 PECP1 Camber spin reduction factor parameter in camber stiffnessp 2 PECP2 Camber spin reduction factor varying with load parameter in

camber stiffnesspDx 1 PDXP1 Peak Fx reduction due to spin parameterpDx 2 PDXP2 Peak Fx reduction due to spin with varying load parameterpDx 3 PDXP3 Peak Fx reduction due to spin with kappa parameterpDy 1 PDYP1 Peak Fy reduction due to spin parameterpDy 2 PDYP2 Peak Fy reduction due to spin with varying load parameterpDy 3 PDYP3 Peak Fy reduction due to spin with alpha parameterpDy 4 PDYP4 Peak Fy reduction due to square root of spin parameterpKy 1 PKYP1 Cornering stiffness reduction due to spinpHy 1 PHYP1 Fy-alpha curve lateral shift limitationpHy 2 PHYP2 Fy-alpha curve maximum lateral shift parameterpHy 3 PHYP3 Fy-alpha curve maximum lateral shift varying with load

parameterpHy 4 PHYP4 Fy-alpha curve maximum lateral shift parameterqDt 1 QDTP1 Pneumatic trail reduction factor due to turn slip parameterqBr 1 QBRP1 Residual (spin) torque reduction factor parameter due to side

slipqCr 1 QCRP1 Turning moment at constant turning and zero forward speed

parameterqCr 2 QCRP2 Turn slip moment (at alpha=90deg) parameter for increase

with spinqDr 1 QDRP1 Turn slip moment peak magnitude parameterqDr 2 QDRP2 Turn slip moment peak position parameter

εϕεϕ

ϕϕϕϕϕϕϕϕϕϕϕ

ϕϕϕ

ϕ

ϕ

ϕϕ

39

so-called friction ellipse is used to estimate the combined slip forces and moments, see section Combined Slip with friction ellipse

Combined slip with cosine 'weighing' functions• Longitudinal Force at Combined Slip

• Lateral Force at Combined Slip

• Aligning Moment at Combined Slip

• Overturning Moment at Pure and Combined Slip

• Rolling Resistance Moment at Pure and Combined Slip

Formulas for the Longitudinal Force at Combined Slip

(60)

with Gx the weighting function of the longitudinal force for pure slip.

We write:

(61)

(62)

with coefficients:

(63)

(64)

(65)

(66)

(67)

The weighting function follows as:

(68)

Fx Fx0 Gxα α κ Fz, ,( )⋅=

α

Fx Dxα Cxαarc Bxααs Exα Bxααs arc Bxααs( )tan–( )–{ }tan[ ]cos=

αs α SHxα+=

Bxα rBx1 arc rBx2κ{ }tan[ ] λxα⋅cos=

Cxα

DxαFxo

Cxαarc BxαSHxα Exα BxαSHxα arc BxαSHxα( )tan–( )–{ }tan[ ]cos------------------------------------------------------------------------------------------------------------------------------------------------------------------=

Exα rEx1 rEx2dfz with Exα 1≤+=

SHxα rHx1=

GxαCxαarc Bxααs Exα Bxααs arc Bxααs( )tan–( )–{ }tan[ ]cos

Cxαarc BxαSHxα Exα BxαSHxα arc BxαSHxα( )tan–( )–[ ]tan[ ]cos----------------------------------------------------------------------------------------------------------------------------------------------------------------=

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40

Longitudinal Force Coefficients at Combined Slip

Formulas for Lateral Force at Combined Slip

(69)

with Gyk the weighting function for the lateral force at pure slip and SVyk the ' -induced' side force; therefore, the lateral force can be written as:

(70)

(71)

with the coefficients:

(72)

(73)

(74)

(75)

(76)

(77)


property file: Explanation:rBx1 RBX1 Slope factor for combined slip Fx reductionrBx2 RBX2 Variation of slope Fx reduction with kapparCx1 RCX1 Shape factor for combined slip Fx reductionrEx1 REX1 Curvature factor of combined FxrEx2 REX2 Curvature factor of combined Fx with loadrHx1 RHX1 Shift factor for combined slip Fx reduction

Fy Fy0 Gyκ α κ γ Fz, , ,( )⋅=

Fy Dyκ Cyκarc Byκκs Eyκ Byκκs arc Byκκs( )tan–( )–{ }tan[ ] SVyκ+cos=

κs κ SHyκ+=

Byκ rBy1 arc rBy2 α rBy3–( ){ }tan[ ] λyκ⋅cos=

Cyκ rCy1=

DyκFyo

Cyκarc ByκSHyκ Eyκ ByκSHyκ arc ByκSHyκ( )tan–( )–{ }tan[ ]cos---------------------------------------------------------------------------------------------------------------------------------------------------------------=

Eyκ rEy1 rEy2dfz with Eyκ 1≤+=

SHyκ rHy1 rHy2dfz+=

SVyκ DVyκ rVy5arc rVy6κ( )tan[ ]sin=

41

(78)

The weighting function appears is defined as:

(79)

Lateral Force Coefficients at Combined Slip

Formulas for Aligning Moment at Combined Slip

(80)

with:

(81)

Name:Name used in

tire property file: Explanation:rBy1 RBY1 Slope factor for combined Fy reductionrBy2 RBY2 Variation of slope Fy reduction with alpharBy3 RBY3 Shift term for alpha in slope Fy reductionrCy1 RCY1 Shape factor for combined Fy reductionrEy1 REY1 Curvature factor of combined FyrEy2 REY2 Curvature factor of combined Fy with loadrHy1 RHY1 Shift factor for combined Fy reductionrHy2 RHY2 Shift factor for combined Fy reduction with loadrVy1 RVY1 Kappa induced side force Svyk/Muy*Fz at FznomrVy2 RVY2 Variation of Svyk/Muy*Fz with loadrVy3 RVY3 Variation of Svyk/Muy*Fz with inclinationrVy4 RVY4 Variation of Svyk/Muy*Fz with alpharVy5 RVY5 Variation of Svyk/Muy*Fz with kapparVy6 RVY6 Variation of Svyk/Muy*Fz with atan (kappa)

DVyκ μyFz rVy1 rVy2dfz rVy3γ+ +( ) arc rVy4α( )tan[ ]cos⋅ ⋅=

GyκCyκarc Byκκs Eyκ Byκκsarc Byκκs( )tan( )–{ }tan[ ]cos

Cyκarc ByκSHyκ Eyκ ByκSHyκarc ByκSHyκ( )tan( )–{ }tan[ ]cos---------------------------------------------------------------------------------------------------------------------------------------------------------=

M'z t Fy' Mzr s Fx⋅+ +⋅–=

t t αt eq,( )=

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(82)

(83)

(84)

(85)

with the arguments:

(86)

(87)

Aligning Moment Coefficients at Combined Slip

Formulas for Overturning Moment at Pure and Combined SlipFor the overturning moment, the formula reads both for pure and combined slip situations:

(88)

Name:Name used in

tire property file: Explanation:ssz1 SSZ1 Nominal value of s/R0 effect of Fx on Mz

ssz2 SSZ2 Variation of distance s/R0 with Fy/Fznom

ssz3 SSZ3 Variation of distance s/R0 with inclination

ssz4 SSZ4 Variation of distance s/R0 with load and inclination

Dt Ctarc Btαt eq, Et Btαt eq, arc Btαt eq,( )tan–( )–{ }tan[ ] α( )coscos=

F'y γ, 0= Fy SVyκ–=

Mzr Mzr αr eq,( ) Dr arc Brαr eq,( )tan[ ] α( )coscos= =

t t αt eq,( )=

αt eq, arc α2t

KxKy------⎝ ⎠⎛ ⎞

2κ2 αt( )sgn⋅+tantan=

αr eq, arc α2r

KxKy------⎝ ⎠⎛ ⎞

2κ2 αr( )sgn⋅+tantan=

Mx Ro Fz qSx1λVMx qSx2 λ qSx3FyFz0--------⋅+⋅–

⎩ ⎭⎨ ⎬⎧ ⎫

λMx⋅ ⋅=

43

Overturning Moment Coefficients

Formulas for Rolling Resistance Moment at Pure and Combined SlipThe rolling resistance moment is defined by:

(89)

If qsy1 and qsy2 are both zero and FITTYP is equal to 5 (MF-Tyre 5.0), then the rolling resistance is calculated according to an old equation:

(90)

Rolling Resistance Coefficients

Combined Slip with friction ellipseIn case the tire property file does not contain the coefficients for the 'standard' combined slip method (cosine 'weighing functions), the friction ellipse method is used, as described in this section. Note that the method employed here is not part of one of the Magic Formula publications by Pacejka, but is an in-house development of MSC.Software.


property file: Explanation:qsx1 QSX1 Lateral force induced overturning coupleqsx2 QSX2 Inclination induced overturning coupleqsx3 QSX3 Fy induced overturning couple


property file: Explanation:qsy1 QSY1 Rolling resistance moment coefficientqsy2 QSY2 Rolling resistance moment depending on Fxqsy3 QSY3 Rolling resistance moment depending on speedqsy4 QSY4 Rolling resistance moment depending on speed^4Vref LONGVL Measurement speed

My Ro Fz qSy1 qSy3Fx Fz0⁄ qSy3 Vx Vref( )⁄ qSy4Vx Vref( )⁄ 4+ + +{ }⋅ ⋅=

My R0 SVx Kx SHx⋅+( )=

κc κ SHxSVxKx---------+ +=

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The following friction coefficients are defined:

The forces corrected for the combined slip conditions are:

For aligning moment Mx, rolling resistance My and aligning moment Mz the formulae (76) until and

including (85) are used with =0.

αc α SHySVyKy---------+ +=

α∗ αc( )sin=

βκc

κc2 α∗

2+-------------------------⎝ ⎠⎜ ⎟⎛ ⎞

acos=

μx act,Fx 0, SVx–

Fz-------------------------= μy act,

Fy 0, SVy–Fz

-------------------------=

μx max,DxFz------= μy max,

DyFz------=

μx1

1μx act,-------------⎝ ⎠⎛ ⎞ 2 βtan

μy max,----------------⎝ ⎠⎛ ⎞ 2

+---------------------------------------------------------=

μyβtan

1μx max,----------------⎝ ⎠⎛ ⎞ 2 βtan

μy act,-------------⎝ ⎠⎛ ⎞ 2

+---------------------------------------------------------=

Fxμx

μx act,-------------Fx 0,= Fy

μyμy act,-------------Fy 0,=

SVyκ

45

Transient Behavior in PAC2002The previous Magic Formula equations are valid for steady-state tire behavior. When driving, however, the tire requires some response time on changes of the inputs. In tire modeling terminology, the low-frequency behavior (up to 15 Hz) is called transient behavior. PAC2002 provides two methods to model transient tire behavior:

• Stretched String • Contact Mass

Stretched String ModelFor accurate transient tire behavior, you can use the stretched string tire model (see reference [1]). The tire belt is modeled as stretched string, which is supported to the rim with lateral (and longitudinal) springs. Stretched String Model for Transient Tire Behavior shows a top-view of the string model. When rolling, the first point having contact with the road adheres to the road (no sliding assumed). Therefore, a lateral deflection of the string arises that depends on the slip angle size and the history of the lateral deflection of previous points having contact with the road.

Stretched String Model for Transient Tire Behavior

For calculating the lateral deflection v1 of the string in the first point of contact with the road, the following differential equation is valid:

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(91)

with the relaxation length in the lateral direction. The turnslip can be neglected at radii larger than 10 m. This differential equation cannot be used at zero speed, but when multiplying with Vx, the equation can be transformed to:

(92)


A similar approach yields the following for the deflection of the string in longitudinal direction:

(93)

Both the longitudinal and lateral relaxation length are defined as of the vertical load:

(94)

(95)

Now the practical slip quantities, and , are defined based on the tire deformation:

(96)

(97)

Using these practical slip quantities, and , the Magic Formula equations can be used to calculate the tire-road interaction forces and moments:

(98)

(99)

1Vx------

tddv1 v1

σα------+ α( ) aφ+tan=

σα φ

σα tddv1 Vx v1+ σαVsy=

σx tddu1 Vx u1+ σxVsx=

σx Fz pTx1 pTx2dfz+( ) pTx3dfz( ) R0 Fz0⁄( )λσx⋅exp⋅ ⋅=

σα pTy1Fz0 2arcFz

pTy2Fz0λFz0( )---------------------------------

⎩ ⎭⎨ ⎬⎧ ⎫

tan 1 pKy3 γy–( ) R0λFz0λσα⋅⋅ ⋅sin=

κ α

κ'u1σx------ Vx( )sin⋅=

α'v1σα------⎝ ⎠⎛ ⎞atan=

κ α

Fx Fx α' κ' Fz, ,( )=

Fy Fy α' κ' γ Fz, , ,( )=

47

(100)

Coefficients and Transient Response

Contact Mass ModelThe contact mass model is based on the separation of the contact patch slip properties and the tire carcass compliance (see reference [1]). Instead of using relaxation lengths to describe compliance effects, the carcass springs are explicitly incorporated in the model. The contact patch is given some inertia to ensure computational causality. This modeling approach automatically accounts for the lagged response to slip and load changes that diminish at higher levels of slip. The contact patch itself uses relaxation lengths to handle simulations at low speed.

The contact patch can deflect in longitudinal, lateral, and yaw directions with respect to the lower part of the wheel rim. A mass is attached to the contact patch to enable straightforward computations.

The differential equations that govern the dynamics of the contact patch body are:

The contact patch body with mass mc and inertia Jc is connected to the wheel through springs cx, cy, and

c and dampers kx, ky, and k in longitudinal, lateral, and yaw direction, respectively.

The additional equations for the longitudinal u, lateral v, and yaw deflections are:


property file: Explanation:pTx1 PTX1 Longitudinal relaxation length at FznompTx2 PTX2 Variation of longitudinal relaxation length with loadpTx3 PTX3 Variation of longitudinal relaxation length with exponent

of loadpTy1 PTY1 Peak value of relaxation length for lateral directionpTy2 PTY2 Shape factor for lateral relaxation lengthqTz1 QTZ1 Gyroscopic moment constantMbelt MBELT Belt mass of the wheel

M'z M'z α' κ' γ Fz, , ,( )=

mc V· cx Vcyψ·

c–( ) kxu· cxu+ + F=

mc V· cy Vcxψ·

c–( ) kyu· cyu+ + F=

Jcψ··

c kψβ· cψβ+ + Mz=

ψ ψ

β

u· Vcx Vsx–=

v· Vcy Vsy–=

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in which Vcx, Vcy and are the sliding velocity of the contact body in longitudinal, lateral, and yaw

directions, respectively. Vsx, Vsy, and are the corresponding velocities of the lower part of the wheel.

The transient slip equations for side slip, turn-slip, and camber are:

where the calculated deflection angle has been used:

The tire total spin velocity is:

With the transient slip equations, the composite transient turn-slip quantities are calculated:

The tire forces are calculated with and the tire moments with .

β· ψ· c ψ–=

ψ· c

ψ·

σc tdd α' Vx α'+ Vcy Vxβ– Vx βst+=

σc tddα't Vx α't+ Vx α'=

σc tddϕ'c Vx ϕ'c+ ψ· γ=

σF2 tddϕ'F2 Vx ϕ'cF2+ ψ· γ=

σϕ1 tddϕ'1 Vx ϕ'1+ ψ· γ=

σϕ2 tddϕ'2 Vx ϕ'2+ ψ· γ=

βstMzcφ-------=

ψ· γ ψc 1 εγ–( )Ω γsin–=

ϕ'F 2ϕ'c ϕ'F2–=

ϕ'M εϕϕ'c εϕ12 ϕ'1 ϕ'2–( )+=

ϕ'F ϕ'M

49

The relaxation lengths are reduced with slip:

Here a is half the contact length according to:

The composite tire parameter reads:

and the equivalent slip:


Name:Name used in

tire property file: Explanation:mc MC Contact body massIc IC Contact body moment of inertiakx KX Longitudinal dampingky KY Lateral dampingk KP Yaw dampingcx CX Longitudinal stiffnesscy CY Lateral stiffnessc CP Yaw stiffness

σc a 1 θζ–( )⋅=

σ2t0a----σc=

σF2 bF2σc=

σϕ1 bϕ1σc=

σϕ2 bϕ2σc=

a pA1R0 ρ zR0------ pA2

ρzR0------+

⎝ ⎠⎜ ⎟⎛ ⎞

=

θKy0

2μyFx---------------=

ζ 11 κ'+------------- α' aεϕ12 ϕ'1 ϕ'2–+{ }2 Kx0

Ky0---------⎝ ⎠⎛ ⎞

2κ' 2

3---b ϕ'c+

⎩ ⎭⎨ ⎬⎧ ⎫

2

+=

ϕ

ϕ

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The remaining contact mass model parameters are estimated automatically based on longitudinal and lateral stiffness specified in the tire property file.

Gyroscopic Couple in PAC2002When having fast rotations about the vertical axis in the wheel plane, the inertia of the tire belt may lead to gyroscopic effects. To cope with this additional moment, the following contribution is added to the total aligning moment:

(101)

with the parameter (in addition to the basic tire parameter mbelt):

(102)

and:

(103)

The total aligning moment now becomes:

(104)

pA1 PA1 Half contact length with vertical tire deflectionpA2 PA2 Half contact length with square root of vertical tire

deflectionEP Composite turn-slip (moment)EP12 Composite turn-slip (moment) increment

bF2 BF2 Second relaxation length factorb 1 BP1 First moment relaxation length factorb 2 BP2 Second moment relaxation length factor

Name:Name used in

tire property file: Explanation:

εϕεϕ12

ϕϕ

Mz gyr, cgyrmbeltVrl tddv arc Brαr eq,( )tan[ ]cos=

cgyr qTz1 λgyr⋅=

arc Brαr eq,( )tan[ ]cos 1=

Mz M'z Mz gyr,+=

51


Left and Right Side TiresIn general, a tire produces a lateral force and aligning moment at zero slip angle due to the tire construction, known as conicity and plysteer. In addition, the tire characteristics cannot be symmetric for positive and negative slip angles.

A tire property file with the parameters for the model results from testing with a tire that is mounted in a tire test bench comparable either to the left or the right side of a vehicle. If these coefficients are used for both the left and the right side of the vehicle model, the vehicle does not drive straight at zero steering wheel angle.

The latest versions of tire property files contain a keyword TYRESIDE in the [MODEL] section that indicates for which side of the vehicle the tire parameters in that file are valid (TIRESIDE = 'LEFT' or TIRESIDE = 'RIGHT').

If this keyword is available, Adams/Car corrects for the conicity and plysteer and asymmetry when using a tire property file on the opposite side of the vehicle. In fact, the tire characteristics are mirrored with respect to slip angle zero. In Adams/View, this option can only be used when the tire is generated by the graphical user interface: select Build -> Forces -> Special Force: Tire.

Next to the LEFT and RIGHT side option of TYRESIDE, you can also set SYMMETRIC: then the tire characteristics are modified during initialization to show symmetric performance for left and right side corners and zero conicity and plysteer (no offsets).Also, when you set the tire property file to SYMMETRIC, the tire characteristics are changed to symmetric behavior.

Create Wheel and Tire Dialog Box in Adams/View

Name:Name used in

tire property file: Explanation:pTx1 PTX1 Longitudinal relaxation length at FznompTx2 PTX2 Variation of longitudinal relaxation length with loadpTx3 PTX3 Variation of longitudinal relaxation length with exponent of

loadpTy1 PTY1 Peak value of relaxation length for lateral directionpTy2 PTY2 Shape factor for lateral relaxation lengthqTz1 QTZ1 Gyroscopic moment constantMbelt MBELT Belt mass of the wheel

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USE_MODES of PAC2002: from Simple to ComplexThe parameter USE_MODE in the tire property file allows you to switch the output of the PAC2002 tire model from very simple (that is, steady-state cornering) to complex (transient combined cornering and braking).

The options for the USE_MODE and the output of the model have been listed in the table below.

53

USE_MODE Values of PAC2002 and Related Tire Model Output

Quality Checks for the Tire Model ParametersBecause PAC2002 uses an empirical approach to describe tire - road interaction forces, incorrect parameters can easily result in non-realistic tire behavior. Below is a list of the most important items to ensure the quality of the parameters in a tire property file:

• Rolling Resistance

• Camber (Inclination) Effects

• Validity Range of the Tire Model Input

USE_MODE: State: Slip conditions:

PAC2002 output(forces and moments):

0 Steady state Acts as a vertical spring & damper

0, 0, Fz, 0, 0, 0

1 Steady state Pure longitudinal slip Fx, 0, Fz, 0, My, 02 Steady state Pure lateral (cornering) slip 0, Fy, Fz, Mx, 0, Mz

3 Steady state Longitudinal and lateral (not combined)

Fx, Fy, Fz, Mx, My, Mz

4 Steady state Combined slip Fx, Fy, Fz, Mx, My, Mz

11 Transient Pure longitudinal slip Fx, 0, Fz, 0, My, 012 Transient Pure lateral (cornering) slip 0, Fy, Fz, Mx, 0, Mz

13 Transient Longitudinal and lateral (not combined)


14 Transient Combined slip Fx, Fy, Fz, Mx, My, Mz

15 Transient Combined slip and turn-slip Fx, Fy, Fz, Mx, My, Mz

21 Advanced transient Pure longitudinal slip Fx, 0, Fz, My, 022 Advanced transient Pure lateral (cornering slip) 0, Fy, Fz, Mx, 0, Mz

23 Advanced transient Longitudinal and lateral (not combined)


24 Advanced transient Combined slip Fx, Fy, Fz, Mx, My, Mz

25 Advanced transient Combined slip and turn-slip/parking


Note: Do not change Fz0 (FNOMIN) and R0 (UNLOADED_RADIUS) in your tire property file. It will change the complete tire characteristics because these two parameters are used to make all parameters without dimension.

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Rolling ResistanceFor a realistic rolling resistance, the parameter qsy1 must be positive. For car tires, it can be in the order of 0.006 - 0.01 (0.6% - 1.0%); for heavy commercial truck tires, it can be around 0.006 (0.6%).

Tire property files with the keyword FITTYP=5 determine the rolling resistance in a different way (see equation (85)). To avoid the ‘old’ rolling resistance calculation, remove the keyword FITTYP and add a section like the following:

$---------------------------------------------------rolling resistance[ROLLING_COEFFICIENTS]QSY1 = 0.01QSY2 = 0QSY3 = 0QSY4 = 0

Camber (Inclination) EffectsCamber stiffness has not been explicitly defined in PAC2002; however, for car tires, positive inclination should result in a negative lateral force at zero slip angle. If positive inclination results in an increase of the lateral force, the coefficient may not be valid for the ISO but for the SAE coordinate system. Note that PAC2002 only uses coefficients for the TYDEX W-axis (ISO) system.

Effect of Positive Camber on the Lateral Force in TYDEX W-axis (ISO) System

The table below lists further checks on the PAC2002 parameters.

55

Checklist for PAC2002 Parameters and Properties

Validity Range of the Tire Model InputIn the tire property file, a range of the input variables has been given in which the tire properties are supposed to be valid. These validity range parameters are (the listed values can be different):

$--------------------------------------------------long_slip_range[LONG_SLIP_RANGE]KPUMIN = -1.5 $Minimum valid wheel slip KPUMAX = 1.5 $Maximum valid wheel slip $-------------------------------------------------slip_angle_range[SLIP_ANGLE_RANGE]ALPMIN = -1.5708 $Minimum valid slip angle ALPMAX = 1.5708 $Maximum valid slip angle $--------------------------------------------inclination_slip_range[INCLINATION_ANGLE_RANGE]CAMMIN = -0.26181 $Minimum valid camber angle CAMMAX = 0.26181 $Maximum valid camber angle $----------------------------------------------vertical_force_range[VERTICAL_FORCE_RANGE]FZMIN = 225 $Minimum allowed wheel load FZMAX = 10125 $Maximum allowed wheel load

If one of the input parameters exceeds a minimum or maximum validity value, the calculation in the tire model is performed with the minimum or maximum value of this range to avoid non-realistic tire behavior. In that case, a message appears warning you that one of the inputs exceeds a validity value.

Standard Tire Interface (STI) for PAC2002Because all Adams products use the Standard Tire Interface (STI) for linking the tire models to Adams/Solver, below is a brief background of the STI history (see also reference [4]).

Parameter/property: Requirement: Explanation:LONGVL 1 m/s Reference velocity at which parameters are

measuredVXLOW Approximately 1 m/s Threshold for scaling down forces and momentsDx > 0 Peak friction (see equation (24))pDx1/pDx2 < 0 Peak friction Fx must decrease with increasing loadKx > 0 Long slip stiffness (see equation (27))Dy > 0 Peak friction (see equation (36))pDy1/pDy2 < 0 Peak friction Fx must decrease with increasing loadKy < 0 Cornering stiffness (see equation (39))qsy1 > 0 Rolling resistance, in the range of 0.005 - 0.015

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At the First International Colloquium on Tire Models for Vehicle Dynamics Analysis on October 21-22, 1991, the International Tire Workshop working group was established (TYDEX).

The working group concentrated on tire measurements and tire models used for vehicle simulation purposes. For most vehicle dynamics studies, people used to develop their own tire models. Because all car manufacturers and their tire suppliers have the same goal (that is, development of tires to improve dynamic safety of the vehicle) it aimed for standardization in tire behavior description.

In TYDEX, two expert groups, consisting of participants of vehicle industry (passenger cars and trucks), tire manufacturers, other suppliers and research laboratories, had been defined with following goals:

• The first expert group's (Tire Measurements - Tire Modeling) main goal was to specify an interface between tire measurements and tire models. The result was the TYDEX-Format [2] to describe tire measurement data.

• The second expert group's (Tire Modeling - Vehicle Modeling) main goal was to specify an interface between tire models and simulation tools, which resulted in the Standard Tire Interface (STI) [3]. The use of this interface should ensure that a wide range of simulation software can be linked to a wide range of tire modeling software.

Definitions• General

• Tire Kinematics

• Slip Quantities

• Force and Moments

GeneralGeneral Definitions

Term: Definition:Road tangent plane Plane with the normal unit vector (tangent to the road) in the tire-road contact

point C.C-axis system Coordinate system mounted on the wheel carrier at the wheel center

according to TYDEX, ISO orientation.Wheel plane The plane in the wheel center that is formed by the wheel when considered a

rigid disc with zero width.Contact point C Contact point between tire and road, defined as the intersection of the wheel

plane and the projection of the wheel axis onto the road plane.W-axis system Coordinate system at the tire contact point C, according to TYDEX, ISO

orientation.

57

Tire KinematicsTire Kinematics Definitions

Slip QuantitiesSlip Quantities Definitions

Forces and MomentsForce and Moment Definitions

Parameter: Definition: Units:R0 Unloaded tire radius [m]R Loaded tire radius [m]Re Effective tire radius [m]

Radial tire deflection [m]d Dimensionless radial tire deflection [-]

Fz0 Radial tire deflection at nominal load [m]mbelt Tire belt mass [kg]

Rotational velocity of the wheel [rads-1]

Parameter: Definition: Units:V Vehicle speed [ms-1]Vsx Slip speed in x direction [ms-1]Vsy Slip speed in y direction [ms-1]Vs Resulting slip speed [ms-1]Vx Rolling speed in x direction [ms-1]Vy Lateral speed of tire contact center [ms-1]Vr Linear speed of rolling [ms-1]

Longitudinal slip [-]Slip angle [rad]Inclination angle [rad]

Abbreviation: Definition: Units:Fz Vertical wheel load [N]Fz0 Nominal load [N]dfz Dimensionless vertical load [-]

ρρρ

ω

καγ

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References1. H.B. Pacejka, Tyre and Vehicle Dynamics, 2002, Butterworth-Heinemann, ISBN 0 7506 5141 5.2. H.-J. Unrau, J. Zamow, TYDEX-Format, Description and Reference Manual, Release 1.1,

Initiated by the International Tire Working Group, July 1995.3. A. Riedel, Standard Tire Interface, Release 1.2, Initiated by the Tire Workgroup, June 1995.4. J.J.M. van Oosten, H.-J. Unrau, G. Riedel, E. Bakker, TYDEX Workshop: Standardisation of

Data Exchange in Tyre Testing and Tyre Modelling, Proceedings of the 2nd International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Vehicle System Dynamics, Volume 27, Swets & Zeitlinger, Amsterdam/Lisse, 1996.

Example of PAC2002 Tire Property File[MDI_HEADER]FILE_TYPE ='tir'FILE_VERSION =3.0FILE_FORMAT ='ASCII'! : TIRE_VERSION : PAC2002! : COMMENT : Tire 235/60R16! : COMMENT : Manufacturer ! : COMMENT : Nom. section with (m) 0.235 ! : COMMENT : Nom. aspect ratio (-) 60! : COMMENT : Infl. pressure (Pa) 200000! : COMMENT : Rim radius (m) 0.19 ! : COMMENT : Measurement ID ! : COMMENT : Test speed (m/s) 16.6 ! : COMMENT : Road surface ! : COMMENT : Road condition Dry! : FILE_FORMAT : ASCII! : Copyright MSC.Software, Fri Jan 23 14:30:06 2004!! USE_MODE specifies the type of calculation performed:! 0: Fz only, no Magic Formula evaluation! 1: Fx,My only! 2: Fy,Mx,Mz only! 3: Fx,Fy,Mx,My,Mz uncombined force/moment calculation! 4: Fx,Fy,Mx,My,Mz combined force/moment calculation! +10: including relaxation behaviour! *-1: mirroring of tyre characteristics

Fx Longitudinal force [N]Fy Lateral force [N]Mx Overturning moment [Nm]My Braking/driving moment [Nm]Mz Aligning moment [Nm]

Abbreviation: Definition: Units:

59

!! example: USE_MODE = -12 implies:! -calculation of Fy,Mx,Mz only! -including relaxation effects! -mirrored tyre characteristics!$--------------------------------------------------------------units[UNITS]LENGTH ='meter'FORCE ='newton'ANGLE ='radians'MASS ='kg'TIME ='second'$--------------------------------------------------------------model[MODEL]PROPERTY_FILE_FORMAT ='PAC2002'USE_MODE = 14 $Tyre use switch (IUSED)VXLOW = 1 LONGVL = 16.6 $Measurement speed TYRESIDE = 'LEFT' $Mounted side of tyre at vehicle/test bench$---------------------------------------------------------dimensions[DIMENSION]UNLOADED_RADIUS = 0.344 $Free tyre radius WIDTH = 0.235 $Nominal section width of the tyre ASPECT_RATIO = 0.6 $Nominal aspect ratioRIM_RADIUS = 0.19 $Nominal rim radius RIM_WIDTH = 0.16 $Rim width $----------------------------------------------------------parameter[VERTICAL]VERTICAL_STIFFNESS = 2.1e+005 $Tyre vertical stiffness VERTICAL_DAMPING = 50 $Tyre vertical damping BREFF = 8.4 $Low load stiffness e.r.r. DREFF = 0.27 $Peak value of e.r.r. FREFF = 0.07 $High load stiffness e.r.r. FNOMIN = 4850 $Nominal wheel load$----------------------------------------------------long_slip_range[LONG_SLIP_RANGE]KPUMIN = -1.5 $Minimum valid wheel slip KPUMAX = 1.5 $Maximum valid wheel slip $---------------------------------------------------slip_angle_range[SLIP_ANGLE_RANGE]ALPMIN = -1.5708 $Minimum valid slip angle ALPMAX = 1.5708 $Maximum valid slip angle $---------------------------------------------inclination_slip_range[INCLINATION_ANGLE_RANGE]

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CAMMIN = -0.26181 $Minimum valid camber angle CAMMAX = 0.26181 $Maximum valid camber angle $------------------------------------------------vertical_force_range[VERTICAL_FORCE_RANGE]FZMIN = 225 $Minimum allowed wheel load FZMAX = 10125 $Maximum allowed wheel load $-------------------------------------------------------------scaling[SCALING_COEFFICIENTS]LFZO = 1 $Scale factor of nominal (rated) load LCX = 1 $Scale factor of Fx shape factor LMUX = 1 $Scale factor of Fx peak friction coefficient LEX = 1 $Scale factor of Fx curvature factor LKX = 1 $Scale factor of Fx slip stiffness LHX = 1 $Scale factor of Fx horizontal shift LVX = 1 $Scale factor of Fx vertical shift LGAX = 1 $Scale factor of camber for Fx LCY = 1 $Scale factor of Fy shape factor LMUY = 1 $Scale factor of Fy peak friction coefficient LEY = 1 $Scale factor of Fy curvature factor LKY = 1 $Scale factor of Fy cornering stiffness LHY = 1 $Scale factor of Fy horizontal shift LVY = 1 $Scale factor of Fy vertical shift LGAY = 1 $Scale factor of camber for Fy LTR = 1 $Scale factor of Peak of pneumatic trail LRES = 1 $Scale factor for offset of residual torque LGAZ = 1 $Scale factor of camber for Mz LXAL = 1 $Scale factor of alpha influence on Fx LYKA = 1 $Scale factor of alpha influence on Fx LVYKA = 1 $Scale factor of kappa induced Fy

61

LS = 1 $Scale factor of Moment arm of Fx LSGKP = 1 $Scale factor of Relaxation length of Fx LSGAL = 1 $Scale factor of Relaxation length of Fy LGYR = 1 $Scale factor of gyroscopic torque LMX = 1 $Scale factor of overturning couple LVMX = 1 $Scale factor of Mx vertical shift LMY = 1 $Scale factor of rolling resistance torque $-------------------------------------------------------longitudinal[LONGITUDINAL_COEFFICIENTS]PCX1 = 1.6411 $Shape factor Cfx for longitudinal force PDX1 = 1.1739 $Longitudinal friction Mux at Fznom PDX2 = -0.16395 $Variation of friction Mux with load PDX3 = 0 $Variation of friction Mux with camber PEX1 = 0.46403 $Longitudinal curvature Efx at Fznom PEX2 = 0.25022 $Variation of curvature Efx with load PEX3 = 0.067842 $Variation of curvature Efx with load squared PEX4 = -3.7604e-005 $Factor in curvature Efx while driving PKX1 = 22.303 $Longitudinal slip stiffness Kfx/Fz at Fznom PKX2 = 0.48896 $Variation of slip stiffness Kfx/Fz with load PKX3 = 0.21253 $Exponent in slip stiffness Kfx/Fz with load PHX1 = 0.0012297 $Horizontal shift Shx at Fznom PHX2 = 0.0004318 $Variation of shift Shx with load PVX1 = -8.8098e-006 $Vertical shift Svx/Fz at Fznom PVX2 = 1.862e-005 $Variation of shift Svx/Fz with load RBX1 = 13.276 $Slope factor for combined slip Fx reduction RBX2 = -13.778 $Variation of slope Fx reduction with kappa RCX1 = 1.2568 $Shape factor for combined slip Fx reduction REX1 = 0.65225 $Curvature factor of combined Fx

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62

REX2 = -0.24948 $Curvature factor of combined Fx with load RHX1 = 0.0050722 $Shift factor for combined slip Fx reduction PTX1 = 2.3657 $Relaxation length SigKap0/Fz at Fznom PTX2 = 1.4112 $Variation of SigKap0/Fz with load PTX3 = 0.56626 $Variation of SigKap0/Fz with exponent of load $--------------------------------------------------------overturning[OVERTURNING_COEFFICIENTS]QSX1 = 0 $Lateral force induced overturning moment QSX2 = 0 $Camber induced overturning couple QSX3 = 0 $Fy induced overturning couple $------------------------------------------------------------lateral[LATERAL_COEFFICIENTS]PCY1 = 1.3507 $Shape factor Cfy for lateral forces PDY1 = 1.0489 $Lateral friction Muy PDY2 = -0.18033 $Variation of friction Muy with load PDY3 = -2.8821 $Variation of friction Muy with squared camber PEY1 = -0.0074722 $Lateral curvature Efy at Fznom PEY2 = -0.0063208 $Variation of curvature Efy with load PEY3 = -9.9935 $Zero order camber dependency of curvature Efy PEY4 = -760.14 $Variation of curvature Efy with camber PKY1 = -21.92 $Maximum value of stiffness Kfy/Fznom PKY2 = 2.0012 $Load at which Kfy reaches maximum value PKY3 = -0.024778 $Variation of Kfy/Fznom with camber PHY1 = 0.0026747 $Horizontal shift Shy at Fznom PHY2 = 8.9094e-005 $Variation of shift Shy with load PHY3 = 0.031415 $Variation of shift Shy with camber PVY1 = 0.037318 $Vertical shift in Svy/Fz at Fznom PVY2 = -0.010049 $Variation of shift Svy/Fz with load PVY3 = -0.32931 $Variation of shift Svy/Fz with camber

63

PVY4 = -0.69553 $Variation of shift Svy/Fz with camber and load RBY1 = 7.1433 $Slope factor for combined Fy reduction RBY2 = 9.1916 $Variation of slope Fy reduction with alpha RBY3 = -0.027856 $Shift term for alpha in slope Fy reduction RCY1 = 1.0719 $Shape factor for combined Fy reduction REY1 = -0.27572 $Curvature factor of combined Fy REY2 = 0.32802 $Curvature factor of combined Fy with load RHY1 = 5.7448e-006 $Shift factor for combined Fy reduction RHY2 = -3.1368e-005 $Shift factor for combined Fy reduction with load RVY1 = -0.027825 $Kappa induced side force Svyk/Muy*Fz at Fznom RVY2 = 0.053604 $Variation of Svyk/Muy*Fz with load RVY3 = -0.27568 $Variation of Svyk/Muy*Fz with camber RVY4 = 12.12 $Variation of Svyk/Muy*Fz with alpha RVY5 = 1.9 $Variation of Svyk/Muy*Fz with kappa RVY6 = -10.704 $Variation of Svyk/Muy*Fz with atan(kappa) PTY1 = 2.1439 $Peak value of relaxation length SigAlp0/R0 PTY2 = 1.9829 $Value of Fz/Fznom where SigAlp0 is extreme $-------------------------------------------------rolling resistance[ROLLING_COEFFICIENTS]QSY1 = 0.01 $Rolling resistance torque coefficient QSY2 = 0 $Rolling resistance torque depending on Fx QSY3 = 0 $Rolling resistance torque depending on speed QSY4 = 0 $Rolling resistance torque depending on speed ^4 $-----------------------------------------------------------aligning[ALIGNING_COEFFICIENTS]QBZ1 = 10.904 $Trail slope factor for trail Bpt at Fznom QBZ2 = -1.8412 $Variation of slope Bpt with load QBZ3 = -0.52041 $Variation of slope Bpt with load squared QBZ4 = 0.039211 $Variation of slope Bpt with camber

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64

QBZ5 = 0.41511 $Variation of slope Bpt with absolute camber QBZ9 = 8.9846 $Slope factor Br of residual torque Mzr QBZ10 = 0 $Slope factor Br of residual torque Mzr QCZ1 = 1.2136 $Shape factor Cpt for pneumatic trail QDZ1 = 0.093509 $Peak trail Dpt" = Dpt*(Fz/Fznom*R0) QDZ2 = -0.0092183 $Variation of peak Dpt" with load QDZ3 = -0.057061 $Variation of peak Dpt" with camber QDZ4 = 0.73954 $Variation of peak Dpt" with camber squared QDZ6 = -0.0067783 $Peak residual torque Dmr" = Dmr/(Fz*R0) QDZ7 = 0.0052254 $Variation of peak factor Dmr" with load QDZ8 = -0.18175 $Variation of peak factor Dmr" with camber QDZ9 = 0.029952 $Variation of peak factor Dmr" with camber and load QEZ1 = -1.5697 $Trail curvature Ept at Fznom QEZ2 = 0.33394 $Variation of curvature Ept with load QEZ3 = 0 $Variation of curvature Ept with load squared QEZ4 = 0.26711 $Variation of curvature Ept with sign of Alpha-t QEZ5 = -3.594 $Variation of Ept with camber and sign Alpha-t QHZ1 = 0.0047326 $Trail horizontal shift Sht at Fznom QHZ2 = 0.0026687 $Variation of shift Sht with load QHZ3 = 0.11998 $Variation of shift Sht with camber QHZ4 = 0.059083 $Variation of shift Sht with camber and load SSZ1 = 0.033372 $Nominal value of s/R0: effect of Fx on Mz SSZ2 = 0.0043624 $Variation of distance s/R0 with Fy/Fznom SSZ3 = 0.56742 $Variation of distance s/R0 with camber SSZ4 = -0.24116 $Variation of distance s/R0 with load and camber QTZ1 = 0.2 $Gyration torque constant MBELT = 5.4 $Belt mass of the wheel $-----------------------------------------------turn-slip parameters[TURNSLIP_COEFFICIENTS]

65

PECP1 = 0.7 $Camber stiffness reduction factorPECP2 = 0.0 $Camber stiffness reduction factor with loadPDXP1 = 0.4 $Peak Fx reduction due to spinPDXP2 = 0.0 $Peak Fx reduction due to spin with loadPDXP3 = 0.0 $Peak Fx reduction due to spin with longitudinal slipPDYP1 = 0.4 $Peak Fy reduction due to spinPDYP2 = 0.0 $Peak Fy reduction due to spin with loadPDYP3 = 0.0 $Peak Fy reduction due to spin with lateral slipPDYP4 = 0.0 $Peak Fy reduction with square root of spinPKYP1 = 1.0 $Cornering stiffness reduction due to spinPHYP1 = 1.0 $Fy lateral shift shape factorPHYP2 = 0.15 $Maximum Fy lateral shiftPHYP3 = 0.0 $Maximum Fy lateral shift with loadPHYP4 = -4.0 $Fy lateral shift curvature factorQDTP1 = 10.0 $Pneumatic trail reduction factorQBRP1 = 0.1 $Residual torque reduction factor with lateral slipQCRP1 = 0.2 $Turning moment at constant turning with zero speedQCRP2 = 0.1 $Turning moment at 90 deg lateral slipQDRP1 = 1.0 $Maximum turning momentQDRP2 = -1.5 $Location of maximum turning moment$--------------------------------------------contact patch parameters[CONTACT_COEFFICIENTS]PA1 = 0.4147 $Half contact length dependency on Fz)PA2 = 1.9129 $Half contact length dependency on sqrt(Fz/R0)$--------------------------------------------contact patch slip model[DYNAMIC_COEFFICIENTS]MC = 1.0 $Contact massIC = 0.05 $Contact moment of inertiaKX = 409.0 $Contact longitudinal dampingKY = 320.8 $Contact lateral dampingKP = 11.9 $Contact yaw dampingCX = 4.350e+005 $Contact longitudinal stiffnessCY = 1.665e+005 $Contact lateral stiffnessCP = 20319 $Contact yaw stiffnessEP = 1.0EP12 = 4.0BF2 = 0.5BP1 = 0.5BP2 = 0.67$------------------------------------------------------loaded radius[LOADED_RADIUS_COEFFICIENTS]QV1 = 0.000071 $Tire radius growth coefficientQV2 = 2.489 $Tire stiffness variation coefficient with speedQFCX1 = 0.1 $Tire stiffness interaction with FxQFCY1 = 0.3 $Tire stiffness interaction with FyQFCG1 = 0.0 $Tire stiffness interaction with camberQFZ1 = 0.0 $Linear stiffness coefficient, if zero, VERTICAL_STIFFNESS is takenQFZ2 = 14.35 $Tire vertical stiffness coefficient (quadratic)

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Contact MethodsThe PAC2002 model supports the following roads:

• 2D Roads, see Using the 2D Road Model

• 3D Spline Roads, see Adams/3D Spline Road Model

Note that the PAC2002 model has only one point of contact with the road; therefore, the wavelength of road obstacles must be longer than the tire radius for realistic output of the model. In addition, the contact force computed by this tire model is normal to the road plane. Therefore, the contact point does not generate a longitudinal force when rolling over a short obstacle, such as a cleat or pothole.


For ride and comfort analyses, we recommend more sophisticated tire models, such as Ftire.

Using the PAC-TIME Tire ModelThe PAC-TIME Magic-Formula tire model has been developed by MSC.Software according to a publication, A New Tyre Model for TIME Measurement Data, by J.J.M. van Oosten e.a. [5]. PAC-TIME has improved equations for side force and aligning moment under pure slip conditions. For longitudinal pure slip and combined slip, the tire model is similar to PAC-TIME.

Learn about:

• When to Use PAC-TIME

• Modeling of Tire-Road Interaction Forces

• Axis Systems and Slip Definitions

• Contact Point and Normal Load Calculation

• Basics of Magic Formula

• Steady-State: Magic Formula

• Transient Behavior

• Gyroscopic Couple

• Left and Right Side Tires

• USE_MODES OF PAC-TIME: from Simple to Complex

• Quality Checks for Tire Model Parameters

• Standard Tire Interface (STI)

• Definitions

• References

• Example of PAC-TIME Tire Property File

• Contact Methods

When to Use PAC-TIMEMagic-Formula (MF) tire models are considered the state-of-the-art for modeling tire-road interaction forces in vehicle dynamics applications. Since 1987, Pacejka and others have published several versions of this type of tire model. The PAC-TIME model is similar to PAC2002, but has improved equations for side force (Fy) and aligning moment (Mz) under pure side slip conditions.

The following is background information about the PAC-TIME tire model, as stated in the paper, A New Tyre Model for TIME Measurement Data, J.J.M. van Oosten, E. Kuiper, G. Leister, D. Bode, H. Schindler, J. Tischleder, S. Köhne [5]:

In 1999 a new method for tyre Force and Moment (F&M) testing has been developed by a consortium of European tyre and vehicle manufacturers: the TIME procedure. For Vehicle Dynamics studies often a Magic Formula (MF) tyre model is used based upon such F&M data. However when calculating MF parameters for a standard MF model out of the TIME F&M data, several difficulties are observed. These

Adams/Tire

12

are mainly due to the non-uniform distribution of the data points over the slip angle, camber and load area and the mutual dependency in between the slip angle, camber and load. A new MF model for pure cornering slip conditions has been developed that allows the calculation of the MF parameters despite of the dependency of the three input variables in the F&M data and shows better agreement with the measured F&M data points. From mathematical point of view the optimisation process for deriving MF parameters is better conditioned with the new MF-TIME, resulting in less sensitivity to starting values and better convergence to a global minimum. In addition the MF-TIME has improved extrapolation performance compared to the standard MF models for areas where no F&M data points are available. Next to the use for TIME F&M data, the new model is expected to have interesting prospects for converting ‘on-vehicle’ measured tyre data into a robust set of MF parameters.

In general, an MF tire model describes the tire behavior for rather smooth roads (road obstacle wavelengths longer than the tire radius) up to frequencies of 8 Hz. This makes the tire model applicable for all generic vehicle handling and stability simulations, including:

• Steady-state cornering• Single- or double-lane change• Braking or power-off in a turn• Split-mu braking tests• J-turn or other turning maneuvers• ABS braking, when stopping distance is important (not for tuning ABS control strategies)• Other common vehicle dynamics maneuvers on rather smooth roads (wavelength of road


For modeling roll-over of a vehicle, you must pay special attention to the overturning moment characteristics of the tire (Mx), and the loaded radius modeling. The last item may not be sufficiently addressed in this model.

The PAC-TIME model has been developed for car tires with camber (inclination) angles to the road not exceeding 15 degrees.

Modeling of Tire-Road Interaction ForcesFor vehicle dynamics applications, an accurate knowledge of tire-road interaction forces is inevitable because the movements of a vehicle primarily depend on the road forces on the tires. These interaction forces depend on both road and tire properties, and the motion of the tire with respect to the road.

In the radial direction, the MF tire models consider the tire to behave as a parallel linear spring and linear damper with one point of contact with the road surface. The contact point is determined by considering the tire and wheel as a rigid disc. In the contact point between the tire and the road, the contact forces in longitudinal and lateral direction strongly depend on the slip between the tire patch elements and the road.

The figure, Input and Output Variables of the Magic Formula Tire Model, presents the input and output vectors of the PAC2002 tire model. The tire model subroutine is linked to the Adams/Solver through the Standard Tire Interface (STI) [3]. The input through the STI consists of:

13


The tire model routine calculates the vertical load and slip quantities based on the position and speed of the wheel with respect to the road. The input for the Magic Formula consists of the wheel load (Fz), the

longitudinal and lateral slip ( , ), and inclination angle ( ) with the road. The output is the forces (Fx, Fy) and moments (Mx, My, Mz) in the contact point between the tire and the road. For calculating these forces, the MF equations use a set of MF parameters, which are derived from tire testing data.

The forces and moments out of the Magic Formula are transferred to the wheel center and returned to Adams/Solver through STI.


Axis Systems and Slip Definitions• Axis Systems

• Units


κ α γ

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14

Axis SystemsThe PAC-TIME model is linked to Adams/Solver using the TYDEX STI conventions, as described in the TYDEX-Format [2] and the STI [3].

The STI interface between the MF-TIME model and Adams/Solver mainly passes information to the tire model in the C-axis coordinate system. In the tire model itself, a conversion is made to the W-axis system because all the modeling of the tire behavior, as described in this help, assumes to deal with the slip quantities, orientation, forces, and moments in the contact point with the TYDEX W-axis system. Both axis systems have the ISO orientation but have different origin as can be seen in the figure below.

TYDEX C- and W-Axis Systems Used in PAC-TIME , Source [2]



The forces and moments calculated by PAC-TIME using the MF equations in this guide are in the W-axis system. A transformation is made in the source code to return the forces and moments through the STI to Adams/Solver.


UnitsThe units of information transferred through the STI between Adams/Solver and PAC-TIME are according to the SI unit system. Also, the equations for PAC-TIME described in this guide have been developed for use with SI units, although you can easily switch to another unit system in your tire property file. Because of the non-dimensional parameters, only a few parameters have to be changed.

15


SI Units Used in PAC-TIME

Definition of Tire Slip QuantitiesSlip Quantities at Combined Cornering and Braking/Traction

Variable type: Name: Abbreviation: Unit:Angle Slip angle

Inclination angle

Radians


Lateral force

Vertical load

Fx

Fy

Fz

Newton




Mx

My

Mz

Newton.meter


Lateral speed


Lateral slip speed

Vx

Vy

Vsx

Vsy

Meters per second


α

γ

ω

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16

The longitudinal slip velocity Vsx in the contact point (W-axis system, see Slip Quantities at Combined Cornering and Braking/Traction) is defined using the longitudinal speed Vx, the wheel rotational velocity

, and the effective rolling radius Re:

(1)


(2)


(3)

(4)


(5)

Contact Point and Normal Load Calculation• Contact Point



For calculating the kinematics of the tire relative to the road, the road is approximated by its tangent plane at the road point right below the wheel center (see the figure below).


ω

Vsx Vx ΩRe–=

Vsy Vy=

κ α

κVsxVx--------–=

αtanVsyVx---------=

Vr ReΩ=

17

The contact point is determined by the line of intersection of the wheel center-plane with the road tangent (ground) plane and the line of intersection of the wheel center-plane with the plane though the wheel spin axis.

The normal load Fz of the tire is calculated with:

(6)

where is the tire deflection and is the deflection rate of the tire.

Instead of the linear vertical tire stiffness Cz, you can also define an arbitrary tire deflection - load curve in the tire property file in the section [DEFLECTION_LOAD_CURVE] (see the Example of PAC-TIME Tire Property File). If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection data points with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify Cz in the tire property file, but it does not play any role.

Loaded and Effective Tire Rolling RadiusWith the loaded rolling tire radius R defined as the distance of the wheel center to the contact point of the tire with the road, where is the deflection of the tire, and R0 is the free (unloaded) tire radius, then the loaded tire radius Rl is:

(7)

In this tire model, a constant (linear) vertical tire stiffness Cz is assumed; therefore, the tire deflection can be calculated using:

Fz Czρ Kz ρ·⋅+=

ρ ρ

ρ

R1 R0 ρ–=

ρ

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18

(8)


(9)

For radial tires, the effective rolling radius is rather independent of load in its load range of operation because of the high stiffness of the tire belt circumference. Only at low loads does the effective tire radius decrease with increasing vertical load due to the tire tread thickness. See the figure below.


To represent the effective rolling radius Re, an MF type of equation is used:

(10)

ρFzCz------=

ReVxΩ------=

Re R0 ρFz0Darc Bρd( ) Fρd+tan( )–=

19

in which Fz0 is the nominal tire deflection:

(11)

and d is called the dimensionless radial tire deflection, defined by:

(12)



Name:Name Used in Tire

Property File: Explanation:Fz0 FNOMIN Nominal wheel loadRo UNLOADED_RADIUS Free tire radiusB BREFF Low load stiffness effective rolling radiusD DREFF Peak value of effective rolling radius

ρ

ρFz0

Fz0Cz--------=

ρ

ρd ρρFz0

---------=

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20

Basics of the Magic Formula in PAC-TIMEThe Magic Formula is a mathematical formula that is capable of describing the basic tire characteristics for the interaction forces between the tire and the road under several steady-state operating conditions. We distinguish:


For pure slip conditions, the lateral force Fy as a function of the lateral slip , respectively, and the

longitudinal force Fx as a function of longitudinal slip , have a similar shape. Because of the sine - arctangent combination, the basic Magic Formula example is capable of describing this shape:

(13)

where Y(x) is either Fx with x the longitudinal slip , or Fy and x the lateral slip .


F FREFF High load stiffness effective rolling radiusCz VERTICAL_STIFFNESS Tire vertical stiffnessKz VERTICAL_DAMPING Tire vertical damping


Property File: Explanation:

ακ


κ α

21

The self-aligning moment Mz is calculated as a product of the lateral force Fy and the pneumatic trail t added with the residual moment Mzr. In fact, the aligning moment is due to the offset of lateral force Fy, called pneumatic trail t, from the contact point. Because the pneumatic trail t as a function of the lateral slip has a cosine shape, a cosine version the Magic Formula is used:

(14)






α


α

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22

In combined slip conditions, the lateral force Fy will decrease due to longitudinal slip or the opposite, the longitudinal force Fx will decrease due to lateral slip. The forces and moments in combined slip conditions are based on the pure slip characteristics multiplied by the so-called weighting functions. Again, these weighting functions have a cosine-shaped MF examples.


Inclination Effects in the Lateral ForceFrom a historical point of view, the camber stiffness always has been modeled implicit in the Magic Formulas. For deriving coefficients of a Pacejka tire model usually so-called tire tests with slip angle sweeps at various values of constant load and inclination are performed. In the resulting Force & Moment measurement data, the effects of camber on the side force Fy are relatively small compared to side force

23

effects by slip angle, which can easily result in non-realistic camber stiffness properties. Because there is no explicit definition of the camber stiffness, the effects on camber stiffness cannot be controlled in the coefficient optimization process.

The TIME measurement procedure guarantees more realistic tire test data, because they are performed under realistic tire operating conditions and specific parts of the test program concentrate on getting accurate cornering and camber stiffness. Because the inputs to the test program (side and longitudinal slip, inclination, and load) are not independent, for the parameter optimization process, a Pacejka tire model was required that has a better definition of cornering and camber stiffness from mathematical point of view (for a more detailed explanation, see [5]).

Therefore, the PAC-TIME tire model has an explicit definition of camber effects, similar to the tire model for motorcycle tires (PAC_MC). The basic Magic Formula sine function for the lateral force Fy

has been extended with an argument for the inclination as follows:

(15)

In the PAC-TIME tire model, C has been set to ½, and E is not used (zero value). This approach results in an explicit definition of the camber stiffness, because:

(16)


Input Variables

Output VariablesIts output variables are:

Output Variables.

Longitudinal slip [-]Slip angle [rad]Inclination angle [rad]Normal wheel load Fz [N]

Longitudinal force Fx [N]Lateral force Fy [N]

γ

Fy0 Dy Cyarc Byαy Ey Byαy arc Byαy( )tan–( )–{ }Cγarc Byαγ Eγ Bγαγ arc Bγαγ( )tan–( )–{ }tan+

tan[]

cos=

γ γ

Kγ BγCγDγFyoγδ

-------- at αγ∂ 0= = =

καγ

Adams/Tire

24



Basic Tire Parameters


(17)

with the possibly adapted nominal load (using the user-scaling factor, Fz0):

(18)



Overturning couple Mx [Nm]Rolling resistance moment My [Nm]Aligning moment Mz [Nm]




dfzFz F'z0–

F'z0--------------------=

λ

F'z0 Fz0 λFz0⋅=

25

User Scaling FactorsA set of scaling factors is available to easily examine the influence of changing tire properties without the need to change one of the real Magic Formula coefficients. The default value of these factors is 1. You can change the factors in the tire property file. The peak friction scaling factors, factors, and

', are also used for the position-dependent friction in 3D Road Contact and Adams/3D Road. An overview of all scaling factors is shown in the next tables.




k = 1, 2, ...

Name:Name used in

tire property file: Explanation:

Fzo LFZO Scale factor of nominal (rated) load

Cx LCX Scale factor of Fx shape factorLMUX Scale factor of Fx peak friction coefficient

Ex LEX Scale factor of Fx curvature factor

Kx LKX Scale factor of Fx slip stiffness

Vx LVX Scale factor of Fx vertical shift

Hx LHX Scale factor of Fx horizontal shift

x LGAX Scale factor of camber for Fx

Cy LCY Scale factor of Fy shape factor for side slipy LMUY Scale factor of Fy peak friction coefficient

Parameter: Definition:

λμξλγψ

λλλμξλλλλλγλλμ

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26



Steady-State: Magic Formula in PAC-TIME• Steady-State Pure Slip


Ey LEY Scale factor of Fy curvature factorKy LKY Scale factor of Fy cornering stiffness

Vy LVY Scale factor of Fy vertical shiftHy LHY Scale factor of Fy horizontal shiftK LKC Scale factor of camber stiffness (K-factor)

LGAY Scale factor of camber force stiffness

t LTR Scale factor of peak of pneumatic trail

Mr LRES Scale factor for offset of residual torquez LGAZ Scale factor of camber torque stiffness

Mx LMX Scale factor of overturning couple

VMx LVMX Scale factor of Mx vertical shift

My LMY Scale factor of rolling resistance torque


property file: Explanation:x LXAL Scale factor of alpha influence on Fxy LYKA Scale factor of alpha influence on FxVy LVYKA Scale factor of kappa induced Fy

s LS Scale factor of moment arm of Fx


property file: Explanation:LSGKP Scale factor of relaxation length of FxLSGAL Scale factor of relaxation length of Fy

gyr LGYR Scale factor of gyroscopic moment

Name:Name used in

tire property file: Explanation:λλλλλ γλγψλλλγλλλ

λ αλ κλ κλ

λσκλσαλ

27





(19)

(20)

(21)

(22)


(23)

(24)

(25)

(26)


(27)

(28)

(29)


Fx0 Dx Cxarc Bxκx Ex Bxκx arc Bxκs( )tan–( )–{ }tan[ ] SVx+cos=

κx κ SHx+=

γx γ λγx⋅=

Cx pCx1 λcx⋅=

Dx μx Fz⋅=

μx pDx1 pDx2dfz+( ) 1 pDx3 γx2⋅( )γμx–⋅=

Ex pEx1 pEx2dfz pEx2dfz2+ +( ) 1 pEx4 κx( )sgn–{ } λEx with Ex 1≤⋅ ⋅=

Kx Fz pKx1 pKx2dfz+( ) pKx3dfz( )λK

Kx

exp⋅

BxCxDx κx∂∂Fx0 at κx 0

=

= = =

Bx Kx CxDx( )⁄=

SHx pHx1 pHx2dfz+( )λHx=

SVx Fz pVx1 pVx2dfz+( ) λVx λμx⋅ ⋅ ⋅=

Adams/Tire

28



(30)

(31)

(32)


(33)

with coefficients:

(34)

(35)

(36)

(37)



property file: Explanation:pCx1 PCX1 Shape factor Cfx for longitudinal forcepDx1 PDX1 Longitudinal friction Mux at FznompDx2 PDX2 Variation of friction Mux with loadpDx3 PDX3 Variation of friction Mux with inclinationpEx1 PEX1 Longitudinal curvature Efx at FznompEx2 PEX2 Variation of curvature Efx with loadpEx3 PEX3 Variation of curvature Efx with load squaredpEx4 PEX4 Factor in curvature Efx while drivingpKx1 PKX1 Longitudinal slip stiffness Kfx/Fz at FznompKx2 PKX2 Variation of slip stiffness Kfx/Fz with load


Fy0 Dy Cyarc Byαy Ey Byαy arc Byαy( )tan–( )–{ } 12---arc Bγγy( )tan+tan SVy+sin=

αy α SHy+=

γy γ λγy⋅=

Cy pCy1 λCy⋅=

Dy μy Fz⋅=

μy pDy1 pDy2dfz+( ) 1 pDy3γy2–( ) λμy⋅ ⋅=

Ey pEy1 pEy2dfz pEy3 pEy4γy+( ) αy( )sgn+ +{ } λEy⋅=

29

() (38)

(39)

(40)

(41)

(42)

(43)



property file: Explanation:pCy1 PCY1 Shape factor Cfy for lateral forcespDy1 PDY1 Lateral friction MuypDy2 PDY2 Variation of friction Muy with loadpDy3 PDY3 Variation of friction Muy with squared inclinationpEy1 PEY1 Lateral curvature Efy at FznompEy2 PEY2 Variation of curvature Efy with loadpEy3 PEY3 Inclination dependency of curvature EfypEy4 PEY4 Variation of curvature Efy with inclinationpKy1 PKY1 Maximum value of stiffness Kfy/FznompKy2 PKY2 Load at which Kfy reaches maximum valuepKy3 PKY3 Variation of Kfy/Fznom with inclinationpKy4 PKY4 Shape factor of KfypKy5 PKY5 Linear variation of Kγ with loadpKy6 PKY6 Quadratic variation of Kγ with load

Ky α∂∂Fy pKy1Fz0 pKy4arc

FzpKy2Fz0λFz0-------------------------------

⎩ ⎭⎨ ⎬⎧ ⎫

tan 1 pKy3γy2–( ) λKyλFz0⋅ ⋅sin= =

with pKy4 2≤

Kγ γ∂∂Fy Fz pKy5 pKy5dfz+( ) λKy⋅= =

ByKy

CyDy-------------=

Bγ2Kγ

Dy---------=

SHy pHy1 pHy2dfz+( ) λHy⋅=

SHy Fz pVy1 pVy2dfz+( ) λVyλμy⋅=

Adams/Tire

30


(44)


(45)


(46)

(47)

(48)


(49)

with coefficients:

(50)

(51)

(52)

pHy1 PHY1 Horizontal shift Shy at FznompHy2 PHY2 Variation of shift Shy with loadpVy1 PVY1 Vertical shift in Svy/Fz at FznompVy2 PVY2 Variation of shift Svy/Fz with load



M'z Mz0 α γ Fz, ,( )=

Mz0 t Fy0 SVy–( )γ 0= Mzr+⋅–=


αt α SHt+=

Mzr αr( ) Dr arc Brαr( )tan[ ] α( )coscos=

αr α SHt+=

SHr 0=

γz γ λγz⋅=

Bt qBz1 qBz2dfz+( ) 1 qBz4γz2 qBz5 γz+ +( ) λk λμy⁄⋅( )=

Ct qCz1=

Dt Fz qDz1 qDz2dfz+( ) R0 Fz0⁄( ) λt⋅=

31

(53)

(54)

(55)

(56)


(57)

and the aligning stiffness for inclination is:

(58)



property file: Explanation:qBz1 QBZ1 Trail slope factor for trail Bpt at FznomqBz2 QBZ2 Variation of slope Bpt with loadqBz4 QBZ4 Variation of slope Bpt with inclinationqBz5 QBZ5 Variation of slope Bpt with absolute inclinationqCz1 QCZ1 Shape factor Cpt for pneumatic trailqDz1 QDZ1 Peak trail Dpt = Dpt*(Fz/Fznom*R0)qDz2 QDZ2 Variation of peak Dpt with loadqDz6 QDZ6 Peak residual moment Dmr = Dmr/ (Fz*R0)qDz7 QDZ7 Variation of peak factor Dmr with loadqDz8 QDZ8 Variation of peak factor Dmr with inclinationqDz9 QDZ9 Variation of Dmr with inclination and loadqEz1 QEZ1 Trail curvature Ept at Fznom

Et qEz1 qEz2dfz+( ) 1 qEz42π---arc BtCtαt( )tan+

⎩ ⎭⎨ ⎬⎧ ⎫

with Et 1≤

=

SHt qHz1 qHz2dfz qHz3 qHz4dfz+( )γz+ +=

Br λKz λμy⁄=

Dr Fz qDz6 qDz7dfz+( )λr qDz8 qDz9dfz+( )γz+{ }R0λμy=

α∂∂Mz tKy– Fz qDz1 qDz2dfz+( ) R0 Fz0⁄( ) pKy5 pKy6dfz+( )Fz λtλKy⋅= =

γddMz qDz8 qDz9dfz+( )R0Fzλμy=

Adams/Tire

32

Steady-State Combined SlipPAC-TIME has two methods for calculating the combined slip forces and moments. If the user supplies the coefficients for the combined slip cosine 'weighing' functions, the combined slip is calculated according to Combined slip with cosine 'weighing' functions (standard method). If no coefficients are supplied, the so-called friction ellipse is used to estimate the combined slip forces and moments, see section Combined Slip with friction ellipse







(59)

with Gx the weighting function of the longitudinal force for pure slip.

We write:

(60)

(61)

with coefficients:

(62)

(63)

qEz2 QEZ2 Variation of curvature Ept with loadqEz4 QEZ4 Variation of curvature Ept with sign of Alpha-tqHz1 QHZ1 Trail horizontal shift Sht at FznomqHz2 QHZ2 Variation of shift Sht with loadqHz3 QHZ3 Variation of shift Sht with inclinationqHz4 QHZ4 Variation of shift Sht with inclination and load




α


αs α SHxα+=

Bxα rBx1 arc rBx2κ{ }tan[ ] λxα⋅cos=

Cxα rCx1=

33

(64)

(65)

(66)


(67)



(68)


(69)

(70)


(71)

(72)


property file: Explanation:rBx1 RBX1 Slope factor for combined slip Fx reductionrBx2 RBX2 Variation of slope Fx reduction with kapparCx1 RCX1 Shape factor for combined slip Fx reductionrEx1 REX1 Curvature factor of combined FxrEx2 REX2 Curvature factor of combined Fx with loadrHx1 RHX1 Shift factor for combined slip Fx reduction

DxαFxo



SHxα rHx1=



Fy Fy0 Gyκ α κ γ Fz, , ,( ) SVyκ+⋅=

κ

Fy Dyκ Cyκarc Byκκs Eyκ Bxακs arc Byκκs( )tan–( )–{ }tan[ ] SVyκ+cos=

κs κ SHyκ+=

Byκ rBy1 arc rBy2 α rBy3–( ){ }tan[ ] λyκ⋅cos=

Cyκ rCy1=

Adams/Tire

34

(73)

(74)

(75)

(76)


(77)



(78)

with:

(79)


property file: Explanation:rBy1 RBY1 Slope factor for combined Fy reductionrBy2 RBY2 Variation of slope Fy reduction with alpharBy3 RBY3 Shift term for alpha in slope Fy reductionrCy1 RCY1 Shape factor for combined Fy reductionrEy1 REY1 Curvature factor of combined FyrEy2 REY2 Curvature factor of combined Fy with loadrHy1 RHY1 Shift factor for combined Fy reductionrHy2 RHY2 Shift factor for combined Fy reduction with loadrVy1 RVY1 Kappa induced side force SVyk/μy·Fz at FznomrVy2 RVY2 Variation of SVyk/μy·Fz with loadrVy3 RVY3 Variation of SVyk/μy·Fz with inclinationrVy4 RVY4 Variation of SVyk/μy·Fz with αrVy5 RVY5 Variation of SVyk/μy·Fz with κrVy6 RVY6 Variation of SVyk/μy·Fz with atan(κ)

DyκFyo

Cyκarc ByκSHyκ Eyκ BxαSHyκ arc ByκSHyκ( )tan–( )–{ }tan[ ]cos---------------------------------------------------------------------------------------------------------------------------------------------------------------=




GyκCyκarc Byκκs Eyκ Bxακs arc Byκκs( )tan–( )–{ }tan[ ]cos

Cyκarc ByκSHyκ Eyκ BxαSHyκ arc ByκSHyκ( )tan–( )–{ }tan[ ]cos---------------------------------------------------------------------------------------------------------------------------------------------------------------=

M'z t F'y Mzr s Fx⋅+ +⋅–=

t t αt eq,( )=

35

(80)

(81)

(82)

with the arguments:

(83)

(84)



(85)



property file: Explanation:ssz1 SSZ1 Nominal value of s/R0 effect of Fx on Mzssz2 SSZ2 Variation of distance s/R0 with Fy/Fznomssz3 SSZ3 Variation of distance s/R0 with inclinationssz4 SSZ4 Variation of distance s/R0 with load and inclination


property file: Explanation:qsx1 QSX1 Lateral force induced overturning coupleqsx2 QSX2 Inclination induced overturning coupleqsx3 QSX3 Fy induced overturning couple

Dt Ctarc Btαt eq, Et Btαt eq, arc Btαt eq,( )tan–( )–{ }tan[ ] α( )coscos=



t t αt eq,( )=

αt eq, arc α2t

KxKy------⎝ ⎠⎛ ⎞

2κ2 αt( )sgn⋅+tantan=

αr eq, arc α2r

KxKy------⎝ ⎠⎛ ⎞

2κ2 αr( )sgn⋅+tantan=

Mx Ro Fz qsx1λVMx qsx2 qsx3FyFz0--------⋅+–

⎩ ⎭⎨ ⎬⎧ ⎫

λMx⋅ ⋅=

Adams/Tire

36


(86)






My Ro Fz qSy1 qSy2Fx Fz0⁄ qSy3 Vx Vref( )⁄ qSy4 Vx Vref⁄( )4+ +{ }⋅ ⋅=



α∗ αc( )sin=

βκc

κc2 α∗

2+-------------------------⎝ ⎠⎜ ⎟⎛ ⎞

acos=


Fz-------------------------= μy act,

Fy 0, SVy–Fz

-------------------------=


DyFz------=

37




Transient Behavior in PAC-TIMEThe previous Magic Formula equations are valid for steady-state tire behavior. When driving, however, the tire requires some response time on changes of the inputs. In tire modeling terminology, the low-frequency behavior (up to 8 Hz) is called transient behavior.

For accurate transient tire behavior, you can use the stretched string tire model (see reference [1]). The tire belt is modeled as stretched string, which is supported to the rim with lateral (and longitudinal) springs. Stretched String Model for Transient Tire Behavior shows a top-view of the string model. When rolling, the first point having contact with the road adheres to the road (no sliding assumed). Therefore, a lateral deflection of the string arises that depends on the slip angle size and the history of the lateral deflection of previous points having contact with the road.


μx1

1μx act,-------------⎝ ⎠⎛ ⎞ 2 βtan

μy max,----------------⎝ ⎠⎛ ⎞ 2

+---------------------------------------------------------=

μyβtan

1μx max,----------------⎝ ⎠⎛ ⎞ 2 βtan

μy act,-------------⎝ ⎠⎛ ⎞ 2

+---------------------------------------------------------=

Fxμx

μx act,-------------Fx 0,= Fy

μyμy act,-------------Fy 0,=

SVyκ

Adams/Tire

38


(87)


(88)



1Vx------

tddv1 v1

σα------+ α( ) aφ+tan=

σα φ


39

(89)


(90)

(91)


(92)

(93)

Using these practical slip quantities, and , the Magic Formula equations can be used to calculate the tire-road interaction forces and moments:

(94)

(95)

(96)

Gyroscopic Couple in PAC-TIMEWhen having fast rotations about the vertical axis in the wheel plane, the inertia of the tire belt may lead to gyroscopic effects. To cope with this additional moment, the following contribution is added to the total aligning moment:

(97)

with the parameters (in addition to the basic tire parameter mbelt):

(98)

and:

σx tddu1 Vx u1+ σxVsx–=

σx Fz pTx1 pTx2dfz+( ) pTx3dfz( ) R0 Fz0⁄( )λσκ⋅exp⋅ ⋅=

σα pTy1Fz0 pKy4arcFz

pTy2Fz0λFz0

-----------------------------⎩ ⎭⎨ ⎬⎧ ⎫

tan 1 pKy3γ2–( ) R0λFz0λσα⋅ ⋅sin=

κ' α'

κ'u1σx------ Vx( )sin=

α'v1σα------⎝ ⎠⎛ ⎞atan=

κ' α'

Fx Fx α' κ' Fz, ,( )=

Fy Fy α' κ' γ Fz, , ,( )=

Mz Mz α' κ' γ Fz, , ,( )=

Mz gyr, cgyrmbeltVr1 tddv arc Brαr eq,( )tan[ ]cos=

cgyr qTz1 λgyr⋅=

Adams/Tire

40

(99)






If this keyword is available, Adams/Car corrects for the conicity, plysteer, and asymmetry when using a tire property file on the opposite side of the vehicle. In fact, the tire characteristics are mirrored with respect to slip angle zero. In Adams/View, this option can only be used when the tire is generated by the graphical user interface: select Build -> Forces -> Special Force: Tire, as shown in the figure below.



property file: Explanation:pTx1 PTX1 Longitudinal relaxation length at FznompTx2 PTX2 Variation of longitudinal relaxation length with loadpTx3 PTX3 Variation of longitudinal relaxation length with exponent

of loadpTy1 PTY1 Peak value of relaxation length for lateral directionpTy2 PTY2 Shape factor for lateral relaxation lengthqTz1 QTZ1 Gyroscopic moment constantMbelt MBELT Belt mass of the wheel

arc Brαr eq,( )tan[ ]cos 1=

Mz Mz' Mz gyr,+=

41

Next to the LEFT and RIGHT side option of TYRESIDE, you can also set SYMMETRIC: then the tire characteristics are modified during initialization to show symmetric performance for left and right side corners and zero conicity and plysteer (no offsets). Also, when you set the tire property file to SYMMETRIC, the tire characteristics are changed to symmetric behavior.

USE_MODES of PAC-TIME: from Simple to ComplexThe parameter USE_MODE in the tire property file allows you to switch the output of the PAC-TIME tire model from very simple (that is, steady-state cornering) to complex (transient combined cornering and braking).

Adams/Tire

42

The options for the USE_MODE and the output of the model have been listed in the table below.

USE_MODE Values of PAC-TIME and Related Tire Model Output

Quality Checks for the Tire Model ParametersBecause PAC-TIME uses an empirical approach to describe tire - road interaction forces, incorrect parameters can easily result in non-realistic tire behavior. Below is a list of the most important items to ensure the quality of the parameters in a tire property file:




Rolling ResistanceFor a realistic rolling resistance, the parameter qsy1 must be positive. For car tires, it can be in the order of 0.006 - 0.01 (0.6% - 1.0%).

$---------------------------------------------------rolling resistance[ROLLING_COEFFICIENTS]QSY1 = 0.01QSY2 = 0QSY3 = 0

USE_MODE: State: Slip conditions:PAC-TIME output

(forces and moments):0 Steady state Acts as a vertical spring and

damper0, 0, Fz, 0, 0, 0

1 Steady state Pure longitudinal slip Fx, 0, Fz, 0, My, 02 Steady state Pure lateral (cornering) slip 0, Fy, Fz, Mx, 0, Mz









43

QSY4 = 0

Camber (Inclination) EffectsCamber stiffness has been explicitly defined in PAC-TIME, so camber stiffness can be easily checked by the tire model parameters itself, see the table, Checklist for PAC-TIME Parameters and Properties, below. For car tires, positive inclination should result in a negative lateral force at zero slip angle (see Effect of Positive Camber on the Lateral Force in TYDEX W-axis (ISO) System below). If positive inclination results in an increase of the lateral force, the coefficient may not be valid for the ISO, but for the SAE coordinate system. Note that PAC-TIME only uses coefficients for the TYDEX W-axis (ISO) system.


The following table lists further checks on the PAC-TIME parameters.

Checklist for PAC-TIME Parameters and Properties

Parameter/property: Requirement: Explanation:LONGVL 1 m/s Reference velocity at which parameters are measuredVXLOW Approximately 1 m/s Threshold for scaling down forces and momentsDx > 0 Peak friction (see equation (24))

Adams/Tire

44


$-----------------------------------------------------long_slip_range[LONG_SLIP_RANGE]KPUMIN = -1.5 $Minimum valid wheel slip KPUMAX = 1.5 $Maximum valid wheel slip $----------------------------------------------------slip_angle_range[SLIP_ANGLE_RANGE]ALPMIN = -1.5708 $Minimum valid slip angle ALPMAX = 1.5708 $Maximum valid slip angle $----------------------------------------------inclination_slip_range[INCLINATION_ANGLE_RANGE]CAMMIN = -0.26181 $Minimum valid camber angle CAMMAX = 0.26181 $Maximum valid camber angle $------------------------------------------------vertical_force_range[VERTICAL_FORCE_RANGE]FZMIN = 225 $Minimum allowed wheel load FZMAX = 10125 $Maximum allowed wheel load

If one of the input parameters exceeds a minimum or maximum validity value, the calculation in the tire model is performed with the minimum or maximum value of this range to avoid non-realistic tire behavior. In that case, a message appears warning you that one of the inputs exceeds a validity value.

Standard Tire Interface (STI) for PAC-TIMEBecause all Adams products use the Standard Tire Interface (STI) for linking the tire models to Adams/Solver, below is a brief background of the STI history (see reference [4]).


The working group concentrated on tire measurements and tire models used for vehicle simulation purposes. For most vehicle dynamics studies, people previously developed their own tire models.

pDx1/pDx2 < 0 Peak friction Fx must decrease with increasing loadKx > 0 Long slip stiffness (see equation (27))Dy > 0 Peak friction (see equation (35))pDy1/pDy2 < 0 Peak friction Fx must decrease with increasing loadKy < 0 Cornering stiffness (see equation (38))Kg < 0 Camber stiffness (see equation (39))qsy1 > 0 Rolling resistance, in the range of 0.005 - 0.015

Parameter/property: Requirement: Explanation:

45

Because all car manufacturers and their tire suppliers have the same goal (that is, development of tires to improve dynamic safety of the vehicle), it aimed for standardization in the tire behavior description.





• Tire Kinematics

• Slip Quantities



Term: Definition:Road tangent plane Plane with the normal unit vector (tangent to the road) in the tire-road contact

point C.C-axis system Coordinate system mounted on the wheel carrier at the wheel center according to

TYDEX, ISO orientation.Wheel plane The plane in the wheel center that is formed by the wheel when considered a rigid

disc with zero width.Contact point C Contact point between tire and road, defined as the intersection of the wheel


orientation.

Adams/Tire

46










Abbreviation: Definition: Units:Fz Vertical wheel load [N]Fz0 Nominal load [N]dfz Dimensionless vertical load [-]Fx Longitudinal force [N]

ρρρ

ω

καγ

47


Initiated by the International Tire Working Group, July 1995.3. A. Riedel, Standard Tire Interface, Release 1.2, Initiated by the Tire Workgroup, June 1995.4. J.J.M. van Oosten, H.-J. Unrau, G. Riedel, E. Bakker, TYDEX Workshop: Standardisation of

Data Exchange in Tyre Testing and Tyre Modelling, Proceedings of the 2nd International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Vehicle System Dynamics, Volume 27, Swets & Zeitlinger, Amsterdam/Lisse, 1996.

5. J.J.M. van Oosten, E. Kuiper, G. Leister, D. Bode, H. Schindler, J. Tischleder, S. Köhne,A new tyre model for TIME measurement data,Tire Technology Expo 2003, Hannover.

Example of PAC-TIME Tire Property File[MDI_HEADER]FILE_TYPE ='tir'FILE_VERSION =3.0FILE_FORMAT ='ASCII'! : TIRE_VERSION : MF-TIME! : COMMENT : Tire 205/55 R16 90H ! : COMMENT : Manufacturer Continental! : COMMENT : Nom. section with (m) 0.205 ! : COMMENT : Nom. aspect ratio (-) 55! : COMMENT : Infl. pressure (Pa) 250000! : COMMENT : Rim radius (m) 0.2032 ! : COMMENT : Measurement ID ! : COMMENT : Test speed (m/s) 11.11 ! : COMMENT : Road surface ! : COMMENT : Road condition ! : FILE_FORMAT : ASCII! : Copyright MSC.Software, Thu Oct 14 13:52:26 2004!! USE_MODE specifies the type of calculation performed:! 0: Fz only, no Magic Formula evaluation! 1: Fx,My only! 2: Fy,Mx,Mz only! 3: Fx,Fy,Mx,My,Mz uncombined force/moment calculation! 4: Fx,Fy,Mx,My,Mz combined force/moment calculation! +10: including relaxation behaviour

Fy Lateral force [N]Mx Overturning moment [Nm]My Braking/driving moment [Nm]Mz Aligning moment [Nm]

Abbreviation: Definition: Units:

Adams/Tire

48

! *-1: mirroring of tyre characteristics!! example: USE_MODE = -12 implies:! -calculation of Fy,Mx,Mz only! -including relaxation effects! -mirrored tyre characteristics!$---------------------------------------------------------------units[UNITS]LENGTH ='meter'FORCE ='newton'ANGLE ='radians'MASS ='kg'TIME ='second'$---------------------------------------------------------------model[MODEL]PROPERTY_FILE_FORMAT ='PAC-TIME'USE_MODE = 14 $Tyre use switch (IUSED)VXLOW = 2 LONGVL = 30 $Measurement speed TYRESIDE = 'LEFT' $Mounted side of tyre at vehicle/test bench$----------------------------------------------------------dimensions[DIMENSION]UNLOADED_RADIUS = 0.317 $Free tyre radius WIDTH = 0.205 $Nominal section width of the tyre ASPECT_RATIO = 0.55 $Nominal aspect ratioRIM_RADIUS = 0.203 $Nominal rim radius RIM_WIDTH = 0.165 $Rim width $-----------------------------------------------------------parameter[VERTICAL]VERTICAL_STIFFNESS = 2.648e+005 $Tyre vertical stiffness VERTICAL_DAMPING = 500 $Tyre vertical damping BREFF = 4.90 $Low load stiffness e.r.r. DREFF = 0.41 $Peak value of e.r.r. FREFF = 0.09 $High load stiffness e.r.r. FNOMIN = 4704 $Nominal wheel load$-----------------------------------------------------long_slip_range[LONG_SLIP_RANGE]KPUMIN = -1.5 $Minimum valid wheel slip KPUMAX = 1.5 $Maximum valid wheel slip $----------------------------------------------------slip_angle_range[SLIP_ANGLE_RANGE]ALPMIN = -1.5708 $Minimum valid slip angle ALPMAX = 1.5708 $Maximum valid slip angle $----------------------------------------------inclination_slip_range[INCLINATION_ANGLE_RANGE]

49

CAMMIN = -0.26181 $Minimum valid camber angle CAMMAX = 0.26181 $Maximum valid camber angle $-----------------------------------------------vertical_force_range[VERTICAL_FORCE_RANGE]FZMIN = 140 $Minimum allowed wheel load FZMAX = 10800 $Maximum allowed wheel load $------------------------------------------------------------scaling[SCALING_COEFFICIENTS]LFZO = 1 $Scale factor of nominal load LCX = 1 $Scale factor of Fx shape factor LMUX = 1 $Scale factor of Fx peak friction coefficient LEX = 1 $Scale factor of Fx curvature factor LKX = 1 $Scale factor of Fx slip stiffness LHX = 1 $Scale factor of Fx horizontal shift LVX = 1 $Scale factor of Fx vertical shift LGAX = 1 $Scale factor of camber for Fx LCY = 1 $Scale factor of Fy shape factor LMUY = 1 $Scale factor of Fy peak friction coefficient LEY = 1 $Scale factor of Fy curvature factor LKY = 1 $Scale factor of Fy cornering stiffness LHY = 1 $Scale factor of Fy horizontal shift LVY = 1 $Scale factor of Fy vertical shift LKC = 1 $Scale factor of camber stiffnessLGAY = 1 $Scale factor of camber for Fy LTR = 1 $Scale factor of Peak of pneumatic trail LRES = 1 $Scale factor of Peak of residual torque LGAZ = 1 $Scale factor of camber torque stiffness LXAL = 1 $Scale factor of alpha influence on Fx LYKA = 1 $Scale factor of kappa influence on Fy

Adams/Tire

50

LVYKA = 1 $Scale factor of kappa induced Fy LS = 1 $Scale factor of Moment arm of Fx LSGKP = 1 $Scale factor of Relaxation length of Fx LSGAL = 1 $Scale factor of Relaxation length of Fy LGYR = 1 $Scale factor of gyroscopic torque LMX = 1 $Scale factor of overturning couple LVMX = 1 $Scale factor of Mx vertical shift LMY = 1 $Scale factor of rolling resistance torque $--------------------------------------------------------longitudinal[LONGITUDINAL_COEFFICIENTS]PCX1 = 1.3178 $Shape factor Cfx for longitudinal force PDX1 = 1.0455 $Longitudinal friction Mux at Fznom PDX2 = 0.063954 $Variation of friction Mux with load PDX3 = 0 $Variation of friction Mux with camber PEX1 = 0.15798 $Longitudinal curvature Efx at Fznom PEX2 = 0.41141 $Variation of curvature Efx with load PEX3 = 0.1487 $Variation of curvature Efx with load squared PEX4 = 3.0004 $Factor in curvature Efx while driving PKX1 = 23.181 $Longitudinal slip stiffness Kfx/Fz at Fznom PKX2 = -0.037391 $Variation of slip stiffness Kfx/Fz with load PKX3 = 0.80348 $Exponent in slip stiffness Kfx/Fz with load PHX1 = -0.00058264 $Horizontal shift Shx at Fznom PHX2 = -0.0037992 $Variation of shift Shx with load PVX1 = 0.045118 $Vertical shift Svx/Fz at Fznom PVX2 = 0.058244 $Variation of shift Svx/Fz with load RBX1 = 13.276 $Slope factor for combined slip Fx reduction RBX2 = -13.778 $Variation of slope Fx reduction with kappa RCX1 = 1.0 $Shape factor for combined slip Fx reduction

51

REX1 = 0 $Curvature factor of combined Fx REX2 = 0 $Curvature factor of combined Fx with load RHX1 = 0 $Shift factor for combined slip Fx reduction PTX1 = 0.85683 $Relaxation length SigKap0/Fz at Fznom PTX2 = 0.00011176 $Variation of SigKap0/Fz with load PTX3 = -1.3131 $Variation of SigKap0/Fz with exponent of load $--------------------------------------------------------overturning[OVERTURNING_COEFFICIENTS]QSX1 = 0 $Lateral force induced overturning moment QSX2 = 0 $Camber induced overturning moment QSX3 = 0 $Fy induced overturning moment $------------------------------------------------------------lateral[LATERAL_COEFFICIENTS]PCY1 = 1.18 $Shape factor Cfy for lateral forces PDY1 = 0.90312 $Lateral friction Muy PDY2 = -0.17023 $Exponent lateral friction Muy PDY3 = -0.76512 $Variation of friction Muy with squared camber PEY1 = -0.57264 $Lateral curvature Efy at Fznom PEY2 = -0.13945 $Variation of curvature Efy with load PEY3 = 0.030873 $Zero order camber dependency of curvature Efy PEY4 = 0 $Variation of curvature Efy with camber PKY1 = -25.128 $Maximum value of stiffness Kfy/Fznom PKY2 = 3.2018 $Load with peak of cornering stiffness PKY3 = 0 $Variation with camber squared of cornering stiffness PKY4 = 1.9998 $Shape factor for cornering stiffness with load PKY5 = -0.50726 $Camber stiffness/Fznom PKY6 = 0 $Camber stiffness depending on Fz squared PHY1 = 0.0031414 $Horizontal shift Shy at Fznom PHY2 = 0 $Variation of shift Shy with load PVY1 = 0.0068801 $Vertical shift in Svy/Fz at Fznom

Adams/Tire

52

PVY2 = -0.0051 $Variation of shift Shv with load RBY1 = 7.1433 $Slope factor for combined Fy reduction RBY2 = 9.1916 $Variation of slope Fy reduction with alpha RBY3 = -0.027856 $Shift term for alpha in slope Fy reduction RCY1 = 1.0 $Shape factor for combined Fy reduction REY1 = 0 $Curvature factor of combined Fy REY2 = 0 $Curvature factor of combined Fy with load RHY1 = 0 $Shift factor for combined Fy reduction RHY2 = 0 $Shift factor for combined Fy reduction with load RVY1 = 0 $Kappa induced side force Svyk/Muy*Fz at Fznom RVY2 = 0 $Variation of Svyk/Muy*Fz with load RVY3 = 0 $Variation of Svyk/Muy*Fz with camber RVY4 = 0 $Variation of Svyk/Muy*Fz with alpha RVY5 = 0 $Variation of Svyk/Muy*Fz with kappa RVY6 = 0 $Variation of Svyk/Muy*Fz with atan(kappa) PTY1 = 4.1114 $Peak value of relaxation length SigAlp0/R0 PTY2 = 6.1149 $Value of Fz/Fznom where SigAlp0 is extreme $--------------------------------------------------rolling resistance[ROLLING_COEFFICIENTS]QSY1 = 0.01 $Rolling resistance torque coefficient QSY2 = 0 $Rolling resistance torque depending on Fx QSY3 = 0 $Rolling resistance torque depending on speed QSY4 = 0 $Rolling resistance torque depending on speed^4 $-----------------------------------------------------------aligning[ALIGNING_COEFFICIENTS]QBZ1 = 5.6241 $Trail slope factor for trail Bpt at Fznom QBZ2 = -2.2687 $Variation of slope Bpt with load QBZ4 = 6.891 $Variation of slope Bpt with camber QBZ5 = -0.35587 $Variation of slope Bpt with absolute camber

53

QCZ1 = 1.0904 $Shape factor Cpt for pneumatic trail QDZ1 = 0.082871 $Peak trail Dpt = Dpt*(Fz/Fznom*R0) QDZ2 = -0.012677 $Variation of peak Dpt with load QDZ6 = 0.00038069 $Peak residual torque Dmr = Dmr/(Fz*R0) QDZ7 = 0.00075331 $Variation of peak factor Dmr with load QDZ8 = -0.083385 $Variation of peak factor Dmr with camber QDZ9 = 0 $Variation of peak factor Dmr with camber and load QEZ1 = -34.759 $Trail curvature Ept at Fznom QEZ2 = -37.828 $Variation of curvature Ept with load QEZ4 = 0.59942 $Variation of curvature Ept with sign of Alpha-t QHZ1 = 0.0025743 $Trail horizontal shift Sht at Fznom QHZ2 = -0.0012175 $Variation of shift Sht with load QHZ3 = 0.038299 $Variation of shift Sht with camber QHZ4 = 0.044776 $Variation of shift Sht with camber and load SSZ1 = 0.0097546 $Nominal value of s/R0: effect of Fx on Mz SSZ2 = 0.0043624 $Variation of distance s/R0 with Fy/Fznom SSZ3 = 0 $Variation of distance s/R0 with camber SSZ4 = 0 $Variation of distance s/R0 with load and camber QTZ1 = 0 $Gyroscopic torque constant MBELT = 0 $Belt mass of the wheel -kg-

Contact MethodsThe PAC-TIME model supports the following roads:


• 3D Spline Roads, see Adams/3D Spline Road Model

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Note that the PAC-TIME model has only one point of contact with the road; therefore, the wavelength of road obstacles must be longer than the tire radius for realistic output of the model. In addition, the contact force computed by this tire model is normal to the road plane. Therefore, the contact point does not generate a longitudinal force when rolling over a short obstacle, such as a cleat or pothole.


For ride and comfort analyses, we recommend more sophisticated tire models, such as Ftire.

Using Pacejka '89 and '94 ModelsAdams/Tire provides you with the handling force models, Pacejka '89 and Pacejka '94.

• About Pacejka '89 and '94• Using Pacejka '89 Handling Force Model• Using Pacejka '94 Handling Force Model• Combined Slip• Left and Right Side Tires• Contact Methods

About Pacejka '89 and '94The Pacejka '89 and '94 handling models are special versions of the Magic-Formula Tyre model as cited in the following publications:

• Pacejka '89 - H.B Pacejka, E. Bakker, and L. Lidner. A New Tire Model with an Application in Vehicle Dynamics Studies, SAE paper 890087, 1989.

• Pacejka '94 - H.B Pacejka and E. Bakker. The Magic Formula Tyre Model. Proceedings of the 1st International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Swets & Zeitlinger B.V., Amsterdam/Lisse, 1993.

PAC2002 is technically superior, continuously kept up to date with latest Magic Formula developments, and MSC’s recommended handling model. However, because many Adams/Tire users have pre-existing tire data or new data from tire suppliers and testing organizations in a format that is compatible with the Pacejka '89 and '94 models, the Adams/Tire Handling module includes these models in addition to the PAC2002.

The material in this help is intended to illustrate only the formulas used in the Pacejka '89 and '94 tire models. For general information on the PAC2002 and the Magic Formula method, see the papers cited above or the PAC2002 help.

• History of the Pacejka Name in Adams/Tire• About Coordinate Systems• Normal Force

History of the Pacejka Name in Adams/TireThe formulas used in the Pacejka '89 and '94 tire models are derived from publications by Dr. H.B. Pacejka, and are commonly referred to as the Pacejka method in the automotive industry. Dr. Pacejka himself is not personally associated with the development of these tire models, nor does he endorse them in any way.

About Coordinate SystemsThe coordinate systems used in tire modeling and measurement are sometimes confusing. The coordinate systems employed in the Pacejka ’89 and ’94 tire models are no exception. They are derived from the

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12

tire-measurement systems that the majority of Adams/Tire customers were using at the time when the models were originally developed.

The Pacejka '89 and '94 tire models were developed before the implementation of the TYDEX STI. As a result, Pacejka ’89 conforms to a modified SAE-based tire coordinate system and sign conventions, and Pacejka ’94 conforms to the standard SAE tire coordinate system and sign conventions. MSC maintains these conventions to ensure file compatibility for Adams/Tire customers.

Future tire models will adhere to one single coordinate system standard, the TYDEX C-axis and W-axis system. For more information on the TYDEX standard, see Standard Tire Interface (STI).

Normal ForceThe normal force Fz is calculated assuming a linear spring (stiffness: kz) and damper (damping constant

cz), so the next equation holds:

If the tire loses contact with the road, the tire deflection and deflection velocity become zero, so the resulting normal force Fz will also be zero. For very small positive tire deflections, the value of the damping constant is reduced and care is taken to ensure that the normal force Fz will not become negative.

In stead of the linear vertical tire stiffness cz , also an arbitrary tire deflection - load curve can be defined in the tire property file in the section [DEFLECTION_LOAD_CURVE], see also the example tire property files, Example of Pacejka ’89 Property File and Example of Pacejka ’94 Property File. If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection datapoints with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify VERTICAL_STIFFNESS in the tire property, but it does not play any role.

Definition of Tire Slip QuantitiesSlip Quantities at combined cornering and braking/traction

Fz kzρ czρ·+=

ρ ρ·

13


wheel rotational velocity , and the loaded rolling radius Rl:



and

Note that for realistic tire forces the slip angle is limited to 900 and the longitudinal slip in between -1 (locked wheel) and 1.

Lagged longitudinal and lateral slip quantities (transient tire behavior)In general, the tire rotational speed and lateral slip will change continuously because of the changing interaction forces in between the tire and the road. Often the tire dynamic response will have an important role on the overall vehicle response. For modeling this so-called transient tire behavior, a first-order system is used both for the longitudinal slip ? as the side slip angle, ?. Considering the tire belt as a stretched string, which is supported to the rim with lateral springs, the lateral deflection of the belt can be estimated (see also reference [1]). The figure below shows a top-view of the string model.

Stretched String Model for Transient Tire behavior

Ω

Vsx Vx ΩRl–=

Vsy Vy=

κ α

κVsxVx--------–= αtan

VsyVx---------=

α κ

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For calculating the lateral deflection v1 of the string in the first point of contact with the road, the following differential equation is valid during braking slip:


10 m. This differential equation cannot be used at zero speed, but when multiplying with Vx, the equation can be transformed to:





The longitudinal and lateral relaxation length are estimated with the longitudinal and lateral stiffness of the non-rolling tire:

For BCDx and BCDy see section Force and Moment Formulation for Pacejka '89 or '94.

1Vx------

dv1dt

--------v1σα------+ αtan aφ+=

σα φ

σαdv1dt

-------- Vx v1+ σαVsy=

σκdu1dt

-------- Vx u1+ σ– κVsx=

κ' α'

κ'u1σκ------ Vx( )sgn=

α'v1σα------⎝ ⎠⎛ ⎞atan=

κ' α' κ α

σκBCDx

longitudinal_stiffness--------------------------------------------------------= and σα

BCDylateral_stiffness-------------------------------------------=

15

In case the longitudinal stiffness is not available in the tire property file the longitudinal stiffness is estimated with:

Using Pacejka '89 Handling Force ModelLearn about the Pacejka '89 handling force model:

• Using Correct Coordinate System and Units

• Force and Moment Formulation for Pacejka ’89

• Example of Pacejka ’89 Property File

Using Correct Coordinate System and Units in Pacejka '89The test data and resulting coefficients that come from the Pacejka '89 tire model conform to a modified SAE tire coordinate system. The standard SAE tire coordinate system is shown next and the modified sign conventions for Pacejka '89 are described in the table below.

SAE Tire Coordinate System

longitudinal_stiffness 4 lateral_stiffness×=

Note: The section [UNITS] in the tire property file does not apply to the Magic Formula coefficients.

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Force and Moment Formulation for Pacejka '89• Longitudinal Force for Pacejka '89

• Lateral Force

• Self-Aligning Torque

• Overturning Moment


• Smoothing

Longitudinal Force for Pacejka '89C - Shape Factor

C=B0

D - Peak Factor

D=(B1*FZ2+B2*FZ)

BCD

BCD=(B3*FZ2+B4*FZ)*EXP(-B5*FZ)

B - Stiffness Factor

B=BCD/(C*D)

Variable name and abbreviation: Description:Normal load Fz (kN) Positive when the tire is penetrating the

road.*Lateral force Fy (N) Positive in a right turn.

Negative in a left turn.Longitudinal force Fx (N) Positive during traction.

Negative during braking.Self-aligning torque Mz (Nm) Positive in a left turn.

Negative in a right turn.Inclination angle (deg) Positive when the top of the tire tilts to the

right (when viewing the tire from the rear).*

Sideslip angle (deg) Positive in a right turn.*Longitudinal slip (%) Negative in braking (-100%: wheel lock).

Positive in traction.* Opposite convention to standard SAE coordinate system shown in SAE Tire Coordinate System.

γ

ακ

17

Horizontal Shift

Sh=B9*FZ+B10

Vertical Shift

Sv=0.0

Composite

X1=(κ+Sh)

E Curvature Factor

E=(B6*FZ2+B7*FZ+B8)

FX Equation

FX=(D*SIN(C*ATAN(B*X1-E*(B*X1-ATAN(B*X1)))))+Sv

Longitudinal Force

Example Longitudinal Force Plot for Pacejka ’89

Parameters: Description:B0 Shape factorB1, B2 Peak factorB3, B4, B5 BCD calculationB6, B7, B8 Curvature factorB9, B10 Horizontal shift

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Lateral Force for Pacejka '89C - Shape Factor

C=A0

D - Peak Factor

D=(A1*FZ2+A2*FZ)

BCD

BCD=A3*SIN(ATAN(FZ/A4)*2.0)*(1.0-A5*ABS(γ))


B=BCD/(C*D)

Horizontal Shift

Sh=A9*FZ+A10+A8*γ

Vertical Shift

Sv=A11*FZ*γ+A12*FZ+A13

Composite

X1=(α+Sh)

E - Curvature Factor

19

E=(A6*FZ+A7)

FY Equation

FY=(D*SIN(C*ATAN(B*X1-E*(B*X1-ATAN(B*X1)))))+Sv

Parameters for Lateral Force

Example Lateral Force Plot for Pacejka ’89

Self-Aligning TorqueC - Shape Factor

C=C0

Parameters: Description:A0 Shape factorA1, A2 Peak factorA3, A4, A5 BCD calculationA6, A7 Curvature factorA8, A9, A10 Horizontal shiftA11, A12, A13 Vertical shift

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D - Peak Factor

D=(C1*FZ2+C2*FZ)

BCD

BCD=(C3*FZ2+C4*FZ)*(1-C6*ABS(γ))*EXP(-C5*FZ)


B=BCD/(C*D)

Horizontal Shift

Sh=C11*γ+C12*FZ+C13

Vertical Shift

Sv= (C14*FZ2+C15*FZ)*γ+C16*FZ+C17

Composite

X1=(α+Sh)


E=(C7*FZ2+C8*FZ+C9)*(1.0-C10*ABS(γ))

MZ Equation

MZ=(D*SIN(C*ATAN(B*X1-E*(B*X1-ATAN(B*X1)))))+Sv

Parameters for Self-Aligning Torque

Example Self-Aligning Torque Plot for Pacejka ’89

Parameters: Description:C0 Shape factorC1, C2 Peak factorC3, C4, C5, C6 BCD calculationC7, C8, C9, C10 Curvature factorC11, C12, C13 Horizontal shiftC14, C15, C16, C17 Vertical shift

21

Overturning MomentThe lateral stiffness is used to calculate an approximate lateral deflection of the contact patch when there is a lateral force present:

deflection = Fy / lateral_stiffness

This deflection, in turn, is used to calculate an overturning moment due to the vertical force:

Mx (overturning moment) = -Fz * deflection

And an incremental aligning torque due to longtiudinal force (Fx)

Mz = Mz,Magic Formula + Fx * deflection

Here Mz,Magic Formula is the magic formula for aligning torque and Fx * deflection is the contribution due to the longitudinal force.

Rolling ResistanceThe rolling resistance moment My is opposite to the wheel angular velocity. The magnitude is given by:

My = Fz * Lrad * rolling_resistance

Where Fz equals the vertical force and Lrad is the tyre loaded radius. The rolling resistance coefficient can be entered in the tire property file:

[PARAMETER]ROLLING_RESISTANCE = 0.01

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A value of 0.01 introduces a rolling resistance force that is 1% of the vertical load.

SmoothingWhen you indicate smoothing by setting the value of use mode in the tire property file, Adams/Tire smooths initial transients in the tire force over the first 0.1 seconds of simulation. The longitudinal force, lateral force, and aligning torque are multiplied by a cubic step function of time. (See STEP in the Adams/Solver online help.)

Longitudinal Force

FLon = S*FLon

Lateral Force

FLat = S*FLat

Overturning Moment

Mx = S*Mx


My = S*My

Aligning Torque

Mz = S*Mz


• USE_MODE = 1 or 2, smoothing is off• USE_MODE = 3 or 4, smoothing is on

Example of Pacejka '89 Property File$---------------------------------------------------------MDI_HEADER[MDI_HEADER]FILE_TYPE = 'tir'FILE_VERSION = 2.0FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'Tire - XXXXXX''Pressure - XXXXXX''Test Date - XXXXXX''Test tire'$-------------------------------------------------------------UNITS[UNITS]LENGTH = 'mm'FORCE = 'newton'ANGLE = 'radians'MASS = 'kg'TIME = 'sec'

23

$-------------------------------------------------------------MODEL[MODEL]! use mode 123411121314! -----------------------------------------------------------------! smoothingXXXX! combinedXXXX! transient X X X X!PROPERTY_FILE_FORMAT = 'PAC89'USE_MODE = 12.0TYRESIDE = 'LEFT'$----------------------------------------------------------DIMENSION[DIMENSION]UNLOADED_RADIUS = 326.0WIDTH = 245.0ASPECT_RATIO = 0.35$----------------------------------------------------------PARAMETER[PARAMETER]VERTICAL_STIFFNESS = 310.0VERTICAL_DAMPING = 3.1LATERAL_STIFFNESS = 190.0ROLLING_RESISTANCE = 0.0$---------------------------------------------------------LOAD_CURVE$ For a non-linear tire vertical stiffness (optional)$ Maximum of 100 points[DEFLECTION_LOAD_CURVE]{pen fz} 0 0.0 1 212.0 2 428.0 3 648.0 5 1100.010 2300.020 5000.030 8100.0$-----------------------------------------------LATERAL_COEFFICIENTS[LATERAL_COEFFICIENTS]a0 = 1.65000a1 = -34.0a2 = 1250.00a3 = 3036.00a4 = 12.80a5 = 0.00501a6 = -0.02103a7 = 0.77394a8 = 0.0022890a9 = 0.013442a10 = 0.003709a11 = 19.1656a12 = 1.21356a13 = 6.26206$--------------------------------------------------------longitudinal[LONGITUDINAL_COEFFICIENTS]

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b0 = 1.67272b1 = -9.46000b2 = 1490.00b3 = 30.000b4 = 176.000b5 = 0.08860b6 = 0.00402b7 = -0.06150b8 = 0.20000b9 = 0.02990b10 = -0.17600$----------------------------------------------------------aligning[ALIGNING_COEFFICIENTS]c0 = 2.34000c1 = 1.4950c2 = 6.416654c3 = -3.57403c4 = -0.087737c5 = 0.098410c6 = 0.0027699c7 = -0.0001151c8 = 0.1000c9 = -1.33329c10 = 0.025501c11 = -0.02357c12 = 0.03027c13 = -0.0647c14 = 0.0211329c15 = 0.89469c16 = -0.099443c17 = -3.336941$--------------------------------------------------------------shape[SHAPE]{radial width} 1.0 0.0 1.0 0.2 1.0 0.4 1.0 0.5 1.0 0.6 1.0 0.7 1.0 0.8 1.0 0.85 1.0 0.9 0.9 1.0

Using Pacejka '94 Handling Force ModelLearn about the Pacejka '94 handling force model:

• Using Correct Coordinate System and Units

• Force and Moment Formulation for Pacejka ’94

• Example of Pacejka ’94 Property File

25

Using Correct Coordinate System and Units in Pacejka '94The test data and resulting coefficients that come from the Pacejka '94 tire model conform to the standard SAE tire coordinate system. The standard SAE coordinates are shown in SAE Tire Coordinate System. (See also About Coordinate Systems.) The corresponding sign conventions for Pacejka '94 are described next


Force and Moment Formulation for Pacejka '94• Longitudinal Force for Pacejka '94

• Lateral Force for Pacejka '94

• Self-Aligning Torque

• Overturning Moment


• Smoothing

Longitudinal Force for Pacejka '94C - Shape Factor

C=B0

D - Peak Factor

Note: The section [UNITS] in the tire property file does not apply to the Magic Formula coefficients.

Variable name and abbreviation: Description:Normal load Fz (kN) Positive when the tire is penetrating the road.Lateral force Fy (N) Positive in a right turn.

Negative in a left turn.Longitudinal force Fx (N) Positive during traction.

Negative during braking.Self-aligning torque Mz (Nm) Positive in a left turn.

Negative in a right turn.Inclination angle (deg) Positive when the top of the tire tilts to the right

(when viewing the tire from the rear).Sideslip angle (deg) Positive in a left turn.Longitudinal slip (%) Negative in braking (-100%: wheel lock).

Positive in traction.

γ

ακ

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26

D=(B1*FZ2+B2*FZ) * DLON

BCD

BCD=((B3*FZ2+B4*FZ)*EXP(-B5*FZ)) * BCDLON


B=BCD/(C*D)

Horizontal Shift

Sh=B9*Fz+B10

Vertical Shift

Sv=B11*FZ+B12

Composite

X1=(κ+Sh)

E Curvature Factor

E=((B6*FZ+B7)*FZ+B8)*(1-(B13*SIGN(1,X1))))

FX Equation

FX=(D*SIN(C*ATAN(B*X1-E*(B*X1-ATAN(B*X1)))))+Sv

Parameters for Longitudinal Force

Lateral Force for Pacejka '94C - Shape Factor

C=A0

D - Peak Factor

D=((A1*FZ+A2) *(1-A15* 2)*FZ) * DLAT

Parameters: Description:B0 Shape factorB1, B2 Peak factorB3, B4, B5 BCD calculationB6, B7, B8, B13 Curvature factorB9, B10 Horizontal shiftB11, B12 Vertical shiftDLON, BCDLON Scale factor

γ

27

BCD

BCD=(A3*SIN(ATAN(FZ/A4)*2.0)*(1-A5*ABS( )))* BCDLAT


B=BCD/(C*D)

Horizontal Shift

Sh=A8*FZ+A9+A10*

Vertical Shift

Sv=A11*FZ+A12+(A13*FZ2+A14*FZ)*

Composite

X1=(α+Sh)


E=(A6*FZ+A7)*(1-(((A16*γ)+A17)*SIGN(1,X1))))

FY Equation

FY=(D*SIN(C*ATAN(B*X1-E*(B*X1-ATAN(B*X1)))))+Sv

Parameters for Lateral Force

Self-Aligning Torque for Pacejka '94C - Shape Factor

C=C0

D - Peak Factor

D=(C1*FZ2+C2*FZ)*(1-C18* 2)

BCD

Parameters: Description:A0 Shape factorA1, A2, A15 Peak factorA3, A4, A5 BCD calculationA6, A7, A16, A17 Curvature factorA8, A9, A10 Horizontal shiftA11, A12, A13, A14 Vertical shiftDLAT, BCDLAT Scale factor

γ

γ

γ

γ

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28

BCD=(C3*FZ2+C4*FZ)*(1-(C6*ABS(γ)))*EXP(-C5*FZ)


B=BCD/(C*D)

Horizontal Shift

Sh=C11*FZ+C12+C13*

Vertical Shift

Sv=C14*FZ+C15+(C16*FZ2+C17*FZ)*

Composite

X1=( +Sh)


E=(((C7*FZ2)+(C8*FZ)+C9)*(1-(((C19* )+C20)*SIGN(1,X1))))/(1-(C10*ABS( )))

MZ Equation

MZ=(D*SIN(C*ATAN(B*X1-E*(B*X1-ATAN(B*X1)))))+Sv

Parameters for Self-Aligning Torque

Overturning MomentThe lateral stiffness is used to calculate an approximate lateral deflection of the contact patch when there is a lateral force present:

deflection = Fy / lateral_stiffness

This deflection, in turn, is used to calculate an overturning moment due to the vertical force:

Mx (overturning moment) = -Fz * deflection

And an incremental aligning torque due to longtiudinal force (Fx):

Mz = Mz,Magic Formula + Fx * deflection

Parameters: Description:C0 Shape factorC1, C2, C18 Peak factorC3, C4, C5, C6 BCD calculationC7, C8, C9, C19, C20 Curvature factorC11, C12, C13 Horizontal shiftC14, C15, C16, C17 Vertical shift

γ

γ

α

γ γ

29

Here Mz,Magic Formula is the magic formula for aligning torque and Fx * deflection is the contribution due to the longitudinal force.

Rolling ResistanceThe rolling resistance moment My is opposite to the wheel angular velocity. The magnitude is given by:

My = Fz * Lrad * rolling_resistance

Where Fz equals the vertical force and Lrad is the tyre loaded radius. The rolling resistance coefficient can be entered in the tire property file:

[PARAMETER]ROLLING_RESISTANCE = 0.01

A value of 0.01 will introduce a rolling resistance force, which is 1% of the vertical load.

SmoothingAdams/Tire smooths initial transients in the tire force over the first 0.1 seconds of simulation. The longitudinal force, lateral force, and aligning torque are multiplied by a cubic step function of time. (See STEP in the Adams/Solver online help.)

Longitudinal Force

FLon = S*FLon

Lateral Force

FLat = S*FLat

Overturning Moment

Mx = S*Mx


My = S*My

Aligning Torque

Mz = S*Mz


• USE_MODE = 1 or 2, smoothing is off• USE_MODE = 3 or 4, smoothing is on

Example of Pacejka '94 Property File!:FILE_TYPE: tir!:FILE_VERSION: 2!:TIRE_VERSION: PAC94

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!:COMMENT: New File Format v2.1!:FILE_FORMAT: ASCII!:TIMESTAMP: 1996/02/15,13:22:12!:USER: ncos$--------------------------------------------------------------units[UNITS] LENGTH = 'inch' FORCE = 'pound_force' ANGLE = 'radians' MASS = 'pound_mass' TIME = 'second'$--------------------------------------------------------------model[MODEL]! use mode 12341234! ---------------------------------------------------------------! smoothingXXXX! combinedXXXX! transient X X X X! PROPERTY_FILE_FORMAT = 'PAC94' USE_MODE = 12.0 TYRESIDE = 'LEFT'$---------------------------------------------------------dimensions[DIMENSION] UNLOADED_RADIUS = 12.95 WIDTH = 10.0 ASPECT_RATIO = 0.30$---------------------------------------------------------parameter[PARAMETER] VERTICAL_STIFFNESS = 2500 VERTICAL_DAMPING = 250.0 LATERAL_STIFFNESS = 1210.0 ROLLING_RESISTANCE = 0.01$---------------------------------------------------------load_curve$ Maximum of 100 points (optional)[DEFLECTION_LOAD_CURVE]{pen fz}0.000 00.039 9430.079 19040.118 28820.197 48930.394 102310.787 222411.181 36031$-----------------------------------------------------------scaling[SCALING_COEFFICIENTS] DLAT = 0.10000E+01 DLON = 0.10000E+01 BCDLAT = 0.10000E+01 BCDLON = 0.10000E+01 $-----------------------------------------------------------lateral [LATERAL_COEFFICIENTS] A0 = 1.5535430E+00

31

A1 = -1.2854474E+01 A2 = -1.1133711E+03 A3 = -4.4104698E+03 A4 = -1.2518279E+01 A5 = -2.4000120E-03 A6 = 6.5642332E-02 A7 = 2.0865589E-01 A8 = -1.5717978E-02 A9 = 5.8287762E-02 A10 = -9.2761963E-02 A11 = 1.8649096E+01 A12 = -1.8642199E+02 A13 = 1.3462023E+00 A14 = -2.0845180E-01 A15 = 2.3183540E-03 A16 = 6.6483573E-01 A17 = 3.5017404E-01$------------------------------------------------------longitudinal[LONGITUDINAL_COEFFICIENTS] B0 = 1.4900000E+00 B1 = -2.8808998E+01 B2 = -1.4016957E+03 B3 = 1.0133759E+02 B4 = -1.7259867E+02 B5 = -6.1757933E-02 B6 = 1.5667623E-02 B7 = 1.8554619E-01 B8 = 1.0000000E+00 B9 = 0.0000000E+00 B10 = 0.0000000E+00 B11 = 0.0000000E+00 B12 = 0.0000000E+00 B13 = 0.0000000E+00$----------------------------------------------------------aligning[ALIGNING_COEFFICIENTS] C0 = 2.2300000E+00 C1 = 3.1552342E+00 C2 = -7.1338826E-01 C3 = 8.7134880E+00 C4 = 1.3411892E+01 C5 = -1.0375348E-01 C6 = -5.0880786E-03 C7 = -1.3726071E-02 C8 = -1.0000000E-01 C9 = -6.1144302E-01 C10 = 3.6187314E-02 C11 = -2.3679781E-03 C12 = 1.7324400E-01 C13 = -1.7680388E-02 C14 = -3.4007351E-01 C15 = -1.6418691E+00 C16 = 4.1322424E-01 C17 = -2.3573702E-01 C18 = 6.0754417E-03

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32

C19 = -4.2525059E-01 C20 = -2.1503067E-01$--------------------------------------------------------------shape[SHAPE]{radial width} 1.0 0.0 1.0 0.2 1.0 0.4 1.0 0.5 1.0 0.6 1.0 0.7 1.0 0.8 1.0 0.85 1.0 0.9 0.9 1.0

Combined Slip of Pacejka '89 and '94The combined slip calculation of the Pacejka '89 and '94 tire models is identical. Note that the method employed here is not part of the Magic Formula as developed by Professor Pacejka, but is an in-house development of MSC.

Inputs:

• Dimensionless longitudinal slip κ (range –1 to 1) and side slip angle α in radians• Longitudinal force Fx and lateral force Fy calculated using the Magic Formula

• Horizontal/vertical shifts and peak values of the Magic Formula (Sh, Sv, D)

Output:

• Adjusted longitudinal force Fx and lateral force Fy to incorporate the reduction due to combined slip:

Friction coefficients:

κ* κ Shx+=

α* α Shy+=

SAG α*( )sin=

β arc κ*

κ*( )2 SAG2+---------------------------------------⎝ ⎠⎜ ⎟⎛ ⎞

cos=

33

Forces corrected for combined slip conditions:




If this keyword is available, Adams/Car corrects for the conicity and plysteer and asymmetry when using a tire property file on the opposite side of the vehicle. In fact, the tire characteristics are mirrored with respect to slip angle zero.

In AdamsS/View this option can only be used when the tire is generated by the graphical user interface: select Build -> Forces -> Special Force: Tire.

Next to the LEFT and RIGHT side option of TYRESIDE, you can also select SYMMETRIC: then the tire characteristics are modified during initialization to show symmetric performance for left and right side corners and zero conicity and plysteer (no offsets). Also, when you set the tire property file to SYMMETRIC, the tire characteristics are changed to symmetric behavior.

μx act,Fx Svx–

Fz-------------------- μy act,

Fy Svy–Fz

--------------------

μx max,DxFz------ μy max,

DyFz------

= =

= =

μx1

1μx act,-------------⎝ ⎠⎛ ⎞ 2 βtan

μy max,----------------⎝ ⎠⎛ ⎞ 2

+--------------------------------------------------------- μy

βtan1

μx max,----------------⎝ ⎠⎛ ⎞ 2 βtan

μy max,----------------⎝ ⎠⎛ ⎞ 2

+------------------------------------------------------------= =

Fx comb,μx

μx act,------------- Fx Svx+( ) Fy comb,

μyμy act,------------- Fy Svy+( )= =

Adams/Tire

34

Figure 1 Create Wheel and Tire Dialog Box in Adams/View

Contact MethodsThe Pacejka '89 and '94 models support the following roads:

• 2D roads, see Using the 2D Road Model.• 3D Spline roads, see Adams/3D Spline Road Model

These tire models use a one point of contact method; therefore, the wavelength of road obstacles must be longer than the tire radius for realistic output of the model.

• 3D Shell roads, see Adams/Tire 3D Shell Road Model

35

Adams/Tire

36

PAC MCLearn about using the University of Arizona (UA) tire model:

When to Use PAC MotorcycleMagic-Formula (MF) tire models are considered the state-of-the-art for modeling of the tire-road interaction forces in Vehicle Dynamics applications. First versions of the mode that were published by Pacejka considered tire models for car and truck tires. In his book, Tyre and Vehicle Dynamics [1], he also described a model for motorcycle tires that is backwards compatible with the MF-MCTyre, previously resold by MSC.Software, and contains the latest developments in this field.

In general, a MF tire model describes the tire behavior for rather smooth roads (road obstacle wavelengths longer than the tire radius) up to frequencies of 8 Hz. This makes the tire model applicable for all generic vehicle handling and stability simulations, including:

• Steady-state cornering• Lane-change maneuvers• Braking or power-off in a turn• Split-mu braking tests• J-turn or other turning maneuvers• ABS braking, when stopping distance is important (not for tuning ABS control strategies)• Shimmy and weave phenomena, which can be analyzed when the tire model is used in transient

mode (see USE_MODES of PAC MC: from Simple to Complex)• All other common vehicle dynamics maneuvers on rather smooth road (wavelength of road


The PAC MC model has proven to be applicable to motorcycle tires with inclination angles to the road up to 60 degrees. In some cases, it can be used for car tires when exposed to large camber.

PAC MC and Previous Magic Formula ModelsCompared to previous versions, PAC MC is backward compatible with all MF-MCTyre 1.x tire models, generates the same output, and deals with all previous versions of MF-MCTyre property files.

In addition to PAC MC in Adams, the PAC MC in v2 contins a more advanced tire-road contact modeling method that takes the tire's cross-section shape into account, which plays an important role at large inclination angles of the wheel with the road. Learn more about the tire cross-section profile contact method.

Adams/Tire

12

Modeling Tire-Road Interaction ForcesFor vehicle dynamics applications, accurate knowledge of tire-road interaction forces is inevitable because the movements of a vehicle primarily depend on the road forces on the tires. These interaction forces depend on both road and tire properties and the motion of the tire with respect to the road.

In the radial direction, the MF tire models consider the tire to behave as a parallel linear spring and linear damper with one point of contact with the road surface. The contact point is determined by considering the tire and wheel as a rigid disc. In the contact point between the tire and the road the contact forces in longitudinal and lateral direction strongly depend on the slip between the tire patch elements and the road.

The figure, Input and Output Variables of the Magic Formula Tire Model, presents the input and output vectors of the PAC MC tire model. The tire model subroutine is linked to the Adams/Solver through the Standard Tire Interface (STI) ([3]). The input through the STI consists of the:


The tire model routine calculates the vertical load and slip quantities based on the position and speed of the wheel with respect to the road. The input for the Magic Formula consists of the wheel load ( ), the

longitudinal and lateral slip ( , ), and inclination angle ( ) with the road. The output is the forces

( , ) and moments ( , , ) in the contact point between the tire and the road. For

calculating these forces, the MF equations use a set of MF parameters, which are derived from tire testing data.

The forces and moments out of the Magic Formula are transferred to the wheel center and returned to Adams/Solver through the STI.


Fz

κ α γFx Fy Mx My Mz

13

Axis Systems and Slip Definitions• Axis System

• Units


Axis SystemThe PAC MC model is linked to Adams/Solver using the TYDEX STI conventions as described in the TYDEX-Format [2] and the STI [3].

The STI interface between the PAC MC model and Adams/Solver mainly passes information to the tire model in the C-axis coordinate system. In the tire model itself, a conversion is made to the W-axis system because all the modeling of the tire behavior, as described in this help, assumes to deal with the slip quantities, orientation, forces, and moments in the contact point with the TYDEX W-axis system. Both axis systems have the ISO orientation but have a different origin as can be seen in the figure below.

TYDEX C- and W-Axis Systems Used in PAC MC, Source[2]

Adams/Tire

14



The forces and moments calculated by PAC MC using the MF equations in this guide are in the W-axis system. A transformation is made in the source code to return the forces and moments through the STI to Adams/Solver.


UnitsThe units of information transferred through the STI between Adams/Solver and PAC MC are according to the SI unit system. Also, the equations for PAC MC described in this guide have been developed for use with SI units, although you can easily switch to another unit system in your tire property file. Because of the non-dimensional parameters, only a few parameters have units to be changed.


15

SI Units Used in PAC MC


The longitudinal slip velocity in the contact point (W-axis system, see the figure, Slip Quantities at

Combined Cornering) is defined using the longitudinal speed , the wheel rotational velocity , and

the effective rolling radius :

Variable Type: Name: Abbreviation: Unit:Angle Slip angle

Inclination angle

Radians


Lateral force

Vertical load

Newton




Newton.meter


Lateral speed


Lateral slip speed

Meters per second


α

γFx

Fy

FzMx

My

Mz

Vx

Vy

Vsx

Vsyω

Vsx

Vx ω

Re

Adams/Tire

16

(1)


(2)


(3)

(4)


(5)

Contact-Point and Normal Load Calculation• Contact Point



For calculating the kinematics of the tire relative to the road, the road is approximated by its tangent plane at the road point right below the wheel center (see figure below).


Vsx Vx ΩRe–=

Vsy Vy=

κ α

κVsxVx--------–=

α( )tanVsyVx---------=

Vr ReΩ=

17

The contact point is determined by the line of intersection of the wheel center-plane with the road tangent (ground) plane and the line of intersection of the wheel center-plane with the plane though the wheel spin axis.

The normal load of the tire is calculated with:

(6)

where is the tire deflection and is the deflection rate of the tire.

To take into account the effect of the tire cross-section profile, you can choose a more advanced method (see the Tire Cross Section Profile Contact Method).

Instead of the linear vertical tire stiffness Cz, also an arbitrary tire deflection - load curve can be defined in the tire property file in the section [DEFLECTION_LOAD_CURVE]. If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection datapoints with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify

in the tire property file, but it does not play any role.

Fz


ρ ρ·

Cz

Adams/Tire

18

Loaded and Effective Tire Rolling RadiusWith the loaded rolling tire radius R defined as the distance of the wheel center to the contact point of the tire with the road (see Effective Rolling Radius and Longitudinal Slip), where ρ is the deflection of the tire, and R0 is the free (unloaded) tire radius, then the loaded tire radius Rl reads:

(7)

In this tire model, a constant (linear) vertical tire stiffness is assumed; therefore, the tire deflection

can be calculated using:

(8)


(9)

For radial tires, the effective rolling radius is rather independent of load in its load range of operation due to the high stiffness of the tire belt circumference. Only at low loads does the effective tire radius decrease with increasing vertical load due to the tire tread thickness. See the figure below.


R1 R0 ρ–=

Cz

ρ

ρFzCz------=

ReVxΩ------=

19

To represent the effective rolling radius Re, a MF-type of equation is used:

(10)

in which is the nominal tire deflection:

(11)

and is called the dimensionless radial tire deflection, defined by:

Re R0 ρFz0D Bρd( ) Fρd+( )atan⋅( )–=

ρFz0

ρFz0

Fz0Cz--------=

ρd

Adams/Tire

20

(12)

Example of the Loaded and Effective Tire Rolling Radius as a Function of the Vertical Load



Property File: Explanation:FNOMIN Nominal wheel loadUNLOADED_RADIUS Free tire radiusBREFF Low load stiffness effective rolling radiusDREFF Peak value of effective rolling radiusFREFF High load stiffness effective rolling radiusVERTICAL_STIFFNESS Tire vertical stiffnessVERTICAL_DAMPING Tire vertical damping

ρd ρρFz0

---------=

Fz0R0BDFCzKZ

21

Basics of the Magic Formula in PAC MCThe Magic Formula is a mathematical formula that is capable of describing the basic tire characteristics for the interaction forces between the tire and the road under several steady-state operating conditions. We distinguish:


For pure slip conditions, the lateral force as a function of the lateral slip , respectively, and the

longitudinal force as a function of longitudinal slip , have a similar shape (see the figure,

Characteristic Curves for Fx and Fy Under Pure Slip Conditions). Because of the sine - arctangent combination, the basic Magic Formula example is capable of describing this shape:

(13)

where Y(x) is either with x the longitudinal slip , or and x the lateral slip .


The self-aligning moment is calculated as a product of the lateral force and the pneumatic trail t

added with the residual moment . In fact, the aligning moment is due to the offset of lateral force ,

called pneumatic trail t, from the contact point. Because the pneumatic trail t as a function of the lateral slip has a cosine shape, a cosine version the Magic Formula is used:

Fy α

Fx κ

Y x( ) D c bx E bx bx( )atan–( )–( )atan⋅[ ]cos⋅=

Fx κ Fy α

Mz Fy

Mzr Fy

α

Adams/Tire

22

(14)






Y x( ) D C Bx E Bx Bx( )atan–( )–( )atan⋅[ ]cos⋅=

α

23

In combined slip conditions, the lateral force decreases due to longitudinal slip or the opposite, the

longitudinal force decreases due to lateral slip. The forces and moments in combined slip conditions

Fy

Fx

Adams/Tire

24

are based on the pure slip characteristics multiplied by the so-called weighting functions. Again, these weighting functions have a cosine-shaped MF examples.


Inclination Effects in the Lateral ForceFrom a historical point of view, the basic Magic Formulas have always been developed for car and truck tires, which cope with inclinations angles of not more than 10 degrees. To be able to describe the effects at large inclinations, an extension of the basic Magic Formula for the lateral force Fy has been developed.

A contribution of the inclination has also been added within the MF sine function:

(15)

This elegant formulation has the advantage of an explicit definition of the camber stiffness, because this results now in:

(16)


Input Variables

Output VariablesIts output variables are:

Output Variables

Longitudinal slip [-]Slip angle [rad]Inclination angle [rad]Normal wheel load Fz [N]

Longitudinal force Fx [N]Lateral force Fy [N]

γ

Fy0 Dy Cyarc Byαy Ey Byαy arc Byαy( )tan–( )–{ }Cγarc Bγγy Eγ Bγγy arc Bγγy( )tan–( )–{ }tan+

tan[]

sin=

Kγ BγCγDγ γ∂∂Fyo= = at αy 0=

καγ

25



Basic Tire Parameters


(17)

with the possibly adapted nominal load (using the user-scaling factor, ):

(18)



Overturning couple Mx [Nm]Rolling resistance moment My [Nm]Aligning moment Mz [Nm]




dfzFz F'z0–

F'z0--------------------=

λFz0

F'z0 Fz0 λFz0⋅=

Adams/Tire

26

User Scaling FactorsA set of scaling factors is available to easily examine the influence of changing tire properties without the need to change one of the real Magic Formula coefficients. The default value of these factors is 1. You can change the factors in the tire property file. The peak friction scaling factors, and , are also used for the position-dependent friction in 3D Road Contact and Adams/3D Road. An overview of all scaling factors is shown in the next tables.




k = 1, 2, ...

Name:Name used in

tire property file: Explanation:LFZO Scale factor of nominal (rated) load

Cx LCX Scale factor of Fx shape factorLMUX Scale factor of Fx peak friction coefficient

Ex LEX Scale factor of Fx curvature factorKx LKX Scale factor of Fx slip stiffnessVx LVX Scale factor of Fx vertical shift

x LGAX Scale factor of camber for FxCy LCY Scale factor of Fy shape factor

y LMUY Scale factor of Fy peak friction coefficientEy LEY Scale factor of Fy curvature factor

Parameter: Definition:

λμξ λγψ

λFz0

λλμξλλλλγλλμλ

27



Ky LKY Scale factor of Fy cornering stiffnessC LCC Scale factor of camber shape factorK LKC Scale factor of camber stiffness (K-factor)E LEC Scale factor of camber curvature factorHyy LHY Scale factor of Fy horizontal shift

LGAY Scale factor of camber force stiffnesst LTR Scale factor of peak of pneumatic trailMr LRES Scale factor for offset of residual torquegz LGAZ Scale factor of camber torque stiffnessMx LMX Scale factor of overturning coupleVMx LVMX Scale factor of Mx vertical shiftMy LMY Scale factor of rolling resistance torque


property file: Explanation:x LXAL Scale factor of alpha influence on Fxy LYKA Scale factor of alpha influence on FxVy LVYKA Scale factor of kappa induced Fys LS Scale factor of Moment arm of Fx


property file: Explanation:x LXAL Scale factor of alpha influence on Fxy LYKA Scale factor of alpha influence on FxVy LVYKA Scale factor of kappa induced Fys LS Scale factor of Moment arm of Fx

Name:Name used in

tire property file: Explanation:λλ γλ γλ γλλγψλλλλλλ

λ αλ κλ κλ

λ αλ κλ κλ

Adams/Tire

28


Steady-State: Magic Formula for PAC MC• Steady-State Pure Slip






(19)

(20)

(21)

(22)


(23)

(24)

(25)

(26)



property file: Explanation:LSGKP Scale factor of relaxation length of FxLSGAL Scale factor of relaxation length of Fy

gyr LGYR Scale factor of gyroscopic moment

σκσαλ


Fx0 Dx Cxarc Bxκx Ex Bxκx arc Bxκx( )tan–( )–{ }tan[ ] SVx+sin=

κx κ SHx+=

γx γ λγx⋅=

Cx pCx1 λCx⋅=

Dx μx Fz ζ1⋅ ⋅=

μx pDx1 pDx2dfz+( ) 1 pDx3 γx2⋅–( )λμx⋅=

Ex pEx1 pEx2dfz pEx3dfz2+ +( ) 1 pEx4 κx( )sgn–{ } λEx with Ex 1≤⋅ ⋅=

29

(27)

(28)

(29)

(30)



(31)

(32)


property file: Explanation:pCx1 PCX1 Shape factor Cfx for longitudinal forcepDx1 PDX1 Longitudinal friction Mux at FznompDx2 PDX2 Variation of friction Mux with loadpDx3 PDX3 Variation of friction Mux with camberpEx1 PEX1 Longitudinal curvature Efx at FznompEx2 PEX2 Variation of curvature Efx with loadpEx3 PEX3 Variation of curvature Efx with load squaredpEx4 PEX4 Factor in curvature Efx while drivingpKx1 PKX1 Longitudinal slip stiffness Kfx/Fz at FznompKx2 PKX2 Variation of slip stiffness Kfx/Fz with loadpKx3 PKX3 Exponent in slip stiffness Kfx/Fz with loadpVx1 PVX1 Vertical shift Svx/Fz at FznompVx2 PVX2 Variation of shift Svx/Fz with load

Kx Fz pKx1 pKx2dfz+( ) pKx3dfz( ) λK

(Kx

⋅exp⋅ ⋅

BxCxDx κx∂∂Fx0 at κx 0 )

=

= = =

Bx Kx CxDx( )⁄=

SHx psy1FzλMy SVx+( ) Kx⁄–=

SVx Fz pVx1 pVx2dfz+( ) λVx λμx ζ1⋅ ⋅ ⋅ ⋅=


Fy0 Dy Cyarc Byαy Ey Byαy arc Byαy( )tan–( )–{ }

Cγarc Bγγy Eγ Bγγy arc Bγγy( )tan–( )–{ }tan+

tan[

]

sin=

Adams/Tire

30

(33)


(34)

with coefficients:

(35)

(36)

(37)

(38)


(39)

(40)

(41)

(42)

and the explicit camber stiffness:

(43)

(44)

(45)

αy α SHy Cy Cγ 2<+( )+=

γy γ λγy⋅=

Cy pCy1 λCy⋅=

Dy μy Fz ζ2⋅ ⋅=

μy pDy1 pDy2dfz( ) 1 pDy3γy2–( ) λμy⋅ ⋅exp⋅=

Ey pEy1 pEy2γy2 pEy3 pEy4γy+( ) αy( )sin⋅–+{ } λEy with Ey 1≤⋅=

Ky pKy1Fzo pKy2arcFz

pKy3 pKy4γy2+( )FzoλFzo

-----------------------------------------------------------⎩ ⎭⎨ ⎬⎧ ⎫

tan

1 pKy5γy2–( ) λFzo λKy

(Ky

⋅ ⋅

sin

ByCyDy αy∂∂Fyo at αy 0 )

=

= = =

By Ky CyDy( )⁄=

SHy pHy1 λHy⋅=

Cγ pCy2 λCγ⋅=

Kγ pKy6 pKy7dfz+( ) Fz λKγ (=BγCγDγ⋅ ⋅γ∂

∂Fyo at αy 0= = =

Eγ pEy5 λEγ with Eγ 1≤⋅=

Bγ Kγ CγDγ( )⁄=

31



(46)


(47)

(48)


(49)

Name:Name used in

tire property file: Explanation:pCy1 PCY1 Shape factor Cfy for lateral forcespCy2 PCY2 Shape factor Cfc for camber forcespDy1 PDY1 Lateral friction MuypDy2 PDY2 Exponent lateral friction MuypDy3 PDY3 Variation of friction Muy with squared camberpEy1 PEY1 Lateral curvature Efy at FznompEy2 PEY2 Variation of curvature Efy with camber squaredpEy3 PEY3 Asymmetric curvature Efy at FznompEy4 PEY4 Asymmetric curvature Efy with camberpEy5 PEY5 Camber curvature EfcpKy1 PKY1 Maximum value of stiffness Kfy/FznompKy2 PKY2 Curvature of stiffness KfypKy3 PKY3 Peak stiffness factorpKy4 PKY4 Peak stiffness variation with camber squaredpKy5 PKY5 Lateral stiffness dependency with camber squaredpKy6 PKY6 Camber stiffness factor KfcpKy7 PKY7 Vertical load dependency of camber stiffness KfcpHy1 PHY1 Horizontal shift Shy at Fznom

Mz' Mz0 α γ Fz, ,( )=

Mz0 t Fy0 Mzr+⋅–=


αt α SHt+=

Mzr αr( ) Dr Crarc Brαr( )tan[ ] α( )cos⋅cos=

Adams/Tire

32

μy

(50)


(51)

with coefficients:

(52)

(53)

(54)

(55)

(56)

(57)

(58)

(59)

(60)


(61)



property file: Explanation:qBz1 QBZ1 Trail slope factor for trail Bpt at FznomqBz2 QBZ2 Variation of slope Bpt with loadqBz3 qBz3 Variation of slope Bpt with load squaredqBz4 QBZ4 Variation of slope Bpt with camberqBz5 QBZ5 Variation of slope Bpt with absolute camber

αr α SHr+=

γz γ λγz⋅=

Bt qBx1 qBx2dfz qBx3dfz2+ +( ) 1 qBx4γz qBz5 γz+ +{ } λKy λμy⁄⋅ ⋅=

Ct qCz1=

Dt Fz qDz1 qDz2dfz+( ) 1 qDz3 γz qDz4γz2+ +( ) R0 Fz0⁄( )⋅ ⋅ ⋅=

Et qEx1 qEx2dfz qEx3dfz2+ +( )=

1 qEz4 qEz5γz+( ) 2π---⎝ ⎠⎛ ⎞ arc Bt Ct αt⋅ ⋅( )tan⋅ ⋅+

⎩ ⎭⎨ ⎬⎧ ⎫

with Et 1≤

SHt 0=

Br qBz9 λKy λμy⁄⋅=

Dr Fz qDz6 qDz7dfz+( )λr qDz8 qDz9dfz+( )γz qDz10 qDz11dfz+( ) γz γz⋅( )+ +[ ]R0λ=

SHr qHz1 qHz2dfz qHz3 qHz4dfz+( )γz+ +=

Kz t Ky αddMz at α–≈⎝ ⎠

⎛ ⎞⋅– 0 )= =

33

Steady-State Combined SlipPAC-TIME has two methods for calculating the combined slip forces and moments. If the user supplies the coefficients for the combined slip cosine 'weighing' functions, the combined slip is calculated according to Combined slip with cosine 'weighing' functions (standard method). If no coefficients are supplied, the so-called friction ellipse is used to estimate the combined slip forces and moments, see section Combined Slip with friction ellipse





qBz9 QBZ9 Slope factor Br of residual torque MzrqCz1 QCZ1 Shape factor Cpt for pneumatic trailqDz1 QDZ1 Peak trail Dpt = Dpt*(Fz/Fznom*R0)qDz2 QDZ2 Variation of peak Dpt with loadqDz3 QDZ3 Variation of peak Dpt with camberqDz4 QDZ4 Variation of peak Dpt with camber squared.qDz6 QDZ6 Peak residual moment Dmr = Dmr/ (Fz*R0)qDz7 QDZ7 Variation of peak factor Dmr with loadqDz8 QDZ8 Variation of peak factor Dmr with camberqDz9 QDZ9 Variation of Dmr with camber and loadqDz10 QDZ10 Variation of peak factor Dmr with camber squaredqDz11 QDZ11 Variation of Dmr with camber squared and loadqEz1 QEZ1 Trail curvature Ept at FznomqEz2 QEZ2 Variation of curvature Ept with loadqEz3 QEZ3 Variation of curvature Ept with load squaredqEz4 QEZ4 Variation of curvature Ept with sign of Alpha-tqEz5 QEZ5 Variation of Ept with camber and sign Alpha-tqHz1 QHZ1 Trail horizontal shift Shr at FznomqHz2 QHZ2 Variation of shift Shr with loadqHz3 QHZ3 Variation of shift Shr with camberqHz4 QHZ4 Variation of shift Sht with camber and load



Adams/Tire

34



(62)

with Gx o the weighting function of the longitudinal force for pure slip.

We write:

(63)

(64)

with coefficients:

(65)

(66)

(67)

(68)

(69)


(70)



property file: Explanation:rBx1 RBX1 Slope factor for combined slip Fx reductionrBx2 RBX2 Variation of slope Fx reduction with kapparBx3 RBX3 Influence of camber on stiffness for Fx reductionrCx1 RCX1 Shape factor for combined slip Fx reductionrEx1 REX1 Curvature factor of combined FxrEx2 REX2 Curvature factor of combined Fx with loadrHx1 RHX1 Shift factor for combined slip Fx reduction


α


αs α SHxα+=

Bxα rBx1 rBx3γ2+( ) arc rBx2κ{ }tan[ ] λxα⋅cos=

Cxα rCx1=

DxαFxo



SHxα rHx1=



35


(71)


(72)

(73)


(74)

(75)

(76)

(77)

(78)

(79)

(80)


(81)



property file: Explanation:rBy1 RBY1 Slope factor for combined Fy reductionrBy2 RBY2 Variation of slope Fy reduction with alpharBy3 RBY3 Shift term for alpha in slope Fy reductionrCy1 RCY1 Shape factor for combined Fy reductionrEy1 REY1 Curvature factor of combined Fy

Fy Fy0 Gyκ α κ γ Fz, , ,( ) SVyκ+⋅=

κ

Fy Dyκ Cyκarc Byκκs Eyκ Byκκs arc Byκκs( )tan–( )–{ }tan[ ] SVyκ+cos=

κs κ SHyk+=

Byκ rBy1 rBy4γ2+( ) arc rBy2 α rBy3–( ){ }tan[ ] λyκ⋅cos=

Cyκ rCy1=

DyκFyo




SVyk DVyκ rVy5arc rvy6κ( )tan[ ] λVyκ⋅sin=


GyκCyκarc Byκκs Eyκ Byκκs arc Byκκs( )tan–( )–{ }tan[ ]cos


Adams/Tire

36


(82)

with:

(83)

(84)

(85)

(86)

(87)

with the arguments:

(88)

(89)

rEy2 REY2 Curvature factor of combined Fy with loadrHy1 RHY1 Shift factor for combined Fy reductionrHy2 RHY2 Shift factor for combined Fy reduction with loadrVy1 RVY1 Kappa-induced side force Svyk/Muy*Fz at FznomrVy2 RVY2 Variation of Svyk/Muy*Fz with loadrVy3 RVY3 Variation of Svyk/Muy*Fz with inclinationrVy4 RVY4 Variation of Svyk/Muy*Fz with alpharVy5 RVY5 Variation of Svyk/Muy*Fz with kapparVy6 RVY6 Variation of Svyk/Muy*Fz with atan (kappa)



Mz' t Fy' Mzr s Fx⋅+ +⋅–=

t t αt eq,( )=

Dt Ctarc Btαt eq, Et Btαt eq, ac Btαt eq,( )tan–( )–{ }tan[ ] α( )coscos=



s ssz1 ssz2 Fy Fz0⁄( ) ssz3 ssz4dfz+( )γ+ +{ } R0 λs⋅ ⋅=

αt eq, arc α2t

KxKy------⎝ ⎠⎛ ⎞

2κ2+tan αt( )sgn⋅tan=

αr eq, arc α2r

KxKy------⎝ ⎠⎛ ⎞

2κ2+tan αr( )sgn⋅tan=

37



(90)



(91)



property file: Explanation:ssz1 SSZ1 Nominal value of s/R0 effect of Fx on Mzssz2 SSZ2 Variation of distance s/R0 with Fy/Fznomssz3 SSZ3 Variation of distance s/R0 with inclinationssz4 SSZ4 Variation of distance s/R0 with load and inclination


property file: Explanation:qsx1 QSX1 Lateral force-induced overturning coupleqsx2 QSX2 Inclination-induced overturning coupleqsx3 QSX3 Fy-induced overturning couple



Mx R0 Fz qsx1λVMx qsx2 γ qsx3FyFz0--------⋅+⋅–

⎩ ⎭⎨ ⎬⎧ ⎫

λMx⋅ ⋅=

My R0 Fz qSy1 qSy2Fx Fz0⁄ qSy3 Vx Vref⁄ qSy4 Vx Vref⁄( )4+ + +{ }⋅ ⋅=

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α∗ αc( )sin=

βκc

κc2 α∗

2+-------------------------⎝ ⎠⎜ ⎟⎛ ⎞

acos=


Fz-------------------------= μy act,

Fy 0, SVy–Fz

-------------------------=


DyFz------=

μx1

1μx act,-------------⎝ ⎠⎛ ⎞ 2 βtan

μy max,----------------⎝ ⎠⎛ ⎞ 2

+---------------------------------------------------------=

μyβtan

1μx max,----------------⎝ ⎠⎛ ⎞ 2 βtan

μy act,-------------⎝ ⎠⎛ ⎞ 2

+---------------------------------------------------------=

Fxμx

μx act,-------------Fx 0,= Fy

μyμy act,-------------Fy 0,=

39



Transient Behavior in PAC MCThe previous Magic Formula examples are valid for steady-state tire behavior. When driving, however, the tire requires some response time on changes of the inputs. In tire modeling terminology, the low-frequency behavior (up to 8 Hz) is called transient behavior.


For accurate transient tire behavior, you can use the "stretched string" tire model (see also reference [1]). The tire belt is modeled as stretched string, which is supported to the rim with lateral (and longitudinal) springs. The figure, Stretched String Model for Transient Tire Behavior, shows a top-view of the string model. When rolling, the first point having contact with the road adheres to the road (no sliding assumed). Therefore, a lateral deflection of the string arises that depends on the slip angle size and the history of the lateral deflection of previous points having contact with the road.


SVyκ

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(92)


10 m. This differential example cannot be used at zero speed, but when multiplying with Vx, the example can be transformed to:

(93)



(94)


(95)

(96)


(97)

(98)

Using these practical slip quantities, and , the Magic Formula examples can be used to calculate the tire-road interaction forces and moments:

(99)

(100)

1Vx------

tddv1 v1

σα------+ α( ) aφ+tan=

σα φ


σx tddu1 Vx u1+ σxVsx–=

σx Fz pTx1 pTx2dfz+( ) pTx3dfz( ) R0 Fz0⁄( )λσκ⋅exp⋅ ⋅=

σα pTy1 pTy2arcFz

pTy3 pKy4γ2+( )Fz0λFz0

---------------------------------------------------------⎩ ⎭⎨ ⎬⎧ ⎫

tan 1 pKy5γ2–( ) R0λFz0λσα⋅sin=

κ' α'

κ'u1σx------ Vx( )sin⋅=

α'v1σα------⎝ ⎠⎛ ⎞atan=

κ' α'

Fx' Fx α' κ' Fz, ,( )=

Fy' Fy α' κ' γ Fz, , ,( )=

41

(101)

Gyroscopic Couple in PAC MCWhen having fast rotations about the vertical axis in the wheel plane, the inertia of the tire belt may lead to gyroscopic effects. To cope with this additional moment, the following contribution is added to the total aligning moment:

(102)

with the parameters (in addition to the basic tire parameter mbelt):

(103)

and:

(104)


(105)




property file: Explanation:pTx1 PTX1 Relaxation length sigKap0/Fz at FznompTx2 PTX2 Variation of sigKap0/Fz with loadpTx3 PTX3 Variation of sigKap0/Fz with exponent of loadpTy1 PTY1 Peak value of relaxation length Sig_alphapTy2 PTY2 Shape factor for lateral relaxation lengthpTy3 PTY3 Load where lateral relaxation is at maximumqTz1 QTZ1 Gyroscopic torque constantMbelt MBELT Belt mass of the wheel

Mz' Mz' α' κ' γ Fz, , ,( )=

Mz gyr, cgyrmbeltVr1 tddv arc Brαr eq,( )tan[ ]cos=

cgyr qTz1 λgyr⋅=

arc Brαr eq,( )tan{ }cos 1=

Mz Mz' Mz gyr,+=

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If this keyword is available, Adams/Car corrects for the conicity and plysteer and asymmetry when using a tire property file on the opposite side of the vehicle. In fact, the tire characteristics are mirrored with respect to slip angle zero.

In Adams/View this option can only be used when the tire is generated by the graphical user interface: select Build -> Forces -> Special Force: Tire (see figure of dialog box below).

Next to the LEFT and RIGHT side option of TYRESIDE, you can also select SYMMETRIC: then the tire characteristics are modified during initialization to show symmetric performance for left and right side corners and zero conicity and plysteer (no offsets). Also, when you set the tire property file to SYMMETRIC, the tire characteristics are changed to symmetric behavior.


43

USE_MODES of PAC MC: from Simple to ComplexThe parameter USE_MODE in the tire property file allows you to switch the output of the PAC MC tire model from very simple (that is, steady-state cornering) to complex (transient combined cornering and braking).

The options for USE_MODE and the output of the model are listed in the table below.

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USE_MODE Values of PAC MC and Related Tire Model Output

Contact MethodsThe PAC MC model supports the following roads:


• 3D Spline Roads, see Adams/3D Spline Road Model By default the PAC-MC uses a one point of contact model similar to all the other Adams/Tire Handling models. However the PAC-MC has an option to take the tire cross section shape into account:


Tire Cross-Section Profile Contact MethodIn combination with the 2D Road Model and the 3D Road Model, you can improve the tire-road contact calculation method by providing the tire's cross-section profile, which has an important influence on the wheel center height at large inclination angles with the road.

USE MODE: State: Slip conditions:PAC MC output

(forces and moments)0 Steady state Acts as a vertical spring and damper 0, 0, Fz, 0, 0, 01 Steady state Pure longitudinal slip Fx, 0, Fz, 0, My, 02 Steady state Pure lateral (cornering) slip 0, Fy, Fz, Mx, 0, Mz








45

If the tire model reads a section called [SECTION_PROFILE_TABLE] in the tire property file, the cross section profile will be taken into account for the vertical load calculation of the tire. The method assumes that the tire deformation will not influence the position of the point with largest penetration (P), which is valid for motor cycle tires.

The vertical tire load Fz is calculated using the penetration (effpen = ) of the tire through the tangent road plane in the point C, see Figure above, according to:

(106)

Because in this method the tangent to the cross section profile determines the point P, a high accuracy of the cross section profile is required. The section height y as function of the tire width x must be a continous and monotone increasing function. To avoid singularities and instability, it is highly

ρ


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recommended to fit measured cross section data with a polynom (for example y = a·x2 + b·x4 + c·x6 + ..) and provide the y cross section height data (y) from the polynom in the tire property file up to the maximum width of the tire. The profile is assumed to be symmetric with respect to the wheel plane.

Note that the PAC MC model has only one point of contact with the road; therefore, the wavelength of road obstacles must be longer than the tire radius for realistic output of the model. In addition, the contact force computed by this tire model is normal to the road plane. Therefore, the contact point does not generate a longitudinal force when rolling over a short obstacle, such as a cleat or pothole.

For ride and comfort analysis, we recommend more sophisticated tire models, such as Ftire.

Quality Checks for the Tire Model ParametersBecause PAC MC uses an empirical approach to describe tire - road interaction forces, incorrect parameters can easily result in non-realistic tire behavior. Below is a list of the most important items to ensure the quality of the parameters in a tire property file:



Camber (Inclination) EffectsCamber stiffness has been explicitly defined in PAC MC (see equation (43). For realistic tire behavior, the sign of the camber stiffness must be negative (TYDEX W-axis (ISO) system). If the sign is positive, the coefficients may not be valid for the ISO but for the SAE coordinate system. Note that PAC MC only uses coefficients for the TYDEX W-axis (ISO) system.



47

The table below lists further checks on the PAC MC parameters.

Checklist for PAC MC Parameters and Properties


Parameter/property: Requirement: Explanation:LONGVL 1 m/s Reference velocity at which parameters are measuredVXLOW Approximately 1m/s Threshold for scaling down forces and momentsDx 0 Peak friction (see equation (24))pDx1/pDx2 0 Peak friction Fx must decrease with increasing loadKx 0 Long slip stiffness (see equation (27))Dy 0 Peak friction (see equation (36))pDy1/pDy2 0 Peak friction Fx must decrease with increasing loadKy 0 Cornering stiffness (see equation (39))qsy1 0 Rolling resistance, should in range of 0.005 - 0.015

0 Camber stiffness (see equation (43))

>

><<><<<

Kγ <

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$---------------------------------------------------long_slip_range [LONG_SLIP_RANGE]KPUMIN = -1.5 $Minimum valid wheel slipKPUMAX = 1.5 $Maximum valid wheel slip$--------------------------------------------------slip_angle_range[SLIP_ANGLE_RANGE]ALPMIN = -1.5708 $Minimum valid slip angleALPMAX = 1.5708 $Maximum valid slip angle$--------------------------------------------inclination_slip_range[INCLINATION_ANGLE_RANGE]CAMMIN = -1.0996 $Minimum valid camber angleCAMMAX = 1.0996 $Maximum valid camber angle$----------------------------------------------vertical_force_range[VERTICAL_FORCE_RANGE]FZMIN = 73.75 $Minimum allowed wheel loadFZMAX = 3319.5 $Maximum allowed wheel load

If one of the input parameters exceeds a minimum or maximum validity value, the calculation in the tire model will be performed with the minimum or maximum value of this range to avoid non-realistic tire behavior. In that case, a message appears warning you that one of the inputs exceeds a validity value.

Standard Tire Interface (STI) for PAC MCBecause all Adams products use the Standard Tire Interface (STI) for linking the tire models to Adams/Solver, below is a brief background of the STI history (see reference [4]).


The working group concentrated on tire measurements and tire models used for vehicle simulation purposes. For most vehicle dynamics studies, people previously developed their own tire models. Because all car manufacturers and their tire suppliers have the same goal (that is, development of tires to improve dynamic safety of the vehicle), it aimed for standardization in tire behavior description.




49


• Tire Kinematics

• Slip Quantities




Term: Definition:Road tangent plane Plane with the normal unit vector (tangent to the road) in the tire-road

contact point C.C-axis system Coordinate system mounted on the wheel carrier at the wheel center

according to TYDEX, ISO orientation.Wheel plane The plane in the wheel centre that is formed by the wheel when considered

a rigid disc with zero width.Contact point C Contact point between tire and road, defined as the intersection of the wheel


orientation.





ρρρ

ω

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Initiated by the International Tire Working Group, July 1995.3. A. Riedel, Standard Tire Interface, Release 1.2, Initiated by the Tire Workgroup, June 1995.



Abbreviation: Definition: Units:Fz Vertical wheel load [N]Fz0 Nominal load [N]dfz Dimensionless vertical load [-]Fx Longitudinal force [N]Fy Lateral force [N]Mx Overturning moment [Nm]My Braking/driving moment [Nm]Mz Aligning moment [Nm]

καγ

51

4. J.J.M. van Oosten, H.-J. Unrau, G. Riedel, E. Bakker, TYDEX Workshop: Standardisation of Data Exchange in Tyre Testing and Tyre Modelling, Proceedings of the 2nd International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Vehicle System Dynamics, Volume 27, Swets & Zeitlinger, Amsterdam/Lisse, 1996.

Example of PAC MC Tire Property File[MDI_HEADER]FILE_TYPE ='tir'FILE_VERSION =3.0FILE_FORMAT ='ASCII'! : TIRE_VERSION : PAC Motorcycle ! : COMMENT : Tire 180/55R17! : COMMENT : Manufacturer ! : COMMENT : Nom. section with (m) 0.18 ! : COMMENT : Nom. aspect ratio (-) 55! : COMMENT : Infl. pressure (Pa) 200000! : COMMENT : Rim radius (m) 0.216 ! : COMMENT : Measurement ID ! : COMMENT : Test speed (m/s) 16.7 ! : COMMENT : Road surface ! : COMMENT : Road condition Dry! : FILE_FORMAT : ASCII! : Copyright MSC.Software, Mon Oct 20 10:46:57 2003!! USE_MODE specifies the type of calculation performed:! 0: Fz only, no Magic Formula evaluation! 1: Fx,My only! 2: Fy,Mx,Mz only! 3: Fx,Fy,Mx,My,Mz uncombined force/moment calculation! 4: Fx,Fy,Mx,My,Mz combined force/moment calculation! +10: including relaxation behaviour! *-1: mirroring of tyre characteristics!! example: USE_MODE = -12 implies:! -calculation of Fy,Mx,Mz only! -including relaxation effects! -mirrored tyre characteristics!$-------------------------------------------------------------units[UNITS]LENGTH ='meter'FORCE ='newton'ANGLE ='radians'MASS ='kg'TIME ='second'$-------------------------------------------------------------model[MODEL]PROPERTY_FILE_FORMAT ='PAC_MC'USE_MODE = 14 $Tyre use switch (IUSED)VXLOW = 1

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LONGVL = 16.7 $Longitudinal speed during measurements TYRESIDE = 'SYMMETRIC' $Mounted side of tyre at vehicle/test bench$---------------------------------------------------------dimensions[DIMENSION]UNLOADED_RADIUS = 0.322 $Free tyre radius WIDTH = 0.18 $Nominal section width of the tyre RIM_RADIUS = 0.216 $Nominal rim radius RIM_WIDTH = 0.135 $Rim width $----------------------------------------------------------parameter[VERTICAL]VERTICAL_STIFFNESS = 2e+005 $Tyre vertical stiffness VERTICAL_DAMPING = 50 $Tyre vertical damping BREFF = 8.4 $Low load stiffness eff. rolling radius DREFF = 0.27 $Peak value of eff. rolling radius FREFF = 0.07 $High load stiffness eff. rolling radius FNOMIN = 1475 $Nominal wheel load$----------------------------------------------------long_slip_range[LONG_SLIP_RANGE]KPUMIN = -1.5 $Minimum valid wheel slip KPUMAX = 1.5 $Maximum valid wheel slip $---------------------------------------------------slip_angle_range[SLIP_ANGLE_RANGE]ALPMIN = -1.5708 $Minimum valid slip angle ALPMAX = 1.5708 $Maximum valid slip angle $---------------------------------------------inclination_slip_range[INCLINATION_ANGLE_RANGE]CAMMIN = -1.0996 $Minimum valid camber angle CAMMAX = 1.0996 $Maximum valid camber angle $-----------------------------------------------vertical_force_range[VERTICAL_FORCE_RANGE]FZMIN = 73.75 $Minimum allowed wheel load FZMAX = 3319.5 $Maximum allowed wheel load $------------------------------------------------------------scaling[SCALING_COEFFICIENTS]LFZO = 1 $Scale factor of nominal load LCX = 1 $Scale factor of Fx shape factor LMUX = 1 $Scale factor of Fx peak friction coefficient

53

LEX = 1 $Scale factor of Fx curvature factor LKX = 1 $Scale factor of Fx slip stiffness LVX = 1 $Scale factor of Fx vertical shift LGAX = 1 $Scale factor of camber for Fx LCY = 1 $Scale factor of Fy shape factor LMUY = 1 $Scale factor of Fy peak friction coefficient LEY = 1 $Scale factor of Fy curvature factor LKY = 1 $Scale factor of Fy cornering stiffness LCC = 1 $Scale factor of camber shape factor LKC = 1 $Scale factor of camber stiffness (K-factor) LEC = 1 $Scale factor of camber curvature factor LHY = 1 $Scale factor of Fy horizontal shift LGAY = 1 $Scale factor of camber force stiffness LTR = 1 $Scale factor of Peak of pneumatic trail LRES = 1 $Scale factor of Peak of residual torque LGAZ = 1 $Scale factor of camber torque stiffness LXAL = 1 $Scale factor of alpha influence on Fx LYKA = 1 $Scale factor of kappa influence on Fy LVYKA = 1 $Scale factor of kappa induced Fy LS = 1 $Scale factor of Moment arm of Fx LSGKP = 1 $Scale factor of Relaxation length of Fx LSGAL = 1 $Scale factor of Relaxation length of Fy LGYR = 1 $Scale factor of gyroscopic torque LMX = 1 $Scale factor of overturning couple LVMX = 1 $Scale factor of Mx vertical shift LMY = 1 $Scale factor of rolling resistance torque $------------------------------------------------------longitudinal[LONGITUDINAL_COEFFICIENTS]

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PCX1 = 1.7655 $Shape factor Cfx for longitudinal force PDX1 = 1.2839 $Longitudinal friction Mux at Fznom PDX2 = -0.0078226 $Variation of friction Mux with load PDX3 = 0 $Variation of friction Mux with camber PEX1 = 0.4743 $Longitudinal curvature Efx at Fznom PEX2 = 9.3873e-005 $Variation of curvature Efx with load PEX3 = 0.066154 $Variation of curvature Efx with load squared PEX4 = 0.00011999 $Factor in curvature Efx while driving PKX1 = 25.383 $Longitudinal slip stiffness Kfx/Fz at Fznom PKX2 = 1.0978 $Variation of slip stiffness Kfx/Fz with load PKX3 = 0.19775 $Exponent in slip stiffness Kfx/Fz with load PVX1 = 2.1675e-005 $Vertical shift Svx/Fz at Fznom PVX2 = 4.7461e-005 $Variation of shift Svx/Fz with load RBX1 = 12.084 $Slope factor for combined slip Fx reduction RBX2 = -8.3959 $Variation of slope Fx reduction with kappa RBX3 = 2.1971e-009 $Influence of camber on stiffness for Fx combined RCX1 = 1.0648 $Shape factor for combined slip Fx reduction REX1 = 0.0028793 $Curvature factor of combined Fx REX2 = -0.00037777 $Curvature factor of combined Fx with load RHX1 = 0 $Shift factor for combined slip Fx reduction PTX1 = 0.83 $Relaxation length SigKap0/Fz at Fznom PTX2 = 0.42 $Variation of SigKap0/Fz with load PTX3 = 0.21 $Variation of SigKap0/Fz with exponent of load $--------------------------------------------------------overturning[OVERTURNING_COEFFICIENTS]QSX1 = 0 $Lateral force induced overturning moment QSX2 = 0.16056 $Camber induced overturning moment QSX3 = 0.095298 $Fy induced overturning moment

55

$------------------------------------------------------------lateral[LATERAL_COEFFICIENTS]PCY1 = 1.1086 $Shape factor Cfy for lateral forces PCY2 = 0.66464 $Shape factor Cfc for camber forces PDY1 = 1.3898 $Lateral friction Muy PDY2 = -0.0044718 $Exponent lateral friction Muy PDY3 = 0.21428 $Variation of friction Muy with squared camber PEY1 = -0.80276 $Lateral curvature Efy at Fznom PEY2 = 0.89416 $Variation of curvature Efy with camber squared PEY3 = 0 $Asymmetric curvature Efy at Fznom PEY4 = 0 $Asymmetric curvature Efy with camber PEY5 = -2.8159 $Camber curvature Efc PKY1 = -19.747 $Maximum value of stiffness Kfy/Fznom PKY2 = 1.3756 $Curvature of stiffness Kfy PKY3 = 1.3528 $Peak stiffness factor PKY4 = -1.2481 $Peak stiffness variation with camber squared PKY5 = 0.3743 $Lateral stiffness depedency with camber squared PKY6 = -0.91343 $Camber stiffness factor Kfc PKY7 = 0.2907 $Vertical load dependency of camber stiffn. Kfc PHY1 = 0 $Horizontal shift Shy at Fznom RBY1 = 10.694 $Slope factor for combined Fy reduction RBY2 = 8.9413 $Variation of slope Fy reduction with alpha RBY3 = 0 $Shift term for alpha in slope Fy reduction RBY4 = -1.8256e-010 $Influence of camber on stiffness of Fy combined RCY1 = 1.0521 $Shape factor for combined Fy reduction REY1 = -0.0027402 $Curvature factor of combined Fy REY2 = -0.0094269 $Curvature factor of combined Fy with load RHY1 = -7.864e-005 $Shift factor for combined Fy reduction RHY2 = -6.9003e-006 $Shift factor for combined Fy reduction with load

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RVY1 = 0 $Kappa induced side force Svyk/Muy*Fz at Fznom RVY2 = 0 $Variation of Svyk/Muy*Fz with load RVY3 = -0.00033208 $Variation of Svyk/Muy*Fz with camber RVY4 = -4.7907e+015 $Variation of Svyk/Muy*Fz with alpha RVY5 = 1.9 $Variation of Svyk/Muy*Fz with kappa RVY6 = -30.082 $Variation of Svyk/Muy*Fz with atan(kappa) PTY1 = 0.75 $Peak value of relaxation length Sig_alpha PTY2 = 1 $Shape factor for Sig_alpha PTY3 = 0.6 $Value of Fz/Fznom where Sig_alpha is maximum $-------------------------------------------------rolling resistance[ROLLING_COEFFICIENTS]QSY1 = 0.01 $Rolling resistance torque coefficient QSY2 = 0 $Rolling resistance torque depending on Fx QSY3 = 0 $Rolling resistance torque depending on speed QSY4 = 0 $Rolling resistance torque depending on speed^4 $-----------------------------------------------------------aligning[ALIGNING_COEFFICIENTS]QBZ1 = 9.246 $Trail slope factor for trail Bpt at Fznom QBZ2 = -1.4442 $Variation of slope Bpt with load QBZ3 = -1.8323 $Variation of slope Bpt with load squared QBZ4 = 0 $Variation of slope Bpt with camber QBZ5 = 0.15703 $Variation of slope Bpt with absolute camber QBZ9 = 8.3146 $Slope factor Br of residual torque Mzr QCZ1 = 1.2813 $Shape factor Cpt for pneumatic trail QDZ1 = 0.063288 $Peak trail Dpt = Dpt*(Fz/Fznom*R0) QDZ2 = -0.015642 $Variation of peak Dpt with load QDZ3 = -0.060347 $Variation of peak Dpt with camber QDZ4 = -0.45022 $Variation of peak Dpt with camber squared QDZ6 = 0 $Peak residual torque Dmr = Dmr/(Fz*R0)

57

QDZ7 = 0 $Variation of peak factor Dmr with load QDZ8 = -0.08525 $Variation of peak factor Dmr with camber QDZ9 = -0.081035 $Variation of peak factor Dmr with camber and load QDZ10 = 0.030766 $Variation of peak factor Dmr with camber squared QDZ11 = 0.074309 $Variation of Dmr with camber squared and load QEZ1 = -3.261 $Trail curvature Ept at Fznom QEZ2 = 0.63036 $Variation of curvature Ept with load QEZ3 = 0 $Variation of curvature Ept with load squared QEZ4 = 0 $Variation of curvature Ept with sign of Alpha-t QEZ5 = 0 $Variation of Ept with camber and sign Alpha-t QHZ1 = 0 $Trail horizontal shift Sht at Fznom QHZ2 = 0 $Variation of shift Sht with load QHZ3 = 0 $Variation of shift Sht with camber QHZ4 = 0 $Variation of shift Sht with camber and load SSZ1 = 0 $Nominal value of s/R0: effect of Fx on Mz SSZ2 = 0.0033657 $Variation of distance s/R0 with Fy/Fznom SSZ3 = 0.16833 $Variation of distance s/R0 with camber SSZ4 = 0.017856 $Variation of distance s/R0 with load and camber QTZ1 = 0 $Gyroscopic torque constant MBELT = 0 $Belt mass of the wheel -kg- $

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521-Tire Model

About 521-TireThe 521-Tire model is a simple model that requires a small set of parameters or experimental data to simulate the behavior of tires. The 521-Tire is the first tire model incorporated in Adams. The name “521” (actually “5.2.1”) refers to the version number of Adams/Tire when it was first released.

The slip forces and moments can be calculated in two ways:

• Using the Equation method• Using the Interpolation method

Two dedicated contact methods exist for the 521-Tire:

• Point Follower, used for Handling analysis models• Equivalent Plane Method, used for 3D Contact analysis models

Any combination of force and contact method is allowed.

The road data files used for the 521-Tire are unique and cannot be used in combination with any other Handling tire model. The 521 road file format is described in Road Data File 521_pnt_follow.rdf.

Note that the capability and generality of the 521-Tire have been superseded by other, newer tire models, described throughout this guide. We’ve retained the 521-Tire model primarily for backward compatibility. We recommend that you use other tire models for new work.

Tire Slip Quantities and Transient Tire Behaviour


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The longitudinal slip velocity Vsx in the SAE-axis system is defined using the longitudinal speed Vx, the wheel rotational velocity , and the loaded rolling radius Rl:



Note that for realistic tire forces the slip angle is limited to 90 degrees and the longitudinal slip in between -1 (locked wheel) and 1.

Lagged longitudinal and lateral slip quantities (transient tire behavior)In general, the tire rotational speed and lateral slip will change continuously because of the changing interaction forces in between the tire and the road. Often the tire dynamic response will have an important role on the overall vehicle response. For modeling this so-called transient tire behavior, a first-order system is used both for the longitudinal slip as the side slip angle, . Considering the tire belt as a stretched string, which is supported to the rim with lateral springs, the lateral deflection of the belt can be estimated (see also reference [1]). The figure below shows a top-view of the string model.


Ω

Vsx Vz ΩR1–=

Vsy Vy=

κ α

κVsxVx-------- and αtan–

VsyVx---------= =

α κ

κ α

13






Now the practical slip quantities, and are defined based on the tire deformation:

1Vx------

dv1dt

--------v1σα------+ α( )tan aφ+=

σα φ

σαdv1dt

-------- Vx v1+ σ– κVsx=

σαdu1dt

-------- Vx u1+ σ– κVsx=

κ′ α′

Adams/Tire

14


The longitudinal and lateral relaxation length are read from the tire property file, see Tire Property File 521_equation.tir and 521_interpol.tir

Force CalculationsYou can use the 521-Tire model for handling and durability analyses.

Directional Vectors for the Application of Tire Forces and Torques at the Center of the Tire-Road Surface Contact Patch

The forces act along the directional vectors. From the tire spin vector and various information you supply in the tire property and the road profile data files, Adams/Tire determines the positions and orientations of the tire vertical, lateral, and longitudinal directional vectors. Figure 3 shows these directional vectors.

The tire vertical force acts along the vertical directional vector, the tire aligning torque acts about the same vector, the tire lateral force acts along the lateral directional vector, and the tire longitudinal force acts along the longitudinal directional vector. At this point, Adams/Tire determines the force directions

κ'u1σκ------ Vx( )sin=

α'v1σα------⎝ ⎠

⎛ ⎞atan=

κ′ α′ κ α

15

as if it were going to apply the tire aligning torque and all of the tire forces at the center of the tire-road surface contact patch.

The tire-road surface contact patch may deflect laterally. Adams/Tire calculates the lateral deflection in the direction (and with the sign) of the lateral force. The magnitude of the deflection is equal to the lateral force divided by the tire lateral stiffness you provide in the tire property data file.

The tire vertical, lateral, and longitudinal forces are forces in the tire vertical, lateral, and longitudinal directions (as determined at the tire-road surface contact patch). The tire aligning torque is a torque about the tire vertical vector. The vehicle durability force has components in both the tire vertical and the tire longitudinal directions.

Normal ForceThe tire normal force Fz is calculated based on the tire deflection and radial velocity. A progressive spring and linear damping constant are employed:

where Fstiff is tire stiffness force and Fdamp is tire damping force. The vertical stiffness force is calculated from:

where Kz is the tire vertical stiffness, δ is tire deflection, and is the stiffness exponent. The tire damping force is calculated from:

where Cz is the tire damping constant.

The damping constant is reduced for small tire deflections, which are below 5% of the unloaded tire radius.

The tire vertical stiffness can also be described using a spline function (force versus deflection) in the Adams dataset. The user array is used to switch between tire property file stiffness and spline stiffness. If the first value in the user array is equal to '5215', the spline vertical stiffness is used. The second value of the user array refers to the ID of the spline. The message, 'Using spline data for the vertical spring', is shown in the message file. If the first value in the user array is not equal to '5215', the tire property file stiffness is used.

The following is an example of using the spline vertical stiffness:

! adams_view_name='spline_vertical_stiffness'SPLINE/10, X = -1,0,10,30, Y = 0,0,2000,6000!

Fz Fstiff Fdamp–=

Fstiff Kzδθ=

θ

Fdamp Cz RadialVelocity×=

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! adams_view_name='wheel_user_array'ARRAY/102, NUM=5215,10

Another option for having a non-linear tire stiffness is to introduce a deflection-load table in the tire property file in a section called [DEFLECTION_LOAD_CURVE]. See 521-Tire Tire and Road Property Files on page 20. If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection datapoints with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire.

Longitudinal ForceThe tire longitudinal force Fx can have up to three contributions:

• Traction/braking force• Rolling resistance force• Durability force (in case of durability contact)

Traction/Braking ForceTraction force is developed if the vehicle is starting to move and a braking force if the vehicle is beginning to stop. In either case, the absolute magnitude of the force is calculated from:

where the friction coefficient μ is a function of the longitudinal slip velocity Vsx in the contact patch. Note that this is somewhat unusual, since all the other Handling tire models in Adams/Tire assume that the longitudinal force Fx is a function of the slip ratio.

Schematic of Friction Coefficient Versus Local Slip Velocity

Fx μFz=

17

The μ curve as a function of longitudinal slip velocity is created using standard Adams STEP functions (see body 4 on page 10). You have to specify two points on the curve to define this characteristic:

• The coordinates of the curve at μstatic: (velocity μstatic, μstatic)

• The coordinates of the curve at μdynamic: (velocity μdynamic, μdynamic)

The friction values may be available to you as function of slip ratio instead of slip velocity. Converting Slip Ratio Data to Velocity Data on page 16 explains how the slip ratios can be converted to slip velocities.

Rolling Resistance ForceRolling resistance Moment My is calculated from:

where coefrr is the rolling resistance coefficient that should be supplied in the tire property data file.

Durability ForceDurability force, sometimes known as radial planar force, is a special kind of tire vertical force. It is the durability force that resists the action of road bumps. This force acts along the instantaneous vertical directional vector calculated by Adams/Tire. The Adams/Tire durability tire forces are limited to two-dimensional forces that lie in the plane of the tire and are directed toward the wheel-center marker. Adams/Tire superimposes these forces upon any traction or lateral forces developed in the tire-road surface interaction.

My coefrr Fz⋅=

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You must select the Equivalent Plane Method for generating these durability forces.

Lateral Force and Aligning TorqueTwo methods exist for calculating the lateral force Fy and self-aligning moment Mz:

• Interpolation Method• Equation Method

Interpolation MethodThe AKIMA spline is employed to calculate Fy and Mz as a function of the slip angle α, camber angle γ, and vertical load Fz. You should provide the data in the SAE axis system.

Note that the slip angle α and vertical load Fz input for the force and moment calculation of Fx, Fy, Mx, My, and Mz are limited to minimum and maximum values in the input to avoid unrealistic extrapolated values.

Equation MethodThe Equation Method uses the following equation to generate the lateral force Fy:

where Kα denotes the tire cornering stiffness coefficient.

The aligning moment Mz is calculated using the pneumatic trail t according to:

while the pneumatic trails are calculated with half the contact length a:

with R0 and Rl are, respectively, the unloaded and loaded tire radius.

Overturning MomentIn both methods, the overturning moment Mx calculation is based on the lateral tire force Fy, the lateral tire stiffness Ky, and the vertical load:

Fy μstatFz 1 eKα α–

–( )⋅ sign α( )⋅( )–=

Mz t– Fy⋅=

t 13--- a e

Kα α–⋅⋅=

a R02 R1

2–=

MxFyKy------= Fz

19

Tire Lateral Force as a Function of Slip Angle

• The contribution of the camber is disregarded in the Equation Method.

• The cornering stiffness equals .

Combined Slip of 5.2.1The combined slip calculation of the 5.2.1. is using the friction ellipse and is similar to the combined slip calculation of the Pacejka '89 and '94 tire models.

Inputs:

• Dimensionless longitudinal slip (range -1 to 1) and side slip angle in radians

• Longitudinal force Fx and lateral force Fy calculated using the equations of 521-Tire

• The vertical shift of Fy,a=0 is Fy calculated at zero slip angle

Output:

• Adjusted longitudinal force Fx and lateral force Fy incorporates the reduction due to combined slip:

•

Friction coefficients:

γ

μstatFzKa–

κ α

β k

k2 α2sin+------------------------------

⎝ ⎠⎜ ⎟⎛ ⎞

acos=

μx act,FxFz-----= μy act,

Fy Fy α 0=,–Fz

------------------------------=

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Forces corrected for combined slip conditions:

Due to the lateral deflection of the tire patch, the aligning moment under combined slip conditions increases by the effect of the longitudinal force Fx and the lateral tire stiffness Ky:

and the overturning moment uses the lateral force for combined slip:

SmoothingWhen you indicate smoothing by setting the value of USE_MODE in the tire property file, Adams/Tire smooths initial transients in the tire force over the first 0.1 seconds of the simulation. The longitudinal force, lateral force, and aligning torque are multiplied by a cubic step function of time. (See STEP in the Adams/Solver online help.)

• Longitudinal Force Fx = SFx.

• Lateral Force Fy = SFy

• Overturning moment torque Mx = SMz

• Aligning torque Mz = SMz

Changing the Operating Mode: USE_MODEYou can change the behavior of the tire model by changing the value of USE_MODE in the [MODEL] section of the tire property file. If USE_MODE equals zero, or when it is absent, the smoothing time equals 0.001 seconds and the 521-Tire model is compatible with the previous Adams/Solver implementation.

μx1

1μx act,-------------⎝ ⎠

⎛ ⎞ 2 βtanμstat-----------⎝ ⎠

⎛ ⎞ 2+

----------------------------------------------------= μyβtan

1μstat----------⎝ ⎠

⎛ ⎞ 2 βtanμy act,-------------⎝ ⎠

⎛ ⎞ 2+

---------------------------------------------------=

Fx comb,μx

μx act,-------------Fx= Fy comb,

μyμy act,------------- Fy Fy α 0=,+( )=

Mz comb, Mz pure, Fx comb,+=Fy comb,

Ky------------------⋅

Mx comb,Fy comb,

Ky------------------Fz=

21

By selecting a value of USE_MODE between 1 and 4, smoothing and combined slip correction can be switched on and off, as shown in Table 1. The smoothing time equals 0.1 seconds for these values of USE-MODE.

Converting Slip Ratio Data to Velocity DataAdams/Tire requires that you enter the velocities that correspond to μstatic and μdynamic. You will often obtain this information as the coefficient of friction versus slip ratio. You can calculate the velocities required by Adams/Tire from the coefficient of friction versus slip ratio curve in the following way:

where:

• = Slip ratio

• = Free rolling rotational velocity (no slip)

• = Actual rotational velocity

Kinematic relationships between translational and rotational velocities and the effective rolling radius give:

where:

• = Contact patch velocity reletive to road surface

• = Actual longitudinal velocity

USE_MODE: Smoothing: Combined slip correction:1 off off2 off on3 on off4 on on

κωa ωf–

ωf------------------=

κ

ωf

ωa

ωaVx Vsx–

Re---------------------=

ωfVxRe------=

Vsx

Vx

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• = Effective rolling radius

Substituting these relationships into the original slip ratio equation with some cancelling of variables gives:

Therefore:

During testing for the coefficient of friction as a function of slip ratio, the longitudinal velocity Vx is held constant. Therefore, you can obtain Vsx, the relative velocity of the contact patch with respect to the road surface, from the test data curves for the static and dynamic values of friction.

Contact MethodsFor handling analyses (which use a flat road surface profile), the 521-Tire model uses the point-follower contact method. For durability analyses (which use uneven road surface profiles), the Equivalent Plane Method yields the instantaneous tire radius directly, while finding the new road surface orientation vector.

About the Point-Follower MethodThe point-follower contact method assumes a single contact point between the tire and road. The contact point is the point nearest to the wheel center that lies on the line formed by the intersection of the tire (wheel) plane with the local road plane.

The contact force computed by the point-follower contact method is normal to the road plane. Therefore, in a simulation of a tire hitting a pothole, the point-follower contact method does not generate the expected longitudinal force.

About the Equivalent Plane Method 521-Tire uses the Equivalent Plane method to reorient the vertical road surface vector, which gives the direction of the vertical force, and to calculate the new tire radius. To do this, a new smooth road surface is generated at an angle calculated such that only the shape of the tire is different (see body 6 on page 18).

Equivalent Plane Method

Re

κVsxVx--------–=

Vsx Vxκ–=

23

Both the deflected tire area and its centroid remain unchanged. The vector between the deflected area centroid and the wheel-center marker then determines the orientation of the. vertical vector perpendicular to the road surface.

The Equivalent Plane method is best suited for relatively large obstacles because it assumes the tire encompasses the obstacle uniformly. In reality, the pneumatics and the bending stiffness of the tire carcass prevent this. The result is an uneven pressure distribution and possibly gaps between the tire and the road. If the obstacle is larger than the tire contact patch (such as a pothole or curb), the uniform assumption is good. If the obstacle is much smaller than the tire patch, however (such as a tar strip or expansion joint), the assumption is poor, and the Equivalent Plane method may greatly underestimate the durability force.

Definition of Equivalent Plane Parameters

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When using the Equivalent Plane method the following parameters need to be specified in the tire property file:

Equivalent_plane_angleSpecifies the subtended angle (in degrees) bisected by the z-axis of the wheel-center marker, as shown in Figure 7. This angle determines the extent of the road the tire can envelop. The value of the equivalent_plane_angle must be between 0 and 180 degrees.

Equivalent_plane_incrementsSpecifies the number of increments into which the shadow of the tire subtended section is divided, as shown in Figure 7.

521-Tire Tire and Road Property FilesThis section contains four example input data files. For reference, the files are called:

• 521_equation.tir• 521_interpol.tir• 521_pnt_follow.rdf• 521_equiv_plane.rdf

The first two files are tire property files, and the last two are road files. The file 521_equation.tir illustrates the required format and parameters when you use the Equation method. The file 521_interpol.tir illustrates the Interpolation method. The two *.rdf files show how road data files must be specified when either of the contact methods is used.

25

Tire Property File 521_equation.tir and 521_interpol.tirYou can select the method for calculating the normal force by setting the VERTICAL_FORCE_METHOD parameter to either POINT_FOLLOWER (for the Point Follower method) or EQUIVALENT_PLANE (for the Equivalent Plane method). See Contact Methods on page 17 for details on these methods.

You can select the method for calculating the lateral force by setting the LATERAL_FORCE_METHOD parameter to either INTERPOLATION or symbol. See Lateral Force and Aligning Torque on page 11 for details on these calculation methods.

The following table specifies how some of the parameter names used in the tire property file correspond to parameters introduced in the equations that were presented in the previous sections.

521-equation.tirThe 521-equation.tir example tire property file starts here.

$--------------------------------------------------------MDI_HEADER[MDI_HEADER] FILE_TYPE = 'tir' FILE_VERSION = 3.0 FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'Tire - XXXXXX''Pressure - XXXXXX''Test Date - XXXXXX''Test tire'$-------------------------------------------------------------units

Parameter in file: Used in equation: As parameter:vertical_stiffness [10] Kzvertical_damping [11] Czlateral_stiffness [18] Kycornering_stiffness_coefficient [6] Kα

Mu_Static Figure 4 μstatic

Mu_Dynamic Figure 4 μdynamic

Mu_Static_velocity Figure 4 velocity μstatic

Mu_Dynamic_Velocity Figure 4 velocity μdynamic

rolling_resistance_coefficient [13] coeffrrvertical_stiffness_exponent [141] Note: If you do not specify

vertical_stiffness_exponent in the tire property file, 521-Tire uses the default value of 1.1.

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[UNITS] LENGTH = 'mm' FORCE = 'newton' ANGLE = 'rad' MASS = 'kg' TIME = 'second'$-------------------------------------------------------------model[MODEL]! use mode 123411121314! -----------------------------------------------------------------! smoothingXXXX! combinedXXXX! transient X X X X! PROPERTY_FILE_FORMAT = '5.2.1' USE_MODE = 1$----------------------------------------------------------dimension[DIMENSION] UNLOADED_RADIUS = 310.0 WIDTH = 195.0 ASPECT_RATIO = 0.70 RIM_RADIUS = 195,0 RIM_WIDTH = 139.7$---------------------------------------------------------parameters! VERTICAL_FORCE_METHOD = EQUIVALENT_PLANE LATERAL_FORCE_METHOD = EQUATION! vertical_stiffness = 206.0 vertical_stiffness_exponent = 1.1 vertical_damping = 2.06! lateral_stiffness = 50 cornering_stiffness_coefficient = 50! Mu_Static = 0.95 Mu_Dynamic = 0.75 Mu_Static_Velocity = 3000 Mu_Dynamic_Velocity = 6000! rolling_resistance_coefficient = 0.01! EQUIVALENT_PLANE_ANGLE= 100 EQUIVALENT_PLANE_INCREMENTS= 50!

521_interpol.tirThe 521-interpol.tir example tire property file starts here. In addition to the file for 521_equation.tir, it contains data that is used for calculating the lateral force and aligning moment, instead of using formula 6 to 9. Note that the [DEFLECTION_LOAD_CURVE] can also be used in the tire property file for the Equation method.

27

$--------------------------------------------------------MDI_HEADER[MDI_HEADER] FILE_TYPE = 'tir' FILE_VERSION = 3.0 FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'Tire - XXXXXX''Pressure - XXXXXX''Test Date - XXXXXX''Test tire'$-------------------------------------------------------------units[UNITS] LENGTH = 'mm' FORCE = 'newton' ANGLE = 'rad' MASS = 'kg' TIME = 'second'$--------------------------------------------------------------model[MODEL]! use mode 123411121314! ----------------------------------------------------------------! smoothingXXXX! combinedXXXX! transient X X X X! PROPERTY_FILE_FORMAT = '5.2.1' USE_MODE = 1$----------------------------------------------------------dimension[DIMENSION] UNLOADED_RADIUS = 310.0 WIDTH = 195.0 ASPECT_RATIO = 0.70 RIM_RADIUS = 195,0 RIM_WIDTH = 139.7$---------------------------------------------------------parameters! VERTICAL_FORCE_METHOD = POINT_FOLLOWER ! or EQUIVALENT_PLANE LATERAL_FORCE_METHOD = INTERPOLATION ! or EQUATION! vertical_stiffness = 206.0 vertical_stiffness_exponent = 1.1 vertical_damping = 2.06 lateral_stiffness = 50 cornering_stiffness_coefficient = 50! Mu_Static = 0.95 Mu_Dynamic = 0.75 Mu_Static_Velocity = 3000 Mu_Dynamic_Velocity = 6000! rolling_resistance_coefficient = 0.01! EQUIVALENT_PLANE_ANGLE= 100

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EQUIVALENT_PLANE_INCREMENTS= 50!!------------------CAMBER ANGLE VALUES------------------------------------------! Conversion! No. of pnts factor(D to R) pnt1 pnt2 pnt3 pnt4 pnt5! CAMBER_ANGLE_DATA_LIST 5 0.017453292 -3.0 0.0 3.0 6.0 10.0!!------------------SLIP ANGLE VALUES--------------------------------------------! Conversion! No. of pnts factor(D to R) pnt1 ...... pnt9! SLIP_ANGLE_DATA_LIST 9 0.017453292 -15.0 -10.0 -5.0 -2.5 0.0 2.5 5.0 10.0 15.0!!-----------------VERTICAL FORCE VALUES-----------------------------------------! Conversion ! No. of pnts factor! pnt1 pnt2 pnt3 pnt4 pnt5 ! VERTICAL_FORCE_DATA_LIST 5 4.448 200.0 600.0 1100.0 1500.0 1900.0!!-----------------ALLIGNING TORQUE VALUES---------------------------------------! No. of pnts Conversion! factor!! pnt1 .... pnt225! ALIGNING_TORQUE_DATA_LIST 225 -1355.7504

5.31 6.52 22.88 26.41 30.58 0.11 2.84 5.49 -3.92 -14.04 0.47 -12.44 -37.99 -67.22 -116.07 0.04 -21.38 -69.04 -111.44 -168.11 0.80 -3.70 -27.94 -44.25 -53.74 1.75 17.43 52.20 81.97 145.78 2.54 11.08 40.53 73.54 95.55 -1.28 0.02 14.82 2.93 10.35 1.59 -3.77 -17.17 6.60 -11.91

0.06 14.23 22.93 11.45 15.74 5.95 5.54 13.72 -1.65 -15.64 -1.29 -9.45 -26.98 -57.25 -107.71 -5.05 -17.73 -62.62 -109.03 -161.88

29

0.46 -2.48 -19.48 -33.54 -49.52 4.71 26.10 60.80 90.85 119.51 4.26 16.60 52.46 93.32 141.34 2.41 4.28 2.21 9.11 30.44 -0.92 0.22 12.61 2.51 -18.77

0.43 -4.62 15.36 7.16 11.70 6.70 15.92 0.14 -4.20 -11.81 -2.20 -5.53 -13.28 -47.48 -92.88 -1.39 -17.28 -52.17 -102.80 -161.71 2.87 -0.38 -14.27 -29.03 -42.42 6.99 24.54 66.06 93.27 126.38 7.10 18.78 58.20 104.51 156.39 1.63 2.91 8.33 20.32 42.09 -0.78 10.13 -9.94 -13.02 -11.95

5.62 4.36 23.16 38.03 8.73 2.31 6.41 14.10 6.03 -11.66 7.87 1.33 -16.31 -40.24 -82.58 1.40 -10.04 -50.94 -93.06 -157.50 2.10 0.56 -16.15 -27.15 -40.13 5.60 26.48 62.92 90.16 122.03 3.56 20.63 60.74 108.26 162.97 -0.08 1.81 14.39 34.98 59.72 1.38 -2.13 -2.42 -4.08 -2.72

3.69 1.71 29.06 10.05 11.38 3.09 7.15 -7.92 13.53 -5.78 6.08 0.38 -2.69 -32.10 -62.17 0.76 -7.65 -37.28 -89.05 -145.09 0.70 4.37 -7.59 -23.71 -28.49 5.92 34.39 72.55 92.88 129.34 4.36 29.81 76.70 118.91 180.59 -2.03 5.94 26.18 53.59 89.76 0.39 -5.52 -6.06 10.16 7.81 !-----------------LATERAL FORCE VALUES--------------------------------------- ! No. of pnt Conversion ! factor ! pnt1 .... pnt225 ! LATERAL_FORCE_DATA_LIST 225 4.448 234.08 585.56 1000.29 1307.77 1603.78 269.79 628.82 1040.78 1331.72 1624.83 213.70 565.29 974.49 1198.82 1387.74 150.79 452.18 752.21 885.23 960.13 11.52 50.58 199.87 199.50 208.75 -116.75 -367.42 -618.68 -683.16 -857.81 -224.15 -588.24 -1001.01 -1235.88 -1488.88 -242.08 -612.70 -1059.55 -1344.53 -1658.66 -213.99 -597.29 -988.14 -1343.86 -1689.35

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234.40 572.75 981.30 1352.37 1698.90 239.27 647.77 1007.37 1357.22 1666.30 252.34 603.75 1033.50 1288.76 1483.64 167.55 481.45 826.41 962.64 1028.74 32.23 78.77 231.31 250.14 254.32 -122.59 -423.13 -552.58 -613.52 -607.61 -208.93 -576.28 -948.45 -1149.44 -1314.69 -261.05 -634.90 -1064.15 -1338.52 -1581.84 -241.50 -607.16 -1021.87 -1322.30 -1598.25

210.20 578.56 968.72 1344.05 1730.40 237.91 600.60 1025.67 1377.57 1733.03 226.60 629.48 1084.97 1354.12 1575.22 154.74 496.21 878.72 1028.03 1095.59 34.37 74.19 240.00 284.42 283.85 -130.29 -339.00 -509.04 -543.75 -555.05 -226.48 -557.52 -884.91 -1083.18 -1175.12 -270.70 -595.22 -1059.76 -1314.74 -1564.43 -254.64 -602.76 -1032.71 -1313.22 -1609.96

238.28 531.25 945.70 1305.28 1786.96 227.13 594.51 1038.87 1365.33 1733.29 221.76 633.49 1135.31 1375.28 1619.82 195.50 505.90 899.88 1059.92 1135.28 28.51 68.59 241.99 311.15 331.84 -145.10 -319.56 -464.11 -499.27 -500.83 -230.33 -548.99 -815.88 -991.78 -1108.36 -230.62 -597.10 -1009.76 -1261.43 -1504.09 -218.36 -570.13 -1049.72 -1344.94 -1589.60

228.49 564.69 954.06 1332.84 1687.50 221.19 595.52 1019.74 1378.35 1749.40 224.63 590.58 1108.01 1408.87 1707.09 178.96 474.70 918.87 1125.97 1242.75 42.58 65.26 230.69 306.58 428.45 -144.43 -290.91 -368.02 -398.98 -394.66 -224.99 -494.65 -761.78 -886.03 -941.20 -246.51 -563.13 -980.33 -1249.57 -1462.88 -239.34 -567.10 -1050.56 -1348.66 -1611.11

521-Tire Road Data FilesThe road data files used with the 521-Tire are unique and cannot be used with any other tire model. The data files are fully described by the following two examples.

Road Data File 521_pnt_follow.rdfThis example file shows that, if you use the Point Follower method and indicate it in the associated tire property file, the road_profile_type parameter must be set to FLAT.

$--------------------------------------------------------MDI_HEADER[MDI_HEADER]FILE_TYPE = 'rdf'FILE_VERSION = 5.00

31

FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'flat 2d contact road for testing purposes'$-------------------------------------------------------------UNITS[UNITS] LENGTH = 'mm' FORCE = 'newton' ANGLE = 'radians' MASS = 'kg' TIME = 'sec'$-------------------------------------------------------------MODEL[MODEL] METHOD = '5.2.1' FUNCTION_NAME = 'ARC913'$--------------------------------------------------------PARAMETERSROAD_PROFILE_TYPE = FLATINITIAL_HEIGHT = 0.000

Road Data File 521_equiv_plane.rdfThe following example shows which data the road data file must contain if the Equivalent Plane method is used and specified in the associated tire property file. The main difference with the road data file used in association with the Point Follower method is that here the ROAD_PROFILE_TYPE parameter is set to INPUT and a ROAD_INPUT_DATA_LIST is specified.

$---------------------------------------------------------MDI_HEADER[MDI_HEADER]FILE_TYPE = 'rdf'FILE_VERSION = 5.00FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'5.2.1 input road for testing purposes'$--------------------------------------------------------------UNITS[UNITS] LENGTH = 'mm' FORCE = 'newton' ANGLE = 'radians' MASS = 'kg' TIME = 'sec'$--------------------------------------------------------------MODEL[MODEL] METHOD = '5.2.1' FUNCTION_NAME = 'ARC913'$---------------------------------------------------------PARAMETERSROAD_PROFILE_TYPE = INPUTINITIAL_HEIGHT = 0.000ROAD_INPUT_DATA_LIST 23, 1 -10000.00, 00.00 1740.00, 00.00 1740.94, 1.92 1743.73, 3.55

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1748.31, 4.59 1754.55, 4.79 1762.32, 3.88 1771.41, 1.65 1781.61, 7.89 1792.65, 2.47 1804.28, 5.26 1816.20, 6.20 1828.12, 5.26 1839.75, 2.47 1850.79, 7.89 1860.99, 1.65 1870.08, 3.88 1877.85, 4.79 1884.09, 4.59 1888.67, 3.55 1891.46, 1.92 1892.40, 00.00 40000.00, 00.00

Using the UA-Tire ModelLearn about using the University of Arizona (UA) tire model:

• Background Information

• Tire Model Parameters

• Force Evaluation

• Operating Mode: USE_MODE

• Tire Carcass Shape

• Property File Format Example

• Contact Methods

Background Information for UA-TireThe University of Arizona tire model was originally developed by Drs. P.E. Nikravesh and G. Gim. Reference documentation: G. Gim, Vehicle Dynamic Simulation with a Comprehensive Model for Pneumatic Tires, PhD Thesis, University of Arizona, 1988. The UA-Tire model also includes relaxation effects, both in the longitudinal and lateral direction.

The UA-Tire model calculates the forces at the ground contact point as a function of the tire kinematic states, see Inputs and Output of the UA-Tire Model. A description of the inputs longitudinal slip κ, side slip α and camber angle can be found in About Tire Kinematic and Force Outputs. The tire

deflection and deflection velocity are determined using either a point follower or durability contact model. For more information, see Road Models in Adams/Tire. A description of outputs, longitudinal force Fx, lateral force Fy, normal force Fz, rolling resistance moment My and self aligning moment Mz is given in About Tire Kinematic and Force Outputs. The required tire model parameters are described in Tire Model Parameters.

Inputs and Output of the UA-Tire Model

γ

ρ ρ·

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12


13


wheel rotational velocity , and the effective rolling radius Re:



When the UA Tire is used for the force calculation the slip quantities during positive Vsx (driving) are defined as:


Note that for realistic tire forces the slip angle is limited to 45 degrees and the longitudinal slip Ss

(= ) in between -1 (locked wheel) and 1.

Lagged longitudinal and lateral slip quantities (transient tire behavior)In general, the tire rotational speed and lateral slip will change continuously because of the changing interaction forces in between the tire and the road. Often the tire dynamic response will have an important role on the overall vehicle response. For modeling this so-called transient tire behavior, a first-order system is used both for the longitudinal slip as the side slip angle, . Considering the tire belt as a stretched string, which is supported to the rim with lateral spring, the lateral deflection of the belt can be estimated (see also reference [1]). The figure below shows a top-view of the string model.


ω

Vsx Vx ΩRe–=

Vsy Vy=

κ α

κVsxVx-------- and αtan–

VsyVx---------= =

κVsxVr-------- and αtan–

VsyVr---------= =

Vr ReΩ=

ακ

κ

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When the tire is rolling, the lateral deflection depends on the lateral slip speed; at standstill, the deflection depends on the relaxation length, which is a measure for the lateral stiffness of the tire. Therefore, with this approach, the tire is responding to a slip speed when rolling and behaving like a spring at standstill. When the UA Tire is used for the force calculations, at positive Vsx (traction) the Vx should be replaced by Vr in these differential equations.


1Vx------

tddv1 v1

σα------+ α( ) aφ+tan=

σα φ


15

Now the practical slip quantities, ’ and ’, are defined based on the tire deformation:

These practical slip quantities and are used instead of the usual and definitions for steady-state tire behavior. kVlow_x and kVlow_y are the damping rates at low speed applied below the LOW_SPEED_THRESHOLD speed. For the LOW_SPEED_DAMPING parameter in the tire property file yields:

kVlow_x= 100 · kVlow_y= LOW_SPEED_DAMPING

Tire Model ParametersDefinition of Tire Parameters

σx tddv1 Vx v1+ σ– αVsx=

κ α

κ'u1σκ------ kVlowxVsx–⎝ ⎠⎛ ⎞ Vx( )sin=

α'v1σα------⎝ ⎠⎛ ⎞ kVlowyvsy–⎝ ⎠⎛ ⎞atan=

κ' α' κ α

Note: If the tire property file's REL_LEN_LON or REL_LEN_LAT = 0, then steady-state tire behavior is calculated as tire response on change of the slip and .κ α

Symbol:Name in tire property file: Units*: Description:

r1 UNLOADED_RADIUS

L Tire unloaded radius

kz VERTICAL_STIFFNESS

F/L Vertical stiffness

cz VERTICAL_DAMPING

FT/L Vertical damping

Cr ROLLING_RESISTANCE

L Rolling resistance parameter

Cs CSLIP F Longitudinal slip stiffness, C CALPHA F/A Cornering stiffness, C CGAMMA F/A Camber stiffness,UMIN UMIN - Minimum friction coefficient (Sg=1)

κ∂∂Fx

κ 0=αα∂

∂Fy

α 0=γγ∂

∂Fy

γ 0=

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* L=length, F=force, A=angle, T=time

Force Evaluation in UA-Tire• Normal Force

• Slip Ratios

• Friction Coefficient

Normal ForceThe normal force F z is calculated assuming a linear spring (stiffness: k z ) and damper (damping constant c z ), so the next equation holds:

If the tire loses contact with the road, the tire deflection and deflection velocity become zero so the resulting normal force F z will also be zero. For very small positive tire deflections the value of the damping constant is reduced and care is taken to ensure that the normal force Fz will not become negative.

In stead of the linear vertical tire stiffness cz , also an arbitrary tire deflection - load curve can be defined in the tire property file in the section [DEFLECTION_LOAD_CURVE], see also the Property File Format Example. If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection datapoints with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify VERTICAL_STIFFNESS in the tire property file but it does not play any role.

Slip RatiosFor the calculation of the slip forces and moments a number of slip ratios will be introduced:

Longitudinal Slip Ratio: Ss

The absolute value of longitudinal slip ratio, Ss, is defined as:

Where κ is limited to be within the range -1 to 1.

UMAX UMAX - Maximum friction coefficient (Ssg=0)x REL_LEN_LON L Relaxation length in longitudinal directiony REL_LEN_LAT L Relaxation length in lateral direction

Symbol:Name in tire property file: Units*: Description:

σσ

Fz kzρ czρ·+=

ρ ρ·

Ss κ=

17

Lateral Slip Ratios: Sα , Sγ , Sαγ

The lateral slip ratio due to slip angle, , is defined as:

The lateral slip ratio due to inclination angle, S , is defined as:

A combined lateral slip ratio due to slip and inclination angles, S , is defined as:

where is the length of the contact patch.

Comprehensive Slip Ratio: Ssαγ

A comprehensive slip ratio due to longitudinal slip, slip angle, and inclination angle may be defined as:

Sα

Sα* αtan during braking

1 Ss–( ) αtan during traction

Sα min 1.0 Sα*,( )

=

=

γ

Sγ γsin=

αγ

Sα*

α l γsin2rl

------------–tan during braking

1 Ss–( ) αl γsin2rl

------------tan during traction=

l 8r1ρ=

Sαγ min 1.0 S*αγ,( )=

S*sαγ Ss

2 S2αγ+

Sαγ min 1.0 S*αγ,( )=

=

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18

Friction CoefficientThe resultant friction coefficient between the tire tread base and the terrain surface is determined as a function of the resultant slip ratio (Ss ) and friction parameters (UMAX and UMIN ). The friction parameters are experimentally obtained data representing the kinematic property between the surfaces of tire tread and the terrain.

A linear relationship between Ss and , the corresponding road-tire friction coefficient, is assumed. The figure below depicts this relationship.

Linear Tire-Terrain Friction Model

This can be analytically described as:

μ = UMAX - (UMAX - UMIN) * Ssαγ

The friction circle concept allows for different values of longitudinal and lateral friction coefficients ( x

and y) but limits the maximum value for both coefficients to . See the figure below.

Friction Circle Concept

αγ

αγ μ

μμ μ

19

The relationship that defines the friction circle follows:

or and

where:

Slip Forces and MomentsTo compute longitudinal force, lateral force, and self-aligning torque in the SAE coordinate system, you must perform a test to determine the precise operating conditions. The conditions of interest are:

μxμ-----⎝ ⎠⎛ ⎞

2 μyμ-----⎝ ⎠⎛ ⎞

2+ 1=

μx μ βcos= μy μ βsin=

βcosSs

Ssαγ---------- and βsin

Sαγ

Ssαγ----------= =

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20

• Case 1:

• Case 2: and

• Case 3: and

• Forces and moments at the contact point

The lateral force Fh can be decomposed into two components: Fha and Fhg. The two components are in the same direction if a· g < 0 and in opposite direction if 0.

Case 1. αγ < 0

Before computing the longitudinal force, the lateral force, and the self-aligning torque, some slip parameters and a modified lateral friction coefficient should be determined. If a slip ratio due to the critical inclination angle is denoted by S c, then it can be evaluated as:

If Ssc represents a slip ratio due to the critical (longitudinal) slip ratio, then it can be evaluated as:

If a slip ratio due to the critical slip angle is denoted by S c, then it can be determined as:

when .

The term critical stands for the maximum value which allows an elastic deformation of a tire during pure slip due to pure slip ratio, slip angle, or inclination angle. Whenever any slip ratio becomes greater than its corresponding critical value, an elastic deformation no longer exists, but instead complete sliding state represents the contact condition between the tire tread base and the terrain surface.

A nondimensional slip ratio Sn is determined as:

where:

αγ 0<

αγ 0≥ CαSα CγSγ≥

αγ 0≥ CαSα CγSγ<

αγ <

γ

Sγc μFzCγ------=

Ssc 3μFzCs-----=

α

SαcCsCα------- Ssc

2 Ss2– 3Cγ

Sγ

Cα-------–=

Ss Ssc≤

SnB2 B2

2 B1B3–+B1

-------------------------------------------=

21

A nondimensional contact patch length is determined as:

A modified lateral friction coefficient is evaluated as:

where is the available friction as determined by the friction circle.

To determine the longitudinal force, the lateral force, and the self-aligning torque, consider two subcases separately. The first case is for the elastic deformation state, while the other is for the complete sliding state without any elastic deformation of a tire. These two subcases are distinguished by slip ratios caused by the critical values of the slip ratio, the slip angle, and the inclination angle. Specifically, if all of slip ratios are smaller than those of their corresponding critical values, then there exists an elastic deformation state, otherwise there exists only complete sliding state between the tire tread base and the terrain surface.

(i) Elastic Deformation State: , , and

In the elastic deformation state, the longitudinal force F , the lateral force F , and three components of the self-aligning torque are written as functions of the elastic stiffness and the slip ratio as well as the normal force and the friction coefficients, such as:

B1 3μFz( )2 3CγSγ( )2

B2

–

2CαSαCγSγ

B3 CsSs( )2 CαSα( )2+[ ]–

=

=

=

ln 1 Sn–=

μym( )

μym( ) μy

CγSγ

Fz-----------⎝ ⎠⎛ ⎞–=

μy μ βsin=

Sγ Sγc< Ss Ssc< Sα Sαc<

ξ τ

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22

where:

• is the offset between the wheel plane center and the tire tread base.

• is set to zero if it is negative.

• the length of the contact patch.

Mz is the portion of the self-aligning torque generated by the slip angle . Mzs and Mzs are other components of the self-aligning torque produced by the longitudinal force, which has an offset between the wheel center plane and the tire tread base, due to the slip angle and the inclination angle ,

respectively. The self-aligning torque Mz is determined as combinations of Mz , Mzs and Mzs .

(ii) Complete Sliding State: S S c, Ss Ssc, and S S c

In the complete sliding state, the longitudinal force, the lateral force, and three components of the self-aligning torque are determined as functions of the normal force and the friction coefficients without any elastic stiffness and slip ratio as:

Fξ CsSsln2 μxFz 1 3ln

2– 2ln3+( )

Fη

+

CαSsln2 μy

m( )Fz 1 3ln2– 2ln

3+( ) CγSγ

Mzα

+ +

CαSα12---– 2

3---ln+⎝ ⎠

⎛ ⎞ 32---μy

m( )FzSn2+ lln

2

Mzsα23---CsSsSαln

33μxμyFz

2

5Cα---------------------- 1 10ln

3– 15ln4 6ln

5–+( )

Mzsγ

+

η Fξ

=

=

=

=

=

η Sγ rl2 l'2 4⁄–=

rl2 l2 4⁄–

l 8rlρ=

α α α γ

α γα α γ

γ ≥ γ ≥ α ≥ α

23

Case 2: 0 and C S C S

As in Case 1, a slip ratio due to the critical value of the slip ratio can be obtained as:

A slip ratio due to the critical value of the slip angle can be found as:

when Ss Ssc.

The nondimensional slip ratio Sn, is determined as:

where:

Fξ μxFz

Fη μyFz

Mzα 0

Mzαs3μxμyFz

2l5Cα

------------------------

Mzsγ η Fξ

=

=

=

=

=

α γ ≥ α α ≥ γ γ

Sγc 3μFzCγ------=

SαcCsCα------- Ssc

2 Ss2– 3Cγ

Sγ

Cα-------+=

≤

SnB2 B2

2 B1B3–+B1

-------------------------------------------=

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24

The nondimensional contact patch length ln is found from the equation ln = 1 - Sn, and the modified

lateral friction coefficient is expressed as:

For the longitudinal force, the lateral force and the self-aligning torque two subcases should also be considered separately. A slip ratio due to the critical value of the inclination angle is not needed here since the required condition for Case 2, C S C S , replaces the critical condition of the inclination angle.

(i) Elastic Deformation State: Ss Ssc and S Sac

In the elastic deformation state:

(ii) Complete Sliding State: Ss Ssc and S Sαχ

B1 3μFz( )2 3CγSγ( )2

B2

–

2CαSαCγSγ

B3 CsSs( )2 CαSα( )2+[ ]–

=

=

=

μym( )

μym( ) μy

CγSγ

Fz-----------⎝ ⎠⎛ ⎞+=

α α ≥ γ γ

< α <


2– 2ln3+( )

Fη

+

CαSsln2 μy

m( )Fz 1 3ln2– 2ln

3+( ) CγSγ

Mzα

+ +

CαSα12---– 2

3---ln+⎝ ⎠

⎛ ⎞ 32---μy

m( )FzSn2+ lln

2

Mzsα23---CsSsSαln

33μxμyFz

2

5Cα---------------------- 1 10ln

3– 15ln4 6ln

5–+( )

Mzsγ

+

η Fξ

=

=

=

=

=

≥ α ≥

25

Case 3: 0 and C S C S

Similar to Cases 1 and 2, slip ratios due to the critical values of the inclination angle and the slip ratio are obtained as:

The nondimensional slip ratio Sn, is expressed as:

where:

Fξ μxFz

Fη μyFz

Mzα 0

Mzαs3μxμyFz

2l5Cα

------------------------

Mzsγ η Fξ

=

=

=

=

=

α γ ≥ α α < γ γ

Sγc3μFz CαSα+

3Cγ--------------------------------

Ssc1Cs----- 3μFz( )2 CαSα 3CγSγ–( )–

=

=

SnB2 B2

2 B1B3–+B1

-------------------------------------------=

B1 3μFz( )2 3CγSγ( )2

B2

–

2CαSαCγSγ

B3 CsSs( )2 CαSα( )2+[ ]–

=

=

=

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26

For the longitudinal force, the lateral force, and the self-aligning torque, two subcases should also be considered similar to Cases 1 and 2. A slip ratio due to the critical value of the slip angle is not needed here since the required condition for Case 3, C S C S , replaces the critical condition of the slip angle.

(i) Elastic Deformation State: S S c and Ss Ssc

In the elastic deformation state, F and Mz can be written:

(ii) Complete Sliding State: S S c and Ss Ssc

In the complete sliding state, F , F , Mz , Mzs , and Mzs can be determined by using:

α α < γ γ

γ < γ <

η α


2– 2ln3+( )

Fη

+

CαSsln2 μy

m( )Fz 1 3ln2– 2ln

3+( ) CγSγ

Mzα

+ +

CαSα12---– 2

3---ln+⎝ ⎠

⎛ ⎞ 32---μy

m( )FzSn2+ lln

2

Mzsα23---CsSsSαln

33μxμyFz

2

5Cα---------------------- 1 10ln

3– 15ln4 6ln

5–+( )

Mzsγ

+

η Fξ

=

=

=

=

=

γ ≥ γ ≥

ξ η α α γ

Fξ μxFz

Fη μyFz

Mzα 0

Mzαs3μxμyFz

2l5Cα

------------------------

Mzsγ η Fξ

=

=

=

=

=

27

respectively. The longitudinal force F , the lateral force F , and three components of the self-aligning

torques, Mz , Mzs , and Mzs , always have positive values, but they can be transformed to have

positive or negative values depending on the slip ratio s, the slip angle , and the inclination angle in the SAE coordinate system.

Tire Forces and Moments in the SAE Coordinate SystemFor the general formulations of the longitudinal force Fx, lateral force Fy, and self-aligning torque Mz, in the SAE coordinate system, the three possible combinations of the slip ratio, the slip angle, and the inclination angle are also considered.

Longitudinal Force:

Fx = sin(κ) F , for all cases

Lateral Force:

Fy = -sin( ) F , for cases 1 and 2

Fy = sin( ) F , for case 3

Self-aligning Torque:

Mz = sin( ) Mz - sin( ) [-sin( ) Mzs + sin( )Mzs ]

Rolling Resistance Moment:

My = -Cr Fz, for a forward rolling tire.

My = Cr Fz, for a backward rolling tire.

Operating Mode: USE_MODEYou can change the behavior of the tire model through the switch USE_MODE in the [MODEL] section of the tire property file.

• USE_MODE = 0: Steady-state forces and moments • The tire forces and moments react instantaneously to changes in the tire kinematic states.• USE_MODE = 1: Transient tire behavior• The tire will have a lagged response because of the so-called relaxation length in both

longitudinal and lateral direction. See Lagged Longitudinal and Lateral Slip Quantities (transient tire behavior).

• The effect of the relaxation lengths will be most pronounced at low forward velocity and/or high excitation frequencies.

• USE_MODE = 2: Smoothing of forces and moments on startup of the simulation

ξ ηα α γ

α γ

ξ

α η

γ η

α α κ α α γ γ

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28

• When you indicate smoothing by setting the value of use mode in the tire property file, Adams/Tire smooths initial transients in the tire force over the first 0.1 seconds of simulation. The longitudinal force, lateral force, and aligning torque are multiplied by a cubic step function of time. (See STEP in the Adams/Solver online help.)

Longitudinal Force FLon = S*FLon

Lateral Force FLat = S*FLat

Aligning Torque Mz = S*Mz

Tire Carcass ShapeYou can optionally supply a tire carcass cross-sectional shape in the tire property file in the [SHAPE] block. The 3D-durability, tire-to-road contact algorithm uses this information when calculating the tire-to-road volume of interference. If you omit the [SHAPE] block from a tire property file, the tire carcass cross-section defaults to the rectangle that the tire radius and width define.

You specify the tire carcass shape by entering points in fractions of the tire radius and width. Because Adams/Tire assumes that the tire cross-section is symmetrical about the wheel plane, you only specify points for half the width of the tire. The following apply:

• For width, a value of zero (0) lies in the wheel center plane.• For width, a value of one (1) lies in the plane of the side wall.• For radius, a value of one (1) lies on the tread.

For example, suppose your tire has a radius of 300 mm and a width of 185 mm and that the tread is joined to the side wall with a fillet of 12.5 mm radius. The tread then begins to curve to meet the side wall at >+/- 80 mm from the wheel center plane. If you define the shape table using six points with four points along the fillet, the resulting table might look like the shape block that is at the end of the property format example (see SHAPE).

Property File Format Example$--------------------------------------------------------MDI_HEADER[MDI_HEADER]FILE_TYPE = 'tir' FILE_VERSION = 2.0FILE_FORMAT = 'ASCII'(COMMENTS) {comment_string}'Tire - XXXXXX''Pressure - XXXXXX''TestDate - XXXXXX''Test tire''New File Format v2.1'$-------------------------------------------------------------units[UNITS]LENGTH = 'meter'FORCE = 'newton'ANGLE = 'rad'

29

MASS = 'kg'TIME = 'sec'$-------------------------------------------------------------model[MODEL]! use mode 1 2 3 ! ------------------------------------------! relaxation lengths X ! smoothing X !PROPERTY_FILE_FORMAT = 'UATIRE'USE_MODE = 2$-------------------------------------------------------dimension[DIMENSION]UNLOADED_RADIUS = 0.295WIDTH = 0.195ASPECT_RATIO = 0.55$---------------------------------------------------------parameter[PARAMETER]VERTICAL_STIFFNESS = 190000VERTICAL_DAMPING = 50ROLLING_RESISTANCE = 0.003CSLIP = 80000CALPHA = 60000CGAMMA = 3000UMIN = 0.8UMAX = 1.1REL_LEN_LON = 0.6REL_LEN_LAT = 0.5$-------------------------------------------------------------shape[SHAPE]{radial width}1.0 0.0 1.0 0.2 1.0 0.4 1.0 0.6 1.0 0.8 0.9 1.0$---------------------------------------------------------load_curve$ For a non-linear tire vertical stiffness (optional)$ Maximum of 100 points[DEFLECTION_LOAD_CURVE]{pen fz}0.000 0.00.001 212.00.002 428.00.003 648.00.005 1100.00.010 2300.00.020 5000.00.030 8100.0

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30

Contact MethodsThe UA-Tire Model supports the following roads

• 2D roads, see Using the 2D Road Model.• 3D Splie roads, see Adams/3D Spline Road Model

The UA-Tire Model uses a one point of contact method; therefore, the wavelength of road obstacles must be longer than the tire radius for realistic output of the model.

• 3D Shell roads, see Adams/Tire 3D Shell Road Model

Using FTire Tire ModelLearn about:

• About FTire

• Modeling Approach

• Using FTire with Road Models

• Using FTire with Adams

• Parameters • About FTire Parameters

• Procedure for Parameterizing FTire

• List of FTire Parameters

• About the Tire Data File

• Choosing Operating Conditions

This help describes the Flexible Ring Tire Model (FTire)™, as it is invoked from Adams.

© Michael Gipser, Cosin Consulting

About FTireThe tire model, FTire (Flexible ring tire model), is a sophisticated tire force element. You can use it in MBS-models for vehicle-ride comfort investigations and other vehicle dynamics simulations on even or uneven roadways.

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12

The main benefits of FTire are:

• Fully nonlinear.• Valid in frequency domain up to 120 Hz, and beyond.• Valid for obstacle wave lengths up to half the length of the contact patch, and less.• Parameters, among others, are the natural frequencies and damping factors of the linearized

model, and easy-to-obtain global static properties.• Models both the in-plane and out-of-plane forces and moments.• Computational effort no more than 5 to 20 times real time, depending on platform and model

level.• High accuracy when passing single obstacles, such as cleats and potholes.• Applicable in extreme situations like many kinds of tire misuse and sudden pressure loss.• Sufficiently accurate in predicting steady-state tire characteristics.

In contrast to other tire models, FTire does not need any complicated road data preprocessing. Rather, it takes and resolves road irregularities, and even extremely high and sharp-edged obstacles, just as they are defined.

We recommend that you visit www.ftire.com, to learn more about FTire theory, validation, data supply, and application. Also, at the FTire Web site, you will be kept informed about the latest FTire improvements, and how to receive them. In the download section, you will find a set of auxiliary programs, called FTire/tools for Windows™. These tools help to analyze and parameterize an FTire

http://www.ftire.com/

13

Model. FTire/tools is free for FTire licensees. It comprises static, steady-date, and modal analysis, linearization, data estimation, identification and validation tools, road data visualization, and more. In the site's documentation section, you will find a more detailed and permanently updated FTire documentation, together with as some additional literature.

Modeling ApproachFTire uses the following modeling approach:

• The tire belt is described as an extensible and flexible ring carrying bending stiffnesses, elastically founded on the rim by distributed, partially dynamic stiffnesses in radial, tangential, and lateral directions. The degrees of freedom of the ring are such that rim in-plane as well as out-of-plane movements are possible. The ring is numerically approximated by a finite number of discrete masses, the belt elements. These belt elements are coupled with their direct neighbors by stiff springs and by bending stiffnesses both in-plane and out-of-plane. Belt In-Plane and Out-Of-Plane Bending Stiffness outlines in-plane and out-of-plane bending stiffness placing. In-plane bending stiffness is realized by means of torsional springs about the lateral axis. The torsional deflection of these springs is determined by the angle between three consecutive belt elements, projected onto the rim mid-plane. Similarly, the out-of-plane bending stiffness is described by means of torsional springs about the radial axis. Here, the torsional deflection is determined by the angle between three consecutive belt elements, projected onto the belt tangential plane. Note that in the figure, the yellow plates do not represent the belt elements themselves, but rather the connecting lines between the elements.

Belt In-Plane (left) and Out-Of-Plane (right) Bending Stiffness

• FTire calculates all stiffnesses, bending stiffnesses, and damping factors during preprocessing, fitting the prescribed modal properties (see list of data below).

Adams/Tire

14

• A number of massless tread blocks (5 to 50, for example) are associated with every belt element. These blocks carry nonlinear stiffness and damping properties in the radial, tangential, and lateral direction. The radial deflections of the blocks depend on the road profile, focus, and orientation of the associated belt elements. FTire determines tangential and lateral deflections using the sliding velocity on the ground and the local values of the sliding coefficient. The latter depends on ground pressure and sliding velocity.

• FTire calculates all six components of tire forces and moments acting on the rim by integrating the forces in the elastic foundation of the belt.

Because of this modeling approach, the resulting overall tire model is accurate up to relatively high frequencies both in longitudinal and in lateral directions. There are few restrictions in its applicability with respect to longitudinal, lateral, and vertical vehicle dynamics situations. FTire deals with large- and/or short-wave-length obstacles. It works out of, and up to, a complete standstill, with no additional computing effort nor any model switching. Finally, it is applicable with high accuracy in such delicate simulations as ABS braking on extremely uneven roadways, and so on.

In a full 3D variant, FTire additionally takes into account belt element rotation and bending about the circumferential axis. These new degrees of freedom enable FTire to use contact elements that are distributed not only along a single line, but over the whole contact patch. You can choose the arrangement of the contact elements to be either randomly distributed, or distributed along several parallel lines.

In the full 3D variant, belt torsion about the circumferential axis is described by:

• Torsional stiffnesses between belt elements and rim, about circumferential axis (represented by red torsion springs in the left side of the figure, Belt).

• Torsional stiffnesses between adjacent belt elements, about circumferential axis (represented by blue torsion springs in the left side of figure, Belt).

The right side of the figure, Belt outlines the belt bending stiffness about the circumferential axis. This is done in a somewhat simplified manner. Actually, lateral belt bending is taken into account by introducing a parabolic shape function for each belt element. The curvature of this shape function is treated as a belt elements’ additional degree of freedom.

Belt Torsional and Twisting Stiffness, and Belt Lateral Bending Stiffness

Note: Radial, tangential, and lateral are relative to the orientation of the belt element, whereas sliding velocity is the block end-point velocity projected onto the road profile tangent plane. By polynomial interpolation, certain precautions have been taken not to let the ground pressure distribution mirror the polygonal shape of the belt chain.

15

You should chose the full 3D variant, which takes about 30% more computing time, in situations where a considerable excitation of tire vibrations in lateral direction is expected. This, for example, will happen when the tire runs over cleats that are placed in an oblique direction relative to the tire rolling direction. Similarly, such an excitation will happen when the tire is running over obstacles with large camber angle.

Optionally, FTire can take into account tire non-uniformity, that is, a harmonic variation of vertical or longitudinal stiffness, as well as static and dynamic imbalance, conicity, ply-steer, and geometrical run-out.

All stiffness values may depend on the actual inflation pressure. To take full advantage of that option, it is necessary to provide basic FTire input data, such as radial stiffness data and natural frequencies at two different pressure values. Actual inflation pressure is one of the ‘operating conditions variables,’ which can be made time-dependent, and therefore, can be changed even during a simulation.

There are two more operating conditions: tread depth and model level. The latter signal allows you to switch between the reduced variant of FTire (all contact elements are arranged in one single line near the rim mid-plane), and the full 3D variant (contact elements cover the whole contact patch).

The kernel of the FTire implementation is an implicit integration algorithm (BDF) that calculates the belt shape. The integrator runs parallel but synchronized with the Adams main integrator. By using this specialized implicit BDF integrator, you can choose the belt extensibility so it is extremely small. This also allows the simulation of an inextensible belt without any numerical drawbacks.

Using FTire with Road ModelsFTire supports all MSC road definitions, including Motorsports and all 3D roads. It also supports several customer-specific and third-party roads. For more information about available road descriptions, please contact [email protected].

Adams/Tire

16

Using FTire with AdamsFTire is a high-resolution tire model, with respect to road irregularities and tire vibration modes. To take full advantage of that precision, we recommend that you choose a small step size for the Adams integrator. There should be a minimum of 1,000 steps per one second simulation time (that is, an output time step of 1 ms or less).

Controlling integrator step size in:

• Adams/Car

• Adams/Chassis

• Adams/View

• Adams/Solver

Controlling Integrator Step Size in Adams/CarIn Adams/Car, you can control the integrator step size by selecting:

Settings → Solver → Dynamics

and entering 1ms in the Hmax text box.

Alternatively, you can edit the driver control file (.dcf) that Adams/Car automatically generates when performing a new dynamic maneuver. In that file, override the integrator step size, which is defined in [EXPERIMENT] block, by entering the value 0.001 or less. After editing the file, you can launch subsequent simulation experiments with the same driver's control (and, of course, the new integrator step size) by selecting the following from Adams/Car:

Simulate → Full-Vehicle Analysis → DCF Driven → Driver Control Files → Browse

and selecting the .dcf you just edited.

Controlling Integrator Step Size in Adams/ChassisIn Adams/Chassis, you can control the integrator step size by setting the HMAX value to 0.001 or less. HMAX is defined by selecting the following from Adams/Chassis:

System file → Properties → system_parameters → solver → hmax

Controlling Integrator Step Size in Adams/ViewIn Adams/View, you can control the integrator step size by checking:

Settings → Solver → Dynamics → Customized Settings size, Min Step Size, and Max Step Size.

Controlling Integrator Step Size in Adams/SolverIn Adams/Solver, you can control the integrator step size by setting INTEGRATOR/HMAX to the desired value in the Adams dataset (adm).

17

FTire Parameters• About FTire Parameters

• Procedure for Parameterizing FTire

• Listing of FTire Parameters

About FTire ParametersFTire parameters can be divided into several groups. There are parameters that define:

• Tire size and geometry• Stiffness, damping, and mass distribution of the belt/sidewall structure• Tire imperfections (non-uniformity, imbalance, conicity, and so on)• Stiffness and damping properties of the tread rubber• Friction characteristics of the tread rubber• Numerical properties of the model

For convenience, FTire tries to use data that can be measured as easy as possible. As a consequence, the number of basic data might be larger than the number of internal parameters defined by these basic parameters.

For example, the following four parameters together, after preprocessing, actually result in only two values used in FTire: compression and shear stiffness of the idealized blocks that represent tread rubber:

• tread_depth

• tread_base_height

• stiffness_tread_rubber

• tread_positive

Also, sometimes different combinations of parameters are possible. This is true especially for data of the second group, which determine the structural stiffness and damping properties of FTire. Your choice of which combination of parameters to supply depends on the types of measurements that are available and their accuracy.

Moreover, it is possible to prescribe over-determined subsets of parameters. For example, you may define the belt in-plane bending stiffness by prescribing the frequency of the first bending mode, and at the same time the radial stiffness on a transversal cleat. Both parameters are strongly influenced by the bending stiffness, but might contradict each other.

In such a case, FTire automatically recognizes that the system of equations to be solved is over-determined, and applies an appropriate solver (Householder QR factorization) to determine the solution in the sense of least squares fit. That means, FTire is looking for a compromise to meet both conditions as much as possible. Users can control the compromise by optionally defining weights for the contradicting conditions.

Adams/Tire

18

Note that, among others, FTire uses modal data to calculate internal structural stiffness and damping coefficients. They are processed in such a way that the mathematical model, for small excitations, shows exactly the measured behavior in the frequency domain. FTire is not a modal model, nor is it linear.

First Six Vibration Modes Of An Unloaded Tire With Fixed Rim

When parametrizing FTire, the bending mode frequencies rather sensitively influence the respective bending stiffness. As an alternative, determining the radial stiffness both on a flat surface and on a short obstacle (cleat) is an inexpensive and very accurate way to get both the vertical stiffness between belt nodes and rim and the in-plane bending stiffness.

Other ways to determine the bending stiffness (and other data, as well) are to use the software tools FTire/fit (time- and frequency-domain parameter identification) and FTire/estim (qualified parameter estimation by comparison with a reference tire). For more information, see www.ftire.com.

Unfortunately, there is no direct analogy of the ‘radial stiffness on cleat’ measuring procedure to get the out-of-plane bending stiffness. But this parameter does not seem to be as relevant as the in-plane bending stiffness for ride comfort and durability. An indirect, but also very accurate, way to validate the out-of-plane bending stiffness is to check resulting side-force and self-aligning characteristic. The cornering stiffness, the pneumatic trail, as well as the difference between maximum side force and side force for very large side-slip angles, are very sensitively determined both by the tread rubber friction characteristic and by the out-of-plane bending stiffness. Similarly, the fourth mode (see figure, First Six Vibration Modes Of An Unloaded Tire With Fixed Rim), being itself determined by the stiffness between belt nodes and rim in lateral direction, very strongly influences the side-slip angle where maximum side force occurs.

Procedure for Parameterizing FTireA typical procedure to parametrize FTire might be:

1. Either from tire data sheets, by some simple and inexpensive measurements, or directly from the tire supplier, obtain:

• Tire size, load index, and speed symbol • Rolling circumference • Rim diameter • Tread width • Tire mass


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• Tread depth • Rubber height over steel belt • Shore-A stiffness or Young's modulus of tread rubber • Tread pattern positive

2. Determine the natural frequencies and damping moduli of the first six modes, for an unloaded, inflated tire, where the rim is fixed. Normally, you do this by exciting the tire structure with an impulse hammer, measuring the time histories of at least four acceleration sensors in all three directions, distributed along the tire circumference, and processing these using an FFT signal analyzer. Optionally, repeat this step for a second inflation pressure value.

3. Determine the tire radial stiffness on a flat surface and on a short obstacle, for one or two inflation pressure value(s).

4. Determine (or estimate) the lateral belt curvature radius from the unloaded tire's cross-section. Determine the belt lateral bending stiffness to get a reasonable pressure distribution in the lateral direction.

5. Determine (or estimate) tread rubber adhesion and sliding friction coefficients for ground pressure values 0.5 bar, 2 bar, and 10 bar.

6. Take natural frequencies and damping moduli of modes 1, 2, and 4, together with the radial stiffness on flat surface and on a cleat, for one or two inflation pressure value(s), as well as the remaining basic data. These values result in a first, complete FTire input file for the basic variant (belt circumferential rotation, twisting, and bending not taken in to account; all contact elements are arranged in one line).

7. Let FTire preprocess these data. Compare the resulting additional modal properties of the model with the modal data that are not used so far (modes 3, 5, and 6). If necessary, adjust the preprocessed data to find a compromise with respect to accuracy.

8. If respective measurements are available, validate the data determined so far by means of side force and aligning torque characteristics, and by measurements of vertical and longitudinal force variations induced during rolling over cleats both with low and high speed. The validation can be extended to a full parameter fitting procedure by using TIRE/fit, as mentioned earlier.

9. Estimate the following additional data that are only relevant for 'out-of-plane' excitation: • Belt element torsional stiffness relative to rim (represented by red torsion springs between

yellow belt elements and gray rim in the figure, Belt)• Belt twisting stiffness (represented by blue torsion springs between adjacent yellow belt

elements in the figure, Belt)• Belt bending stiffness/damping about circumferential direction• Belt lateral curvature radius• Coupling coefficient between belt lateral displacement and belt rotation.

Start with the respective values of the sample data file. Then, adjust the values by fitting the model's response to obliquely oriented cleats and handling characteristics for large camber angles at the same time. This identification procedure can be made easier by using the the additional tool FTire/fit.

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Clearly, the performance of this procedure is not very easy in practice. On the other hand, every tire model that is accurate enough for ride comfort and durability calculations will need as much or even more data.

List of FTire ParametersThe following is a comprehensive list of all mandatory and optional FTire parameters. However, many items are explained in greater detail in the extended documentation to be downloaded from the restricted area in www.ftire.com. You will receive your pass-code from [email protected].

FTIRE_DATA Section Parameters

The parameter: Means:tire_section_width Tire section width as specified in the tire size designation (using

length unit as specified in the [UNITS] section).tire_aspect_ratio Tire aspect ratio as specified in the tire size designation. Unit is %.rim_diameter Rim diameter as specified in the tire size designation (using length

unit as specified in the [UNITS] section).rim_width Inner distance between the two rim flanges.load_index Load index of tire, as displayed in tire service description.tread_width Width of tread that comes into contact with the road under normal

running conditions at LI load, without camber angle.rolling_circumference Rolling circumference of tire under the following running

conditions:

• Free rolling at v = 60 km/h and zero camber angle• Vertically loaded by half of the maximum load

The circumference is the distance traveled with one complete wheel revolution.

tire_mass Overall tire mass.inflation_pressure Inflation pressure, at which tire data measurements have been

taken.inflation_pressure_2 Second inflation pressure, at which tire data measurements have

been taken (optional).stat_wheel_load_at_10mm_defl Static wheel load of the inflated tire, when it is deflected by 10

mm, with zero camber angle, on a flat surface, during stand-still, at very low friction value.


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stat_wheel_load_at_20mm_defl Static wheel load of the inflated tire, when it is deflected by 20 mm, with zero camber angle, on a flat surface, during stand-still, at very low friction value.

Note: Instead of using:

stat_wheel_load_at_10mm_defl and stat_wheel_load_at_20mm_defl

Note: You can equally define:

stat_wheel_load_at_20mm_defl and stat_wheel_load_at_40mm_defl.

Note: This will better fit typical operating conditions of truck tires. For extremely heavy vehicles, there are even more pairs of deflection values predefined. These can be found at the extended documentation at www.ftire.com.

dynamical_stiffening Increase of the overall radial stiffness at high speed as compared to radial stiffness during standstill. Unit is %.

speed_at_half_dyn_stiffening Running speed at which dynamic stiffening reaches half of the final value.

belt_extension_at_200_kmh Percentage of rolling circumference growth at a running speed of 200 km/h = 55.55 m/s = 124.3 mph, compared to low speed.

interior_volume Interior tire volume when the tire is mounted on the rim and inflated with inflation_pressure.

Note: This parameter is only needed if you specify the next parameter (volume_gradient) and it is nonzero.

volume_gradient Relative decrease in volume, of a small tire segment, when that segment is deflected vertically.

Note: This parameter is optional and only marginally affects the model’s behavior.

rel_long_belt_memb_tension The percentage by which inflation pressure forces in the belt region are compensated with membrane tension in longitudinal direction, as compared to the total compensation in lateral and longitudinal direction.

Note: This parameter is optional, and can only be calculated using a finite-element (FE) model, or estimated by parameter identification. A value of 70 to 80% seems to be appropriate for many tires. The value will increase with increasing belt lateral curvature radius.

The parameter: Means:


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f1 First natural frequency: in-plane, rigid-body rotation around wheel spin axis. Rim is fixed. See the figure, First Six Vibration Modes.

f2 Second natural frequency: rigid-body movement in fore-aft direction. Rim is fixed. See the figure, First Six Vibration Modes.

f4 Fourth natural frequency: out-of-plane, rigid-body rotation around road normal axis. Rim is fixed. See the figure, First Six Vibration Modes.

Note: f3 (out-of-plane, rigid-body movement) is not needed because it is closely related to f4.

At least one of:f5 Fifth natural frequency: first in-plane bending mode

(quadrilateral-shaped). Rim is fixed.belt_in_plane_bend_stiffn In-plane bending stiffness of the belt ring of deflated and

unloaded tire.wheel_load_at_10_mm_defl_cleat

Static wheel load of the inflated tire, when it is deflected by 10 mm, with zero camber angle, on a cleat as specified below, during stand-still. Cleat must be high enough that the tire does not touch the ground apart from the cleat. The cleat is oriented in the lateral direction, perpendicular to the tire’s rolling direction.

Note: For truck tires, you can specify wheel_load_at_20_mm_defl_ cleat, as well.

weight_f5weight_in_plane_bend_stiffnweight_wheel_load_cleat

If you provide at least two of the data on the previous page to define the in-plane bending stiffness, they constitute an over-determined system of equations for the respective FTire's internal stiffness values. FTire will try to find a compromise. You can control this compromise by setting these weight values. Their relative size controls, in a least-squares approach, the contribution of the respective parameter. If a weight is set to zero, the related parameter is completely ignored.

Note: The weights are optional. Default value is 1.cleat_width Width of cleat that was used to determine all parameters that

require a cleat:

wheel_load_at_10_mm_defl_ cleat

wheel_load_at_10_mm_defl_ cl_lo

and so on.

Note: Parameter is optional. Default value is 20 mm.


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cleat_bevel_edge_width Bevel edge width (measured after projection to x-y-plane) of cleat that was used to determine all parameters that require a cleat:

wheel_load_at_10_mm_defl_ cleat

wheel_load_at_10_mm_defl_ cl_lo

and so on.

Note: Parameter is optional. Default value is 0 mm.At least one of:f6 Sixth natural frequency: first out-of-plane bending mode (banana-

shaped).belt_out_of_plane_bend_stiffn Out-of-plane bending stiffness of the belt ring of inflated but

unloaded tire.weight_f6weight_out_of_plane_bend_st

If you provide both data above (f6 and belt_out_of_plane_bend_stiff) to define the out-of-plane bending stiffness, they constitute an over-determined system of equations for the respective FTire's internal stiffness values. FTire will try to find a compromise. You can control the compromise by setting these weight values. Their relative size controls, in a least-squares approach, the contribution of the respective parameter. If a weight is set to zero, the related parameter is completely ignored.

Note: The weights are optional. Default value is 1.D1 Damping of f1, between 0 and 1:

0 = undamped, ..., 1 = aperiodic limit caseD2 Damping of f2.D4 Damping of f4.

Note: D5 and D6 cannot be prescribed, but result from D1, D2, and D4.

belt_twist_stiffn Belt-twisting stiffness: if the mean torsion angle relative to the rim is 0, the value is the moment in longitudinal direction per 1 degree twist angle for a unit length belt segment. This value is independent on the number of belt segments.

Note: Only needed for full 3D variant. Unit is force*length2/angle.


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belt_torsion_stiffn Belt-torsional stiffness: if twist angle is 0, the value is the moment in longitudinal direction per 1 degree torsion angle relative to rim, for a unit-length belt segment. This value is independent on the number of belt segments.

Note: Only needed for full 3D variant.Unit is force/angle.belt_torsion_lat_displ_coupl If belt twist angle is 0, value is the kinematic belt torsion angle at

1 mm lateral belt displacement.

Note: Optional, and only needed for full 3D variant. Unit is angle/length. Default value is 0.

belt_lat_curvature_radius Curvature radius of belt cross section perpendicular to mid-plane.

Note: Optional, and only needed for full 3D variant. Default value is (nearly) infinity.

belt_lat_bend_stiffn Bending stiffness of belt elements about circumferential direction.

Note: Optional, and only needed for full 3D variant. Unit is force*length2. Default value is (nearly) infinity.

wheel_load_at_10_mm_defl_lo_cl

Wheel load at 10 mm deflection on longitudinal cleat. Static wheel load of the inflated tire, when it is deflected by 10 mm, with zero camber angle, on a cleat as specified above, during stand-still. Cleat must be high enough that the tire does not touch the ground apart from the cleat. The cleat is oriented in longitudinal direction, along foot-print centerline.

Note: This parameter is optional and you can specify it instead of, or in addition to, belt_lat_bend_stiffn. For truck tires, if you specify wheel_load_at_40_mm, FTire looks for wheel_load_at_20_mm_defl_ lo_cl instead.

weight_lat_bend_stweight_wheel_load_lo_cl

If you provide both data on the previous page (belt_lat_bend_stiffn and wheel_load_at_10_mm_defl_lo_cl) to define the lateral belt bending stiffness, they constitute an over-determined system of equations for the respective FTire's internal stiffness values. FTire will try to find a compromise. You can control the compromise by setting these weight values. Their relative size controls, in a least-squares approach, the contribution of the related parameter. If a weight is set to zero, the respective parameter is completely ignored.

Note: The weights are optional. Default value is 1.belt_lat_bend_damp Quotient of bending damping and bending stiffness of belt

elements about circumferential direction.

Note: Optional, and only needed for full 3D variant. Unit is time. Default value is 1 ms.


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f1_p2f2_p2f4_p2f5_p2f6_p2D1_p2D2_p2D4_p2belt_in_plane_bend_st_p2wheel_load_at_10_mm_defl_cl_p2wheel_load_at_20_mm_defl_cl_p2belt_out_of_plane_bend_st_p2belt_lat_bend_stiffn_p2belt_twist_st_p2belt_torsion_st_p2

If measurements for a second inflation pressure (inflation_pressure_2) are available, these are the respective values of the following taken at that pressure:

• f1 • f2 • f4 • f5 • f6 • D1 • D2 • D4 • belt_in_plane_bend_stiffn • wheel_load_at_10_mm_defl_cleat • wheel_load_at_20_mm_defl_cleat • belt_out_of_plane_bend_stiffn • belt_lat_bend_stiffn • belt_twist_stiffn • belt_torsion_stiffn

Note: These data are optional.tread_depth Mean groove depth in tread.tread_base_height Rubber height over steel belt for zero tread depth, which is the

distance between steel belt and grooves.stiffness_tread_rubber Stiffness of tread rubber in Shore-A units.tread_positive Percentage of gross tread contact area with respect to overall

footprint area (tread pattern positive).damping_tread_rubber Quotient of tread rubber damping modulus and tread rubber

elasticity modulus.

Note: Deflection/force phase-lag of elastomers is often assumed to be independent of excitation frequency. This behavior is not yet implemented in FTire; instead, viscous damping is used. The parameter damping_tread_rubber is nothing but the quotient of damper coefficient and spring stiffness of the coupling of blocks and belt. For that reason, the parameter carries the unit time.


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sliding_velocity The sliding velocity of a tread rubber block, when its friction coefficient reaches the my_sliding values.

blocking_velocity The sliding velocity of a tread rubber block, when its friction coefficient reaches the my_blocking values.

low_ground_pressure The first of three ground-pressure values that defines the pressure dependency of the friction coefficient. Default value is 0.1 bar.

med_ground_pressure The second of three ground-pressure values that defines the pressure dependency of the friction coefficient. Default value is 2 bar.

high_ground_pressure The third of three ground-pressure values that defines the pressure dependency of the friction coefficient. Default value is 10 bar.

my_adhesion_at_low_p Coefficient of adhesion friction (which is equal to static friction) between tread rubber and road, at first ground pressure value.

Note: For this parameter and the parameters in the following eight rows, you can still use the parameter names my_..._at_..._bar, used in the previous FTire version. To avoid confusion with the actual ground pressure values, however, we recommend you use the more general names.

my_sliding_at_low_p Coefficient of sliding friction, at a sliding velocity defined by parameter sliding_velocity, between tread rubber and road, at first ground pressure value.

my_blocking_at_low_p Coefficient of sliding friction, at a sliding velocity defined by parameter blocking_velocity, between tread rubber and road, at first ground pressure value.

my_adhesion_at_med_p Coefficient of adhesion friction (which is equal to static friction) between tread rubber and road, at second ground pressure value.

my_sliding_at_med_p Coefficient of sliding friction, at a sliding velocity defined by parameter sliding_velocity, between tread rubber and road, at second ground pressure value.

static_balance_weight Weight that would have put up on the rim horn for static balancing.

Note: Parameter is optional.static_balance_ang_position The angular position at the rim where the static balance weight

would have been placed.

Note: Parameter is optional.


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dynamic_balance_weight One of the two equal weights that would have been placed on the rim outer and inner horns for dynamic balancing.

Note: Parameter is optional.dynamic_balance_ang_position The angular position at the rim where the left dynamic balance

weight would have been placed.

Note: This parameter is optional.radial_non_uniformity Amplitude of the harmonic radial stiffness variation as percentage

of the mean radial stiffness.

Note: Parameter is optional.radial_non_unif_ang_position Angular position where radial stiffness reaches its maximum.

Note: This parameter is optional.tang_non_uniformity Amplitude of the harmonic tangential stiffness variation as

percentage of the mean tangential stiffness.

Note: Parameter is optional.tang_non_unif_ang_position Angular position where tangential stiffness reaches its maximum.

Note: Parameter is optional.conicity Small rotation angle of belt elements at zero moment, about

circumferential axis, resulting in a conical shape of the unloaded belt.

Note: Parameter is optional and can only be used with the full 3D variant. Nonzero conicity will cause a small side-force without side-slip angle. The sign of that force is independent of the tire’s rolling direction.

ply_steer_percentage Percentage of lateral belt displacement relative to radial belt displacement, when a radial force is applied.

Note: Ply-steer, besides conicity, is one of the reasons for nonzero side forces at zero side-slip angle. In contrast to the conicity side-force, this residual side force changes sign when the tire rolling direction is reversed.

run_out The maximum deviation of the local tire radius from the mean tire radius. Run-out is assumed to be a harmonic function of the angular position.

run_out_ang_position The angular belt element position relative to the rim, where maximum run-out occurs.

number_belt_segments Number of numerical belt segments. Maximum value is 200, but can be changed upon request.


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About the FTire Tire Data FileAs with all TeimOrbit files, entries in the [UNITS] block define the physical units of all parameters.

number_blocks_per_belt_segm Number of numerical blocks (= contact elements) per belt segment. Maximum value is 50, but can be changed upon request.

number_tread_strips Number of strips, into which the contact points are arranged in the full 3D variant, using an equal spacing.

Note: If value is greater than or equal to 1000, the contact points are scattered randomly over the tread. Alternatively, it is possible to place tread elements according to the actual tread pattern of the tire. This is done by specifying a bitmap file of the footprint. For more information, see the extended documentation at www.ftire.com.

If you specify neither number_tread_strips nor the bitmap file, FTire uses the basic FTire variant instead of the full 3D variant, regardless of the model-level specification in the operating_conditions section.

maximum_time_step Maximum integration time step allowed.

Note: You can call FTire with very large time steps (if this makes sense for your model). Internally, FTire uses multi-step integration with an internal time step that is chosen on basis of maximum_time_step. This internal time step is kept constant if the external time step does not change.

Changing the external time step can result in considerable longer computation time, because certain time-consuming preprocessing calculations have to be repeated. For that reason, you should avoid changing the external time step whenever possible.

BDF_parameter Numerical parameter to control the internal FTire implicit (BDF) integration scheme, which is independent of the Adams integrator.

0 = Euler explicit

0.5 = Trapezoidal rule

1 = Euler implicit

Theoretically, every value between 0 and 1 are allowed. 0.505 or greater is recommended.



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The basic parameters are preprocessed during initialization, resulting in the preprocessed parameters. These parameters are saved in a separate TeimOrbit-style file, which can be used in further simulations instead of the basic data file. By this, you can omit the preprocessing calculation phase, which may result in a considerable saving of time.

This preprocessed data file is a copy of the original one; the preprocessed data are appended after the bottom line, using a hexadecimal, space-saving coding. In contrast to earlier versions of FTire, it is possible to use this file for parameter changes instead of the original one.

You should, of course, not change the hexadecimal data but only the readable part of the file. The hexadecimal section does not only contain the preprocessed data, but a copy of the original one, as well. Moreover, it carries coded information about the FTire version that was used for creation.

This information helps to automatically determine whether or not an update of the preprocessed data is required. This means that whenever you change some basic data or you download a new FTire version, preprocessing will be repeated automatically, and the preprocessed data file saved in your current working directory. You can (and should) replace the FTire data file in your database with this one, without any loss of information.

From www.ftire.com, you can download a tool (being a member of FTire/tools) to carry out preprocessing outside of Adams.

The FTire interface routine automatically recognizes whether several wheels of the car share the same basic data file. In that case, preprocessing is done only once for all these files. Also, FTire automatically recognizes whether the data file contains basic parameters or pre-processed ones.

FTire does not use the data in the section [VERTICAL]. It is only included for compatibility with other tire models. It is recommended that you set Vertical_Stiffness to the value of stat_wheel_load_at_10_mm_defl, after dividing by 10 mm. For Vertical_Damping, choose 0 (or a small nonzero value). The actual vertical damping of FTire is not just one single value, but will depend on rolling speed, inflation pressure, load, camber, and so on.

The following is an examples of a basic FTire data file. Note that by far not all possible data are defined. For examples, only data for one inflation pressure are provided.

$--------------------------------------------------------MDI_HEADER[MDI_HEADER] FILE_TYPE = 'tir' FILE_VERSION = 4.0 FILE_FORMAT = 'ASCII'(COMMENTS){comment_string} 'Tire Manufacturer - unknown' 'Tire Type - unknown' 'Tire Dimension - 195/65 R 15' 'Pressure - 2.0 bar' 'File Generation Date - 03/03/11 10:32'$-------------------------------------------------------------SHAPE[SHAPE]{radial width} 1.0 0.0 1.0 0.4


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1.0 0.9 0.9 1.0$-------------------------------------------------------------UNITS[UNITS] FORCE = 'NEWTON' MASS = 'GRAM' LENGTH = 'MM' TIME = 'MILLISECOND' ANGLE = 'DEGREE'$---------------------------------------------------------DIMENSION[DIMENSION] UNLOADED_RADIUS = 326.0 $ [mm]$----------------------------------------------------------VERTICAL[VERTICAL] VERTICAL_STIFFNESS = 170.0 $ [N/mm] VERTICAL_DAMPING = 0.0 $ [Nms/mm]$-------------------------------------------------------------MODEL[MODEL] PROPERTY_FILE_FORMAT = 'FTIRE' $ separate_animation = 0 $ [0/1] additional_output_file = 0 $ [0/1] verbose = 0 $ [0/1]$----------------------------------------------OPERATING_CONDITIONS[OPERATING_CONDITIONS] inflation_pressure = 2.0 $ [bar] tread_depth = 8.0 $ [m] model_level = 7 $ [-] $---------------------------------------------------------PARAMETER[FTIRE_DATA]$basic data and geometry ******************************************* tire_section_width = 195 $ [mm] tire_aspect_ratio = 65 $ [%] rim_diameter = 381 $ [mm] rim_width = 152.4 $ [mm] load_index = 91 $ [-] rolling_circumference = 1975 $ [mm] tread_lat_curvature_radius = 800 $ [mm] tread_width = 160 $ [mm] tire_mass = 9000 $ [g] interior_volume = 0.03e9 $ [mm^3] volume_gradient = 1.0 $ [%/mm] belt_torsion_lat_displ_coupl = 0.0 $ [deg/mm]$$static and modal data for 1st infl. pressure *********************** stat_wheel_load_at_10_mm_defl = 1690 $ [N] stat_wheel_load_at_20_mm_defl = 3600 $ [N] dynamic_stiffening = 20 $ [%] speed_at_half_dyn_stiffening = 5.55 $ [mm/ms]=[m/s] radial_hysteretic_stiffening = 0 $ [%] radial_hysteresis_force = 0 $ [N] tang_hysteretic_stiffening = 0 $ [%] tang_hysteresis_force = 0 $ [N] belt_extension_at_200_kmh = 1.0 $ [%] rel_long_belt_memb_tension = 82.0 $ [%]

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$ f1 = 62.1 $ in-plane rotat. [Hz] f2 = 81.4 $ in-plane transl. [Hz] f4 = 80.0 $ out-of-plane rotat. [Hz]$ D1 = 0.05 $ in-plane rotat. [-] D2 = 0.08 $ in-plane transl. [-] D4 = 0.05 $ out-of-plane rotat. [-]$ belt_in_plane_bend_stiffn = 2.0e6 $ [Nmm^2] belt_out_of_plane_bend_stiffn = 200.0e6 $ [Nmm^2] belt_lat_bend_stiffn = 20.0e6 $ [Nmm^2] belt_twist_stiffn = 1.0e6 $ [Nmm^2/deg] belt_torsion_stiffn = 100.0 $ [N/deg]$ rim_flange_contact_stiffness = 3000.0 $ [N/mm] rim_to_flat_tire_distance = 30.0 $ [mm]$$tread properties ************************************************** tread_depth = 8.0 $ [mm] tread_base_height = 3.0 $ [mm] stiffness_tread_rubber = 64 $ [Shore A] tread_positive = 65 $ [%] damping_tread_rubber = 0.025 $ [ms]$ sliding_velocity = 0.1 $ [mm/ms] blocking_velocity = 50.0 $ [mm/ms] low_ground_pressure = 0.01 $ [bar] med_ground_pressure = 2.0 $ [bar] high_ground_pressure = 10.0 $ [bar] mu_adhesion_at_low_p = 1.3 $ [-] mu_sliding_at_low_p = 1.1 $ [-] mu_blocking_at_low_p = 0.8 $ [-] mu_adhesion_at_med_p = 1.3 $ [-] mu_sliding_at_med_p = 1.0 $ [-] mu_blocking_at_med_p = 0.8 $ [-] mu_adhesion_at_high_p = 1.3 $ [-] mu_sliding_at_high_p = 1.0 $ [-] mu_blocking_at_high_p = 0.8 $ [-]$$tire imperfections ************************************************ static_balance_weight = 0.0 $ [g] static_balance_ang_position = 0.0 $ [deg] dynamic_balance_weight = 0.0 $ [g] dynamic_balance_ang_position = 0.0 $ [deg] radial_non_uniformity = 0.0 $ [%] radial_non_unif_ang_position = 0.0 $ [deg] tang_non_uniformity = 0.0 $ [%] tang_non_unif_ang_position = 0.0 $ [deg] ply_steer_percentage = 0.0 $ [%] conicity = 0.0 $ [deg] run_out = 0.0 $ [mm] run_out_angular_position = 0.0 $ [deg]

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$$measuring conditions ********************************************** inflation_pressure = 2.0 $ [bar] rim_inertia = 0.25e9 $ [g*mm^2]$$numerical data **************************************************** number_belt_segments = 80 $ number_blocks_per_belt_segm = 32 $ number_tread_strips = 8 $ maximum_time_step = 0.2 $ [ms] BDF_parameter = 0.505 $ 0.5 .. 1.0 [-]

Choosing FTire Operating ConditionsYou can control certain tire data during a simulation, without rerunning preprocessing. These parameters, listed below, are called operating condition parameters:

• Inflation pressure - The operating condition value of inflation_pressure defines the actual, possibly time-dependent inflation pressure, whereas the [FTIRE_DATA] value describes the inflation pressure at which the remainder of the data measurements had been taken.

• Tread depth -The operating condition value of tread_depth defines the actual, possibly time-dependent tread depth, whereas the [FTIRE_DATA] value describes the tread depth at which the remainder of the data measurements had been taken.

• Model level - The operating condition value of model_level defines what variant of FTire is to be used: the basic version (=6) or the full 3D version (=7). The list of possible variants will be extended in the next release.

Also in the next FTire release, ambient temperature, will be added to the list of operating conditions.

To determine the actual operating conditions, FTire looks for the section [OPERATING_CONDITIONS] in the basic or preprocessed tire data file. If it does not find this section, or it does not contain the respective definitions, FTire uses the data in the sections [FTIRE_DATA] or [FTIRE_PREPROCESSED_DATA] as the measurement conditions.

In case the section [OPERATING_CONDITIONS] is defined, FTire first tries to read a constant value for each operating condition. This value may either be the same for all tires using the data file, or it can have individual values for each such tire instance.

You can enter constant operating conditions as shown the table below.

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OPERATING_CONDITIONS Section Parameters

If no constant value is found, FTire looks for a table that is defining data points for operating condition versus time. These data points then will be piecewise linearly interpolated with respect to simulation time.

You enter such look-up tables as subsections of the section [OPERATING_CONDITIONS]. These subsections can each contain up to 200 data pairs, one pair per line. Every data pair consists of a value for time and a corresponding value for the operating condition. Units are the same as for constant values. Similarly as for constant values, tables which are valid for all tires, or individual tables for each instance are allowed.

The names of these table subsections, with obvious meanings, are:

• (TIME_TABLE_INFLATION_PRESSURE)• (TIME_TABLE_INFLATION_PRESSURE_WHEEL_ i)• (TIME_TABLE_TREAD_DEPTH)• (TIME_TABLE_TREAD_DEPTH_WHEEL_ i)• (TIME_TABLE_MODEL_LEVEL)

The parameter: Means:inflation_pressure Actual inflation pressure, used for all FTire instances that are

parameterized by this data file.inflation_pressure_wheel_i Actual inflation pressure, used only for FTire instance with GFORCE

ID i. This value overrides the inflation_pressure value (i is to be replaced by a numerical GFORCE ID value of the tire instance).

tread_depth Actual tread depth, used for all FTire instances that are parameterized by this data file.

tread_depth_wheel_i Actual tread depth, used only for FTire instance with GFORCE ID i. This value overrides the tread_depth value (i is to be replaced by the numerical GFORCE ID value of the tire instance).

model_level Actual model level, used for all FTire instances that are parameterized by this data file. In the current release, the following model levels are implemented:

• 6: FTire basic version (three degrees of freedom for each belt element, one line of contact elements.

• 7: FTire full 3D version (five generalized degrees of freedom for each belt element, several lines of, or irregularly scattered, contact elements).

model_level_wheel_i Actual model level, used for FTire instance with GFORCE ID i. This value will override the model_level value (’i’ is to be replaced by the numerical GFORCE ID value of the tire instance).

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• (TIME_TABLE_MODEL_LEVEL_WHEEL_ i)

The following examples defines a sudden pressure loss (between 5 and 5.2 s of simulation time) in tire with GFORCE ID 2. In addition, it specifies constant inflation pressure (2.2 bar) for the other tires, and a certain, equal and constant extreme tread wear (0.1 mm every100 s) for all tires. Model level is chosen to be the full 3D variant for all tires at any time:

$-----------------------------------------------OPERATING_CONDITIONS

[OPERATING_CONDITIONS]

MODEL_LEVEL = 7

INFLATION_PRESSURE_WHEEL_1 = 2.2INFLATION_PRESSURE_WHEEL_3 = 2.2INFLATION_PRESSURE_WHEEL_4 = 2.2

(TIME_TABLE_TREAD_DEPTH)0 8.0100 7.9(TIME_TABLE_INFLATION_PRESSURE_WHEEL_2)0 2.25 2.25.2 1.2

Note: If you use the preprocessed data file in subsequent simulations, don't forget to copy the [operating_conditions] section from the basic data file manually into the preprocessed data file. This is not done automatically, because tire operating conditions are not considered to be part of the tire data.

Road Models in Adams/Tire

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12

Using the 2D Road ModelThis section of the help provides detailed technical reference material for using Adams/Tire to define roads along which to maneuver a vehicle. It assumes that you know how to run Adams/Car, Adams/Solver, Adams/View, or Adams/Chassis. It also assumes that you have a moderate level of tire-modeling proficiency.

The 2D Road model lets you model two-dimensional road excitations, including a flat road. Learn about:

• 2D Road Types

• Examples of 2D Roads • 2D Road Model Parameters

2D Road TypesThe available road types are:

• DRUM - Tire test drum (requires a zero-speed-capable tire model).• FLAT - Flat road.• PLANK - Single plank perpendicular, or in oblique direction relative to x-axis, with or without

bevel edges.• POLY_LINE - Piece-wise linear description of the road profile. The profiles for the left and right

track are independent.• POT_HOLE- Single pothole of rectangular shape.• RAMP - Single ramp, either rising or falling.• ROOF - Single roof-shaped, triangular obstacle.• SINE - Sine waves with constant wave length.• SINE_SWEEP - Sine waves with decreasing wave lengths.• STOCHASTIC_UNEVEN - Synthetically generated irregular road profiles that match measured

stochastic properties of typical roads. The profiles for left and right track are independent, or may have a certain correlation.

Examples of 2D RoadsSample files for all the road types for Adams/Car are in the standard Adams/Car database:

install_dir/shared_car_database.cdb/roads.tbl/

Sample files for all the road types for Adams/Tire are in:

install_dir/solver/atire/

Sample files for all the road types for Adams/Chassis are in:

install_dir/achassis/examples/rdf/

13Road Models in Adams/Tire

Note that you must select a specific contact method, such as point-follower or equivalent plane, to define how the roads will interact with the tires. Not all combinations of road, tire, and contact methods are permitted. Allowable combinations are explained in Tire Models help under the description of the specific tire model.

2D Road Model ParametersThe [PARAMETERS] block must contain the following data, some of which are independent of the type of road.

Learn about parameters:

• Independent of Road Type • Drum • Flat • Plank • Polyline • Pothole • Ramp • Roof • Sine • Sweep • Stochastic Uneven

Parameters Independent of Road TypeThe following parameters are required regardless of the road type.

[PARAMETERS] Independent of Road Type

The parameter: Indicates:offset A constant shift of the road height values. For a flat road and offset = 0, the

road height is zero.rotation_angle_xy_plane Rotation angle of the xy-plane about the road z-axis. In Adams/Car,

vehicles start running along the negative x-axis by default. It also might be convenient to use positive x-values in the .rdf. In that case, choose rotation_angle_xy_plane = 180 (deg).

mu Road friction correction factor (not the friction value itself), to be multiplied with the respective rubber friction values of the tire model.

Default setting: mu = 1.0.

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14

Parameters for Road Type of DrumIf ROAD_TYPE = drum, then define the following parameters:

[PARAMETERS] for Road Type of Drum

Parameters for Road Type of FlatIf ROAD_TYPE = flat, then no further parameters are required.

Parameters for Road Type of PlankIf ROAD_TYPE = plank, then define the following parameters:

[PARAMETERS] for Road Type of Plank

The parameter: Indicates:diameter Diameter of the tire test drum. When the diameter is < 0, the road model

simulates the outer drum. With positive rolling speed, the inner drum will rotate clockwise and the outer drum counter-clockwise.

v Rolling speed of drum surface (be sure to keep vehicle at speed zero, otherwise, the wheels move away from the drum).

Drum center is located at x = 0.number_cleats Number of extra cleats on drum (number_cleats = 0 allowed).cleat_height Height of extra cleats.cleat_starting_angle Drum angle coordinate of first cleat.cleat_length Length of cleat, measured in circumferential direction of drum.cleat_bevel_edge_length Length of bevel edge of cleat, measured in circumferential direction of

drum. Bevel edge has 45° slope.acceleration_time Optional time span at the beginning of the simulation, during which the

drum is accelerated to a nominal rolling speed.

The parameter: Indicates:height Height of plank.start Start of plank (travel distance).length Length of plank, measured along x-axis.bevel_edge_length Length of bevel edge, measured along x-axis. Bevel edge has 45° slope. When

bevel_edge_length < 0, rounded corners instead of bevel edges are used. In this case, radius of the corner is |bevel_edge_length|.

direction Direction of plank relative to y-axis. If the plank is placed crosswise, direction = 0. If the plank is along the x-axis, direction = 90.


Parameters for Road Type of PolylineIf ROAD_TYPE = poly_line, then the [PARAMETERS] block must have a (XZ_DATA) subblock. The subblock consists of three columns of numerical data:

• Column one is a set of x-values in ascending order.• Columns two and three are sets of respective z-values for left and right track.

The following is an example of the full [PARAMETERS] Body for a road type of polyline:

$---------------------------PARAMETERS

[PARAMETERS]

OFFSET = 0

ROTATION_ANGLE_XY_PLANE = 180

$ (XZ_DATA)0 0 0

1000 100 502000 -1000 100

3000 -100 100

3001 50 0

4000 -100 100

The XZ_DATA subblock can be extremely large. In this case, only the portion that is needed at the moment is loaded. To facilitate efficient reloading while simulation is running, do not use any comment lines in a subblock that contains more than 2000 lines.

Parameters for Road Type of PotholeIf ROAD_TYPE = pot_hole, then the parameters are:

[PARAMETERS] Data for Road Type of Pothole

Parameters for Road Type of RampIf ROAD_TYPE = ramp, then the parameters are:

The parameter: Indicates:depth Depth of pothole.start Start of pothole (travel distance).length Length of pothole.

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[PARAMETERS] Data for Road Type of Ramp

Parameters for Road Type of RoofIf ROAD_TYPE = roof, then the parameters are:

[PARAMETERS] Data for Road Type of Roof

Parameters for Road Type of SineIf ROAD_TYPE = sine, then the parameters are:

[PARAMETERS] Data for Road Type of Sine

The road height, z, is given by:

Parameters for Road Type of Stochastic UnevenA stochastic uneven road profile both for left and right wheels is generated, with properties very close to measured road profiles.

In a first step, discrete white noise signals are formed on the basis of nearly uniformly distributed random numbers. Two of these numbers are assigned to every 10 mm of travel path. The distribution of these

The parameter: Indicates:height Height of ramp.start Start of ramp (travel distance).slope Slope of ramp. 1 means 45°.

The parameter: Indicates:height Height of roof (triangle-shaped obstacle).start Start of roof (travel distance).length Length of roof, measured along x-axis.

The parameter: Indicates:amplitude Amplitude of sine wave (a).wave_length Wave length of sine wave ( ).

start Start of sine waves (travel distance) (ss).

λe

z s( ) a 2πλ

------ s ss–( )⎝ ⎠⎛ ⎞sin⋅=


random numbers is approximated by summing several equally distributed random numbers, taking advantage of the ‘law of large numbers’ of mathematical statistics.

Next, these values are integrated with respect to travel distance, using a simple first order time-discrete integration filter. The independent variable of that filter is not time, but travel path. That is why the filter cutoff frequency is controlled by a path constant instead of a time constant. The filter process results in two approximate realizations of white velocity noise; that is, two signals, the derivatives of which are close to white noise. Signals with that property are known as road profiles with waviness 2. Several investigations in the past showed that the waviness derived from measured road spectral densities ranges from about 1.8 to 2.2.

The last step is to linearly combine the two realizations of the above process: , , resulting in

the left and right profile , . This is done such that the two signals are completely independent

if , and identical if :

If ROAD_TYPE = stochastic_uneven, then the parameters are:

[PARAMETERS] for Road Type of Stochastic Uneven

Parameters for Road Type of SweepIf ROAD_TYPE = sine_sweep, then the parameters are:

The parameter: Indicates:intensity Variable to control intensity of white velocity noise, which approximates

measured spectra of road profiles fairly well.path_constant Variable to control high-pass integration filter.correlation_rl Variable to control correlation between left and right track:

• If 0, no correlation.• If 1, complete correlation (that is, left track = right track).

Can be any value between 0 and 1.start Start of unevenness (travel distance).

z1 s( ) z2 s( )

zl s( ) zr s( )

corrrl 0.0= corrrl 1.0·=

zl s( ) z1 s( )corrrl

2------------- z2 s( ) z1 s( )–( )+=

zr s( ) z2 s( )corrrl

2-------------⎝ ⎠⎛ ⎞ z2 s( ) z1 s( )–( )–=

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[PARAMETERS] Data for Road Type of Sine Sweep

The parameter: Indicates:start Start of swept sine wave (travel distance) ( ).

end End of swept sine wave (travel distance) ( ).

amplitude_at_start Amplitude of swept sine wave at start travel distance ( ).

amplitude_at_end Amplitude of swept sine wave at end travel distance ( ).

ss

se

as

ae


wave_length_at_start Wave length of swept sine wave a start travel distance ( ).

wave_length_at_end Wave length of swept sine wave at end travel distance. Must be less than or equal to wave_length_at_start ( ).

The parameter: Indicates:

λs

λe

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20

ss– )⎠⎞

sweep_type • sweep_type = 0: frequency increases linearly with respect to travel distance.

• sweep_type = 1: wave length decreases by a constant factor per cycle.

Depending on the value of sweep_type, the road height is given by the following functions,

where:

• Linear sweep: (sweep_type = 0) The frequency increases linearly with respect to travel distance. The road height value z(s) as function of travel distance s is alculated as follows:

Note the factor 2 in the denominator is not an error. The actual frequency (= derivative of the sine function argument with respect to travel path, divided by ; this is not equal to that factor that is multiplied by in the

sine function) is given by the following:

• Logarithmic sweep: (sweep_type = 1) with every cycle, the wave length decreases by a constant factor. The road height value is calculated as follows:

where:

is the travel path where theoretically an infinitely high frequency was

reached, measured relative to sweep start . The actual frequency is given by:

The parameter: Indicates:

fs1λs-----= fe

1λe-----=and

z s( ) asae as–( ) s ss–( )

se ss–( )--------------------------------------+⎝ ⎠

⎛ ⎞ 2π fsfe fs–( ) s ss–( )

2 se ss–( )------------------------------------+⎝ ⎠

⎛ ⎞⋅ s(⋅⎝⎛sin⋅=

2π 2π s ss–( )

f s( ) fs=fe fs–( ) s ss–( )

se ss–------------------------------------+

z s( ) asae as–se ss–--------------- s ss–( )+⎝ ⎠

⎛ ⎞ 2πfss∞s∞

s∞ ss s–+------------------------⎝ ⎠⎛ ⎞ln⎝ ⎠

⎛ ⎞sin⋅=

s∞fe

fe fs–-------------- se ss–( )=

s∞ss

s∞
f s( ) s∞ ss s–+------------------------fs=


Adams/3D Spline Road ModelLearn how to use the Adams/3D Spline Road model to define a road:

• About Adams/3D Spline Road

• Adams/3D Spline Road Perturbation Types

• Adams/3D Spline Road Perturbation Keywords • Using Adams/3D Spline Road • About the Adams/3D Spline Road Property File

About Adams/3D Spline RoadAdams/3D Spline Road lets you define an arbitrary three-dimensional smooth road surface, such as parking structures, racetracks, and so on. A smooth road is a road surface with a curvature, which is less than the curvature of the tire. In addition, Adams/3D Spline Road lets you model three-dimensional road obstacles, which are placed on top of the underlying smooth road surface.

The road centerline, width, bank angle, and left and right friction levels define the road surface completely. The road data is stored in an XML file, which you can create and modify using the Road Builder (Learn more about Using the Road Builder). The legacy TeimOrbit road definition file (.rdf) is still supported, and can be translated to XML using the Road Builder. For a description of the information contained in the .rdf file, see About the Adams/3D Spline Road Property File.

By specifying the coordinates of the road centerline, you can construct any line in three-dimensional space. Adams/3D Spline Road assumes a flat cross-section for which the bank angle and width can be specified for each data point. In addition, you can specify friction levels for left and right road sides.

Using Adams/3D Spline RoadYou can reference the Adams/3D Spline Road just as you do any other .rdf by selecting your desired road from an appropriate database. In addition, both Adams/Car and Adams/Chassis have a Adams/3D Spline Road event, called 3D Spline Road. Graphics for the road are automatically generated for animation purposes.

In the current version of Adams/3D Spline Road, both Adams/Car and Adams/Chassis offer multiple methods to access the Adams/3D Spline Road capabilities:

• When running any full vehicle simulation you may use an Adams/3D Spline Road data file for the road.

• When using with Driving Machine, you may also use a road data file as you would a driver control data (.dcd) file to specify the vehicle path. The Driving Machine will then drive the vehicle along the centerline of the road.

• When using with Adams/SmartDriver, you can use the road data file to replace the driver road data (.drd) file. In this case, the vehicle will use the x, y, and z road centerline to define the vehicle path.

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22

Examples of event (.xml) file for use with Driving Machine and Adams/SmartDriver are shown next:

For Driving Machine:

<DcfMini name="3D_SMOOTH_ROAD" active="true" userDefined="false" smoothingTime="0.1" activeFlag="true" abortTime="1" stepSize="0.01" hMax="0" > <DcfDemand name="steering" active="true" userDefined="false" demandType="steering" actuatorType="rotation" controlMethod="machine" controlMode="absolute" controlType="constant" constantValue="0" initialValue="0" finalValue="0" startTime="0" duration="0" rampValue="0" maximumValue="0" cycleLength="0" amplitude="0" initialFrequency="0" frequencyRate="0" maximumFrequency="0" functionString="0" > … <DcfMachine name="machine" active="true" userDefined="false" steerControl="file" dcdSteerFile="mdids://acar_shared/roads.tbl/3d_road_smooth_ramp.xml" steerRadius="0" steerEntry="0" turnDirection="right" pathPositioning="default" speedControl="lon_accel" velocity="0" acceleration="0" jerk="0" startTime="0.1" samplePeriod="0.01" >

For Adams/SmartDriver:

DcfMini name="3D_SMOOTH_ROAD" active="true" userDefined="false" smoothingTime="0.1" activeFlag="true" abortTime="1" stepSize="0.01" hMax="0" > <DcfDemand name="steering" active="true" userDefined="false" demandType="steering" actuatorType="rotation" controlMethod="SmartDriver" controlMode="absolute"


controlType="constant" constantValue="0" initialValue="0" finalValue="0" startTime="0" duration="0" rampValue="0" maximumValue="0" cycleLength="0" amplitude="0" initialFrequency="0" frequencyRate="0" maximumFrequency="0" functionString="0" > … <DcfSmartDriver name="smartdriver" active="true" userDefined="false" task="vehicle_limits" courseFile="mdids://acar_shared/roads.tbl/3d_road_smooth_ramp.xml" max_driving_accel="70" max_braking_accel="70" max_lh_turn_accel="70" max_rh_turn_accel="70" samplePeriod="0.01" />

Adams/3D Spline Road Perturbation TypesThe available road perturbations are:

• CROWN - Road crown along the road centerline.• CURB - Curb at left, right, or both sides of the road.• PLANK - Single plank with beveled edges or rounded corners.• POLYLINE - Cubic spline description of the road profile for left and right wheel track.• POTHOLE - Pothole of rectangular shape.• RAMP - Ramp, either rising or falling.• ROOF - Roof-shaped, triangular obstacle.• ROUGHNESS - Generated irregular road profiles with stochastic properties similar to measured

roads.• SINE - Sine wave with constant amplitude and wavelength.• SWEEP - Sine wave with variable amplitude and wavelength.

Note that a specific contact method has to be selected, which defines how Adams/3D Spline Road interacts with the tires. Not all combinations of road, tire, and contact methods are permitted. For more information, see the topics under Tire Model in the Table of Contents.

Be aware that Adams/3D Spline Road perturbations can generally have small wavelength content. Therefore, the combination of tire and contact methods should be able to handle this type of excitation.

Any number of perturbations can be defined. If an overlap exists between the perturbations, then Adams/3D Spline Road superpositions the perturbations.

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24

Adams/3D Spline Road Perturbation KeywordsThe following sections explain the keywords for each perturbation type and those independent of the perturbation type:

• Independent of Perturbation Type • Coordinate System • Crown Perturbation Type • Curb Perturbation Type • Plank Perturbation Type • Polyline Perturbation Type • Pothole Perturbation Type • Ramp Perturbation Type • Roof Perturbation Type • Roughness Perturbation Type • Sine Perturbation Type • Sweep Perturbation Type

Keywords Independent of Perturbation TypeYou must specify the following data in the .rdf file, independent of the type of perturbation.

Keywords Independent of Perturbation Type

Keyword: Description:COORDINATE_SYSTEM The type of coordinate system:

• local for a local perturbation-bound coordinate system.• distance if the perturbation is defined along the length of the

road.START The start position of the perturbation.

• '0.0 0.0 0.0' for a local coordinate system.• '0.0' for a distance-defined perturbation.

STOP The stop position of the perturbation.

• '1.0 0.0 0.0' for a local coordinate system. • '1.0' for a distance-defined perturbation.

LENGTH The length of the perturbation. LENGTH is used in defining the local coordinate system.


Coordinate System KeywordsDepending on the COORDINATE_SYSTEM keyword you selected as shown in Keywords Independent of Perturbation Type, you can use two types of coordinate systems:

• Local coordinate system - The START and STOP keywords define the local coordinate system, while the interconnecting line and the LENGTH keyword provide the direction of the perturbation. Adams/3D Spline Road projects the road profile height in the local coordinate system onto the smooth road surface.

• Distance coordinate system - The START and STOP positions are expressed in distance along the road centerline or chord length. The direction and length are, therefore, defined implicitly.

The following combinations of coordinate system and perturbation types are valid:

Valid Combinations of Perturbation Type and Coordinate System

Keywords for Crown Perturbation TypeIf ROAD_TYPE = 'CROWN', then you must specify the keyword DATA_BLOCK = 'CROWN DATA', with the name of the subblock (CROWN_DATA). The subblock consists of three columns of numerical data:

WIDTH The width of the obstacle. The obstacle width can be specified independently of the road width.

FRICTION The friction coefficient of the obstacle.ROAD_TYPE The perturbation type.

Perturbation type:Coordinate system:

Local: Distance:CROWN XCURB XPLANK XPOLYLINE XPOTHOLE XRAMP XROOF XROUGHNESS XSINE XSWEEP X

Keyword: Description:

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26

• The first column is a set of distance-values in ascending order.• The second column contains the height of the crown.• The third column contains the crown coefficient.

The road profile height is a function of width-coordinates , obstacle width , height , and crown

coefficient :

Illustration of CROWN.

Keywords for Curb Perturbation TypeIf ROAD_TYPE = 'CURB', then you must specify the following keywords.

Keywords for Curb Perturbation Type

Keywords for Plank Perturbation TypeIf ROAD_TYPE = 'PLANK', then you must specify the following keywords.

Keywords for Plank Perturbation Type

Keyword: Description:HEIGHT Height of the curb(s).ROUND_OFF Round-off radius of the top of the curb.TOP_WIDTH The width of the top of the curb.EDGE_WIDTH The width of the edge of the curb.SIDE The side of the road where the curb is positioned:

• 'LEFT'• 'RIGHT'• 'BOTH'

Keyword: Description:HEIGHT Height of the plank.BEVEL_EDGE_LENGTH Length of the beveled edge. A beveled edge has a 45º slope. When

BEVEL_EDGE_LENGTH < 0, 3D Spline Road uses rounded corners instead of beveled edges. In this case, the radius of the corner is |BEVEL_EDGE_LENGTH|.

z r w z0

cr

z ρ( ) z0 4crw----ρ2–=


Keywords for Polyline Perturbation TypeIf ROAD_TYPE = 'POLYLINE', then you must specify the keyword DATA_BLOCK = 'XZ_DATA', with the name of the subblock (XZ_DATA). The subblock consists of three columns of numerical data:

• The first column is a set of distance-values in ascending order.• The second and third columns contain the road profile height of the left and right tracks,

respectively.

Keywords for Pothole Perturbation TypeIf ROAD_TYPE = 'POTHOLE', then you must specify the 'DEPTH' keyword, which specifies the depth of the pothole.

Keywords for Ramp Perturbation TypeIf ROAD_TYPE = 'RAMP', then you must specify the following keywords.

Keywords for Ramps Perturbation Type

Keywords for Roof Perturbation TypeIf ROAD_TYPE = 'ROOF', then you must specify the following keywords.

Keywords for Roof Perturbation Type

Keywords for Roughness Perturbation TypeThe roughness perturbation type uses a mathematical model developed by Sayers (1.). The model is empirical; it is based on the observed characteristics of many measured profiles of roads of various types. The model provides the synthesis of profiles for both the left and right wheel tracks.

If ROAD_TYPE = 'ROUGHNESS', then you must provide the following keywords:

Keyword: Description:HEIGHT Height of the ramp.SLOPE Slope of ramp. 1 corresponds to 45º.

Keyword: Description:HEIGHT Height of the roof.LENGTH Length of the base of the triangular roof.

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Keywords for Roughness Perturbation Type

References:1. Sayers, M.W., "Dynamic Terrain Inputs to Predict Structural Integrity of Ground Vehicles."

UMTRI Report No. UMTRI-88-16, April 1988, 114 pp.

Keywords for Sine Perturbation TypeIf ROAD_TYPE = 'SINE', then you must provide the following keywords.

Keywords for Sine Perturbation Type

The road profle height z, is given by:

Keywords for Sweep Perturbation TypeIf ROAD_TYPE = 'SWEEP', then you must provide the following keywords.

Keyword: Description:GE Elevation PSD parameter.GS Velocity PSD parameter.GA Acceleration PSD parameter.SAMPLE_INTERVAL The distance between the road profile data points.CORRELATION_BASELENGTH

Correlation base length for filtering (recommended value = 5.0 m).

SEED Seed for random numbers.

• If seed is negative, the computer's clock is used as a seed. An infinite number of profiles can be generated to match the same set of Sayers-model parameters.

• If seed is greater than zero, the value of the seed is used as the seed to the random-number generator. This is a means of generating reproducible profiles with the Sayers model.

Keyword: Description:AMPLITUDE Amplitude of the sine wave (a).WAVE_LENGTH Wave length of the sine wave (l).

z s( ) a 2πλ

------ s⋅⎝ ⎠⎛ ⎞sin⋅=


s s–---------⎠

⎞

ss)-------⎠⎞ ⋅

Keywords for Sweep Perturbation Type

About the Adams/3D Spline Road Property FileThe following sections explain the data blocks in the Adams/3D Spline Road property file (.rdf). The last section contains a sample .rdf.

• File Details

• Units Details

Keyword: Description:AMPLITUDE_AT_START Amplitude of the sine wave at start (as ).

AMPLITUDE_AT_END Amplitude of the sine wave at end (ae ).

WAVE_LENGTH_AT_START Wave length of the sine wave at start (ls ).

WAVE_LENGTH_AT_END Wave length of the sine wave at end (le ).

SWEEP_TYPE • SWEEP_TYPE = 0, then frequency changes linearly.• SWEEP_TYPE = 1, then frequency changes logarithmically.

Depending on the value of SWEEP_TYPE, the road profile height is given by the following functions:

• Linear sweep - The frequency changes linearly with distance s. The road profile height z is given by:

• Logarithmic sweep - With every cycle, the wavelength decreases by a constant factor. The road profile is given by:

where:

s¥ is the distance at which, theoretically, an infinitely high frequency is reached, with respect to the start ss.

as

ae

ls

le


se ss–--------------------------------------+ 2π fs s∞

s∞s∞ s+---------------⎝⎛ln⋅ ⋅ ⋅sin⋅=


se ss–--------------------------------------+ 2π fs

fe fs–( ) s –(2 se ss–( )

-----------------------------+⎝⎛⋅sin⋅=

s∞fe

fe fs–-------------- se ss–( )=

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• Model Details

• Global Parameters

• Data Points Information

• Sample Road Data File

File DetailsThe first block of data, [MDI_HEADER], describes the TeimOrbit file:

[MDI_HEADER] FILE_TYPE = 'rdf' FILE_VERSION = 5.00 FILE_FORMAT = 'ASCII' {COMMENTS} 'User entered comments go here'

MDI_HEADER Keywords

Units DetailsThe [UNITS] blocks defines the units for the road:

[UNITS]

LENGTH = 'meter'FORCE = 'newton'ANGLE = 'radians'MASS = 'kg'TIME = 'sec'

[UNITS] Keywords

The keywords: Contains:FILE_TYPE The file type.FILE_VERSION Version of file; to be changed when modifications to this file are made.FILE_FORMAT The format of the data; for TeimOrbit, this is always ASCII.{COMMENTS}'User entered comments go here'

Descriptive comments about the file, such as what road this represents, when the data was acquired, and so on.

The keywords: Specifies:LENGTH Unit of length.FORCE Unit of force.


Model DetailsThe [MODEL] block defines the road model and version:

[MODEL]METHOD = '3D_SPLINE'VERSION = 1.00

[MODEL] Keywords

Global ParametersThe [GLOBAL_PARAMETERS]block defines parameters applying to the entire road.

[GLOBAL_PARAMETERS]

CLOSED_ROAD = 'NO'SEARCH_ALGORITHM = 'FAST'ROAD_VERTICAL = '0.0 0.0 1.0'FORWARD_DIR = 'NORMAL'MU_LEFT = 0.5MU_RIGHT = 0.6WIDTH = 5.000BANK = 0.0

ANGLE Angle in radians or degrees.MASS Unit of mass.TIME Unit of time.

The keyword: Determines:METHOD Road contact algorithm that Adams/Tire uses. You must set

method='3D_SPLINE'to instruct Adams/Tire to use the Adams/3D Spline Road spline algorithm.

VERSION Version of 3D_SPLINEalgorithm being used; currently, 1.00.

The keywords: Specifies:

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[GLOBAL_PARAMETERS) Keywords

The keyword: Specifies:CLOSED_ROAD Whether the road is closed or open. If the road is not structured to be

closed (the beginning and end of the road are not facing each other) and you select the closed option, Adams/Tire creates a deformed road.

• 'YES' - The road is closed.• 'NO'- The road is open.

SEARCH_ALGORITHM The type of algorithm to be used to determine the contact location. For smooth roads, we recommend Fast algorithm.

• 'FAST' - Specifies Fast algorithm.With Fast algorithm, caching is

used if the input point is within [m] distance from the previous input point.

• 'SLOW' - Specifies Slow algorithm. With Slow algorithm, no caching is used and the greatest accuracy is achieved.

ROAD_VERTICAL Vector specifying the z-axis of the user-coordinate system with respect to ISO-coordinate system. This option allows you to specify the road data points in your preferred reference frame. During simulation, Adams/Tire converts all the data points to the ISO-reference frame based on the ROAD_VERTICALvalues:

'0.0 0.0 1.0' - The z-axis of user-reference frame with respect to ISO reference frame.

FORWARD_DIR Forward direction of the road:

• 'NORMAL' - Vehicle travels along the specification of road data point.

• 'INVERT' - Vehicle travels in a direction opposite to that of specified road data points.

MU_LEFT Road friction value on the left side of the road with respect to the centerline of the road. Specifying road friction under [GLOBAL_PARAMETERS] overwrites any specification of road friction values in the [DATA_POINTS] block. See Data Points Information.

1 6–×10


Data Points InformationThe [DATA_POINTS] block contains the road information in a tabular form. The following information needs to be supplied for each entry.

[DATA_POINTS]{ X Y Z WIDTH BANK MU_LEFT MU_RIGHT

OBSTACLES }

[DATA_POINTS] Keywords

MU_RIGHT Road friction value on the right side of the road with respect to the centerline of the road. Specifying road friction under [GLOBAL_PARAMETERS] overwrites any specification of road friction values in the [DATA_POINTS] block. See Data Points Information.

WIDTH Width of the road. If you specify WIDTH, it takes precedence over the WIDTH value specified in the [DATA_POINTS] block. Even if this parameter is set, you must specify the WIDTH parameter in [DATA_POINTS]. If this parameter is not required, then you can omit it from the road data file (.rdf). See Data Points Information.

BANK Slope angle of the road around its centerline in each data point. Zero bank means a horizontal width line. A positive value specifies a slope along a clockwise direction in ISO-reference frame.

If you specify this dimension, then it takes precedence over the BANK value specified in the [DATA_POINTS] block. Even if you set this dimension, you must specify a BANK value. If this dimension is not required, then you can omit it from the .rdf file. See Data Points Information.

The keyword: Specifies:X X coordinate of sampled road data point.Y Y coordinate of sampled road data point.Z Z coordinate of sampled road data point.WIDTH Width of road at the sampled point.BANK Angle of road at the sampled point; positive value specifies a slope along a

clockwise direction in ISO-reference frame.

The keyword: Specifies:

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Sample Road Data File$--------------------------------------------------------MDI_HEADER[MDI_HEADER]

FILE_TYPE = 'rdf'FILE_VERSION = 5.00FILE_FORMAT = 'ASCII'(COMMENTS){comment_string}'Example of 3d Smooth road'

$------------------------------------------------------------UNITS[UNITS]

LENGTH = 'meter'FORCE = 'newton'ANGLE = 'radians'MASS = 'kg'TIME = 'sec'

$--------------------------------------------------------DEFINITION[MODEL]METHOD = '3D_SPLINE'

$---------------------------------------------------ROAD_PARAMETERS[GLOBAL_PARAMETERS]CLOSED_ROAD = 'NO'SEARCH_ALGORITHM = 'FAST'ROAD_VERTICAL = '0.0 0.0 1.0'FORWARD_DIR = 'NORMAL'MU_LEFT = 0.5MU_RIGHT = 0.5WIDTH = 5.000BANK = 0.0

$-------------------------------------------------------DATA_POINTS[DATA_POINTS] { X Y Z WIDTH BANK MU_LEFT MU_RIGHT OBSTACLES } 12.50000E+00 4.60432E-15 0.00000E-00 7.000 0.000 0.900 0.900 10.50000E+00 4.60432E-15 0.00000E-00 7.000 0.000 0.900 0.900 5.50000E+00 4.60432E-15 0.00000E-00 7.000 0.000 0.900 0.900 CROWN0.50000E+00 4.60432E-15 0.00000E-00 7.000 0.000 0.900 0.900

MU_LEFT Road friction on the left side of road with respect to the centerline of the road at the sampled point.

MU_RIGHT Road friction on the right side of road with respect to the centerline of the road at the sampled point.

OBSTACLES The name of block that contains the perturbation information. This entry is optional.

The keyword: Specifies:


1.53081E-18 1.42109E-17 0.00000E-00 7.000 0.000 0.900 0.900 -2.50000E+00 4.68958E-16 0.00000E-00 7.000 0.000 0.900 0.900 -5.00000E+00 9.37916E-16 0.00000E-00 7.000 0.000 0.900 0.900 -7.50000E+00 1.39266E-15 0.00000E-00 7.000 0.000 0.900 0.900 -1.00000E+01 1.84741E-15 0.00000E-00 7.000 0.000 0.900 0.900 -1.25000E+01 2.30216E-15 0.00000E-00 7.000 0.000 0.900 0.900 -1.50000E+01 2.77112E-15 0.00000E-00 7.000 0.000 0.900 0.900 -1.75000E+01 3.22586E-15 0.00000E-00 7.000 0.000 0.900 0.900 -2.00000E+01 3.69482E-15 0.00000E-00 7.000 0.000 0.900 0.900 $-----------------------------------------------------END_DATA_POINTS [CROWN]COORDINATE_SYSTEM = 'distance'START = 7STOP = 16WIDTH = 4ROAD_TYPE = 'CROWNDATA_BLOCK = 'CROWN_DATA'FRICTION = 0.900

(CROWN_DATA){S HEIGHT CROWN}7.00000E+00 0.00000E+00 0.00000E+008.00000E+00 1.25000E-02 3.12500E-039.00000E+00 5.00000E-02 1.25000E-021.00000E+01 8.75000E-02 2.18750E-021.10000E+01 1.00000E-01 2.50000E-021.20000E+01 1.00000E-01 2.50000E-021.30000E+01 1.00000E-01 2.50000E-021.40000E+01 1.00000E-01 2.50000E-021.50000E+01 1.00000E-01 2.50000E-021.60000E+01 1.00000E-01 2.50000E-02

Using the Road BuilderThe Road Builder lets you create and edit 3D Spline Road property files in XML format. It is available in Adams/Car and Adams/Chassis.

The following sections explain more about the Road Builder:

• Conversion of TeimOrbit Format 3D Spline Road Property Files to XML Format

• Starting the Road Builder

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• Creating Road Property Files

• Opening Road Property Files

• Changing Units

• Saving Changes

• Displaying Header Information and Adding Comments

• Setting Global Parameters

• Defining Road Data Points

• Defining Obstacles

• Defining Analytical Road

Conversion of TeimOrbit Format 3D Spline Road Property Files to XML FormatThe Road Builder does not use TeimOrbit property files. If you open a TeimOrbit 3D Spline Road property file in the Road Builder, it automatically converts it to XML format. This XML 3D Spline Road property file is stored in the working directory and loaded in the Road Builder.

Starting the Road BuilderTo start the Road Builder in Adams/Car:

• From the Simulate menu, point to Full-Vehicle Analysis, and then select Road Builder.

To start the Road Builder in Adams/Chassis:• In Build mode, from the Utilities menu, select Road Builder.

In both cases, the Road Builder starts with the road_3d_sine_example.xml example road property file loaded as shown in the figure below. The Road Builder consists of five tabs:

• Header - Displays header and units information and lets you enter comments. Learn more.• Global - Sets parameters for the entire road. Learn more.• Road Points - Sets parameters that define the points in the road. Learn more. • Obstacle - Defines obstacles in the road. Learn more.• Road Generator - Allows the user to create/modify road data file using segments. Learn more.


Creating a 3D Spline Road Property File

To create a new 3D Spline Road property file:• From the File menu, select New.

When you create a new 3D Spline Road property file, the default values of the road vertical are set to (0.0, 0.0, 1.0). Note that the road vertical is normalized at the Adams/Solver level.

Opening an Existing 3D Spline Road Property File

To edit an existing 3D Spline Road property file, do one of the following:• From the File menu, select Open, and then browse for the desired file.

• To the right of the Road File text box, select the Browse button , and then browse for the desired file.

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Changing Units

To change the units:1. From the Settings menu, select Units.2. Change the units, and then select OK.

Saving Changes

To save changes you make to the XML file:1. At the bottom of the Road Builder, select either Save or Save As. 2. If you selected Save As, enter the file name, and then select OK.

Displaying Header Information and Adding CommentsThe Header tab shows information about the road file and the units of the 3D Spline Road object. You can add comments in the Revision Comment area, as shown in the figure below.

To display header information and add comments:1. Select the Header tab.2. View the information and in the Revision Comment area, enter any comments to help you

manage the road property file.


Setting Global ParametersParameters that apply to the entire road are defined in the Global Tab, shown below. Learn more about the global parameters.

To edit the parameters:1. Select the Global tab.2. Change the parameters as explained in global parameters.

Enter Comments here

Tip: To help you correctly enter values, the units for the current parameter appear in the Current Field Unit text box.

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Defining Road Data PointsThe Road Points tab shows the Road Data Points table, as shown in the figure below. Learn about 3D Spline Road data points. Using the table, you can add and delete road data points and display the points as a plot so you can visualize the road and make changes to it.

• Working with Data Rows

• Plotting Road Data Points

Displaysunits ofcurrentlyselectedparameter


Working with Data RowsYou can edit any of the data in the rows of the Road Data Points table and add or delete rows. The following provide you with the basics of enter data points in the table.

To edit the values in a row:• Select the value you want to change, and then type a new value. Learn about the data point

values.

To add rows to the Road Data Points table:1. Select Add Road Points, located below the table.2. Enter the number of data points you want to enter, and then select OK.

The Road Builder adds the rows to the end of the table.

To delete rows in the Road Data Point table:• Select the row or rows you want to delete, right-click the column Number, and then select

Delete Row(s).

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The Road Builder renumbers the rows of the table.

To add a single row to the end of the table: • Right-click the column Number, and then select Add Row.

To insert a single row below a selected row:• Right-click the row in the column below which you want to add a row, and then select Insert

Row.

To copy and paste data in rows: • Highlight the text you want to copy, and then select an copy (CTRL + C) data from a source and

paste (CTRL + V) it in the road data points table.

Plotting Road Data PointsYou can visualize the road data plots by plotting them as x-y (x values versus y values) or x-z plots (x values versus z values).

Note that if both the x-y plot and x-z plots are active, changes to road data points in one plot are not automatically updated in the other plot. Close and reopen the plot after updating the main road data points table.


To plot the road data points:• Select Show X-Y Plot or Show X-Z Plot to create a plot of the road, as shown in the figure

above for x-y values.

To fit the display of the plot into the plotting window, do one of the following:• Select Fit.• Right-click the plot, and then select Fit.

To view the data points in the plot:• Right-click the plot, and then select Show Symbols. • To view the data points as a curve:• Right-click the plot, and then select Show Curve.

To zoom the display:1. Select Zoom.2. using the mouse, draw a box around the area of the plot you want to view.

To modify the road data points:1. Right-click the plot, and then select Show Symbols.2. Drag the points using the mouse. The new coordinates for the data points update in the table on

the right.3. Select OK. (The road data points are not updated in the main table until you select OK.)

To exit the plot:• In the upper right corner, select the X.

Defining ObstaclesThe Obstacle tab shows the 3D Spline Road obstacles (also called road perturbations). If there is more than one road obstacle, the Obstacle tab displays the Obstacle table, as shown in the figure below. If there is only one road obstacle, the Obstacle tab shows the Obstacle Property Editor. You can only create a new obstacle in the Obstacle table.

For each obstacle, all parameters are stored in the XML format 3D Spline Road property file. This will make it easy to change obstacle type for a particular obstacle if data already exists.

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Adding, Deleting, and Renaming Obstacles

To create a new road obstacle in the Obstacle table:1. In the Name text box, enter the name of the obstacle.2. Select Add.3. Enter the values for the obstacle as explained in Adams/3D Spline Road Perturbation Keywords

To rename an obstacle:• Right-click the obstacle name in the table, select Rename Obstacle, and then enter a new name.

To delete an obstacle:• Right-click the obstacle name in the table, select Delete Obstacle.

Using the Obstacle Property EditorThe Obstacle Property Editor, shown in the figure below, shows the common and obstacle-specific parameters. The obstacle-specific parameters portion of the dialog box only shows those parameters that belong to the selected obstacle type.

Note that you cannot change the coordinate system in the Common Obstacle portion as the obstacle type determines whether Local or Distance should be used.


You manage the data in the tables for the Polyline and Crown obstacle types in the same way you do road data points. For more information on adding, deleting, and copying/pasting of data, see Defining Road Data Points.

To display the Obstacle Property Editor, do one of the following:• Right-click the obstacle name in the Obstacle table, and then select Modify with

PropertyEditor. • Double-click the obstacle name in the obstacle table.

To return to the Obstacle table:

• Click the arrow at the top left side. • To edit the values:• Change the values as explained in Adams/3D Spline Road Perturbation Keywords.

Tip: To help you correctly enter values, the units for the current parameter appear in the Current Field Unit text box.

Parameterscommonto allobstacles

Parametersspecificto theselectedobstacle

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Defining Analytical RoadFollowing example illustrates how to create/modify a road model analytically from scratch in Adams/Road Builder. Road data can be created with multiple segments, each segment representing predefined formulations like Linear, Curvature, and Transition Curve or through User Defined Functions and User Defined Points.

Steps to Create a Road Data File:New tab Road Generator is added to the Road Builder GUI. This tab allows the user to create/modify road data file using segments.

To create a new segment, enter segment name in the Name field and click Add button. Segment name should be unique. To make it easier for the user to create road profile, some basic functions were created. User can use these functions by giving appropriate values.


To see the road points click on Export points to Data Table this will calculate the road points according to the segment function and export them to the Road Points tab in the GUI.

To see the road points in 2D click button Show X-Y Plot & Show X-Z Plot. To see the road profile with shell graphics click on Generate 3d Road. To see in 3D, user should have Adams/Car license.

Description of Functions:Linear:

This function will create a straight line between two given points. Inputs required are Number of points, Start point, End point, Width, Bank, mu Left and mu Right.

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Curvature:

This function will create a curve. Inputs required for this function are Number of Points, Start point, Center point, Tangent Point, Radius, Arc Length, Width, Bank, mu Left and mu Right.


Transition:

This function will connect the start and end point of the road. Inputs required for this are segment 1, segment 1 point, segment 2, segment 2 point, Width, Bank, mu Left and mu Right.

User Defined Points:

This functionality allows the user to define their road points directly. This functionality is more useful in the case when a user wants to use the existing road point which is already in the old road data file format.

The points are appended to the road points table.

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User Defined Functions:

User can calculate points using their own functions.

For example:

User function = s*75; s*10; 0Function Start = -10Function End = 10

Calculation of Road Point:

-10*75; -10*10; 0-9*75; -9*10; 0-8*75; -8*10; 0


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Adams/Tire 3D Shell Road ModelThe 3D Shell Road utilizes a three-dimensional tire-to-road contact model that computes the volume of intersection between a road and tire. From the intersection volume the method computes an equivalent plane's effective road normal, penetration, tire to road contact point, and effective road friction. The road is modeled as a set of discrete triangular patches, the tire as a set of cylinders. This model lets you simulate a vehicle that is hitting a curb or pothole, or moving on rough, irregular road surfaces.

The 3D Shell Road uses data from both the tire property and road property files. The road model uses these blocks from the tire property file:

• Units• Unloaded_Radius• Width• Shape

From the road property file it uses these blocks:

• Title• Units• Model• Offset• Nodes• Element

Applying the Tire Carcass ShapeThis section discusses how the three-dimensional shell road applies the tire carcass shape, which is defined in the tire property file (for more information on defining shape in the tire property file, see Fiala Tire Carcass Shape). The contact algorithm interpolates the tire carcass shape to a given number of equally spaced points.

You define the tire carcass shape as a set of points in the shape table of the tire property file. Adams/Tire assumes that tire carcass shape is symmetrical over the center line of the tire. Therefore, you need to enter shape points for only half of the tire width. If the tire carcass shape is not defined, Adams/Tire defines it as a rectangular shape based on the radius and width of the tire.

You define carcass shape in terms of relative values (scales). Absolute coordinate values for the shape are computed by multiplying relative values with the unloaded radius and half-width of the tire. The relative width of the tire must be given in ascending order from 0.0 to 1.0, where the value 0.0 corresponds to the center line of the tire.

Tire Carcass Defined Using Given Shape and Interpolated Values


Road Property FileThe contact algorithm works from a triangle tessellated road representation. The figure below depicts a road surface formed by six nodes numbered 1 through 6. The six nodes together form four triangular patch elements denoted as A, B, C, and D. The unit outward normal for each triangular patch is shown for the sake of clarity. Much like finite-element mesh convention, you define a road by first specifying the coordinates of each node in the road-reference-marker axis system. Subsequently, you specify the three nodes that form each triangular patch. For each triangular patch, you can specify a coefficient of friction.

Road Representation in Adams/Tire

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Defining the 3D Shell Road SurfaceYou use a road property file to define the three-dimensional road surface. The road property file consists of five data blocks:

• Header • Units • Model • Nodes • Elements

These blocks of data can appear in any order in the file, and keywords can appear in any order within the block to which they belong.

The road property file can contain more data than what the 3D Shell Road currently requires. The 3D Shell Road searches for the blocks and keywords it needs and disregards any additional information in the file. Any line that is not recognized as input data is treated as a comment, and therefore skipped. Therefore, you can use almost any character to begin a comment line, but we recommend that you use $'s, !'s, or #'s to avoid confusion. Avoid using comment lines beginning with a square bracket ( [ ), or lines that could interfere with keywords.

Tables must always appear as one set of data. No comment or empty lines are allowed between lines. Tables must always have a header line beginning with a brace, ( { ).

A keyword and its value are separated by an equal sign (=). You must enter strings within single (' ') or double (" ") quotes.


Examples of Blocks:

Units BlockBlock header: [UNITS]Keywords: Allowed values:LENGTH = {'meter', 'mm', 'cm', 'km', 'inch', 'mile'}

Model BlockThe method keyword in the block determines the road contact algorithm Adams/Tire uses. You must set method='3D' to instruct Adams/Tire to use the 3D Shell Road algorithm.

Block header: [MODEL]Keywords: Allowed values:METHOD = {'3D'}

Nodes BlockBlock header: [NODES]Keywords: Allowed values:NUMBER_OF_NODES = <an integer number>Tabular data:{ node x_value y_value z_value }1 <a real number (X)> <a real number (Y)> <a real number (Z)>2 <a real number (X)> <a real number (Y)> <a real number (Z)>...<an integer number> <a real number (X)> <a real number (Y)> <a real number (Z)>

Elements BlockBlock header: [ELEMENTS]Keywords: Allowed values:NUMBER_OF_ELEMENTS = <an integer number>Tabular data:{ node_1 node_2 node_3 u }<an integer number> <an integer number> <an integer number> <a real number><an integer number> <an integer number> <an integer number> <a real number>...<an integer number> <an integer number> <an integer number> <a real number>

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User-Written Tire/Road Models

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Overview of Creating User Tire and Road ModelsThis section of the help explains how to create your own tire models for use with Adams/Tire. To use this help, you must have:

• Intermediate proficiency using Adams/Solver, Adams/Car, Adams/Chassis, or Adams/View.• Ability to compile and link user-written subroutines with Adams/Solver to build an

Adams/Solver user library.• Advanced knowledge of tire mechanics and tire modeling.• Basic knowledge of FORTRAN programming.• Access to a source code debugger.

You can create tire or road models that extend the capabilities of Adams/Tire to better meet your needs. You create a tire model by writing a TYRSUB subroutine that Adams/Tire calls to calculate tire forces and moments. You create a road model by writing a ARCSUB subroutine that Adams/Tire calls to determine the tire-road contact point, local road normal, and road coefficient of friction.

The sections introduce you to creating tire and road models:

• How Adams/Tire Works

• What Adams/Tire Expects Tire Models to Do

• Steps to Create a Tire or Road Model

• Example Tire Model

How Adams/Tire WorksBefore you create a tire or road model it is important to know a little about how Adams/Tire works, and how, in particular, Adams/Tire decides what tire model or road model to use. When you add tires to your Adams model and submit it for analysis:

• Adams/Solver invokes Adams/Tire because of the GFORCE and DIFF statements with USER functions in the Adams model.

• Adams/Tire gets the tire property file name from a STRING statement in the Adams model, opens the file, and reads portions of it to determine which tire model to use (for example, Fiala, MF-TYRE, or your tire model). If the [MODEL] block in tire property, for example, looks like this:

[MODEL]PROPERTY_FILE_FORMAT = 'USER'FUNCTION_NAME = 'TYR501'

Adams/Tire uses the tire model implemented in subroutine TYR501.

• Adams/Tire gets the road property file name from another STRING statement in the Adams model, opens the file, and reads portions of it to determine which road model to use (for example, 2D, 3D, or your road model). If the [MODEL] block in the road property file, for example, looks like this:

13User-Written Tire/Road Models

[MODEL]METHOD = 'USER'USER_SUB_ID = 400

Adams/Tire uses the road model implemented in subroutine ARC400.

• Adams/Tire then calls the tire model to initialize it. And, in turn, the tire model calls the road model to initialize it.

• Adams/Tire also calls the tire model many times during a simulation, passing it the wheel states (displacement, orientation, and velocity). The tire model calls the road model, which returns the tire-road contact point, local road normal, and coefficient of friction. The tire model then calculates the tire forces and moments and returns them to Adams/Tire.

The following figure shows the relationship between Adams/Tire, tire models, road models, and the tire and road property files.

Flow of Information in Adams/Tire

What Adams/Tire Expects Tire and Road Models to DoLearn about expectations for:

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• Tire Models

• Road Models

Tire ModelsAdams/Tire executes in two basic phases:

• Initialization - During the initialization phase, Adams/Tire expects a tire model to: • Read parameters from the tire property file and return them to Adams/Tire for storage in

static memory.• Call the road model so it can read the road property file.

• Simulation - During the simulation phase, Adams/Tire expects a tire model to: • Call the road model to obtain the tire-road contact point, local road normal, and coefficient

of friction.• Calculate tire forces and moments and return them in System International (SI) units

(Newton and Newton-meters) in the ISO-C (TYDEX) axis system.• Return other results in an array for plotting and output. For example, return slip angle,

inclination angle, and effective rolling radius.

The interaction between Adams/Tire and tire models generally adheres to the TYDEX Working Group's Standard Tire Interface v1.4 (STI v1.4).To learn more about how Adams/Tire interacts with tire models, including the calling arguments for TYRSUB, see Creating Tire Models.

Road ModelsAdams/Tire does not directly call road models. Instead, Adams/Tire calls the tire, and the tire model (TYRSUB) calls the road model. Again, there are two basic phases of execution:

• Initialization - During initialization, Adams/Tire expects a road model to read parameters from the road property file and return them through the tire model to Adams/Tire for storage in static memory.

• Simulation - During simulation, road models calculate the tire-road contact point, local road normal, and local coefficient of friction. The road model calculates these quantities based on the location and orientation of the wheel center of the tire. To learn more about road models, see Creating Road Models.

Steps to Create a Tire or Road ModelUse the following steps as a guide when creating your own tire or road model:

1. Create your own model using an example tire or road model as a guide. Before you begin you should consider:

• How your model differs from existing models included with Adams/Tire.• How your tire model will calculate tire kinematic quantities, such as slip angle. Adams/Tire

provides utilities you might want to use (see Utilities for Reading Property Files).


• What outputs Adams/Tire requires for tire and road models. And, in the case of a tire model, what additional quantities you might want to output.

2. Create an example property file for use with your tire or road model and the code to read the file. Before you begin you need to know:

• What parameters your tire or road property files will contain, including those required by Adams/Tire.

• How to read the parameters from the file and how to convert these parameters from the units specified in the property file to SI units (meters-kilograms-seconds).

• Where to store the parameters in the tire (TYRARR) or road (ROPAR) parameters array so Adams/Tire can save them between calls to your TYRSUB.

3. Create a private version of an Adams/Car Adams/Solver user library (currently you cannot add a user tire or road models outside of Adams/Car).

4. Test your tire or road model using a simple Adams model and the private Adams/Car Adams/Solver user library. You can find a simple Adams model and Adams/Solver command file for testing tires and roads at install_dir/solver/atire/test_rig.{adm,acf}. Access to a debugger is helpful to verify that your tire model is working properly.

Example Tire ModelAdams/Tire includes an example tire model and its related files that implement a Fiala tire model with relaxation effects.

The example illustrates all the tasks a typical tire model must perform and provides you with a starting point when creating your own tire models. The example consists of the following files located at install_dir/solver/atire/usrsubs:

• A tire property file incorporating a relaxation length parameter: usr_fiala.tir• A subroutine for reading the tire property file: rpf501.f• A TYRSUB that calls rpf501 to read the tire property file and that computes the tire forces and

moments: tyr501.f• An include file that tyr501.f and rpf501.f share. The include file defines the locations in the

TYRARR array of parameters read from the tire property file: tyr501.inc• Other include files that tyr501.f requires: abg_varptr.inc and ac_tir_jobflg.inc

To learn more about the default Fiala tire model supplied with Adams/Tire, see Using the Fiala Handling Force Model.

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Creating Tire ModelsYou create a user tire model by writing a TYRSUB subroutine that Adams/Tire calls to calculate tire forces and moments. Learn about:

• Instructing Adams/Tire to Call Your TYRSUB

• Tasks Your TYRSUB Must Perform

• TYRSUB Arguments

Instructing Adams/Tire to Call Your TYRSUBYou instruct Adams/Tire to call your TYRSUB by defining a tire property file that specifies a user property file format and subroutine ID that matches your TYRSUB. For example, Adams/Tire calls TYR501 if it finds the following in the tire property file:

[MODEL]PROPERTY_FILE_FORMAT = 'USER'FUNCTION_NAME = 'TYR501'

Your TYRSUB generally will read data it needs from the tire property file. In addition, Adams/Tire requires each tire property file to contain specific information about units, tire dimensions, tire stiffness, and tire damping. For more information about defining and reading tire property files, see Defining and Reading Tire Property Files.

Tasks Your TYRSUB Must PerformAll TYRSUBs must perform these tasks:

1. Read any data it requires from the tire property file.2. Call the ROAD subroutine to initialize the road model and to determine the road location, local

road normal, and road coefficient of friction.3. Calculate the tire forces and moments in units of Newtons and Newton-meters and return them to

Adams/Tire at the wheel center in the ISO-C axis system (see About Axis Systems and Sign Conventions).

4. Load results, such as slip angle, in the VARINF array for plotting.5. Handle errors. For example, report when needed data is missing from the tire property file.

The TYDEX Working Group's Standard Tire Interface version 1.4 (STI v1.4), to which Adams/Tire generally adheres, governs how and when your TYRSUB performs these tasks. According to STI v1.4, the TYRSUB performs specific tasks based on the value of the integer argument JOBFLG. The skeletal TYRSUB example, shown below, shows which tasks the TYRSUB performs based on JOBFLG. The arguments and their declarations are omitted here for brevity. For complete descriptions of the arguments.

Skeletal TYRSUB ExampleSUBROUTINE TYRxxx(....)include 'ac_sti_jobflg.inc'include 'abg_varptr.inc'

IF ( JOBFLG .EQ. INIT .OR.. JOBFLG .EQ. RESET ) THEN


c Read Tire Property File

ENDIF

c Call The ROAD Subroutine

CALL ROAD(....)

IF ( JOBFLG .EQ. NORMAL .OR.. JOBFLG .EQ. DIFF ) THEN

C Calculate The Tire Forces And Moments

c Tire Kinematics

c Tire Forces And Moments At Contact Patch

c Transfer Forces And Moments to Wheel Center in ISO C-Axis System

c Load Results In VARINF Array

ENDIF

c Handle Errors

RETURNEND

Reading The Tire Property FileDuring the initialization process, Adams/Tire calls your TYRSUB with JOBFLG = 2 (INIT ). When JOBFLG = INIT, your TYRSUB should open and read the tire property file. Your TYRSUB can statically store the data read from the property file or return it to Adams/Tire in the TYPARR array. Adams/Tire stores the contents of TYPARR in static memory between calls to your TYRSUB.

Adams/Tire requires all tire property files to contain specific information in TeimOrbit format that it reads before calling your TYRSUB. For more information about these requirements. Finally, Adams/Tire provides utilities for reading property files employing TeimOrbit format. For information about these utilities and TeimOrbit format.

Calling the ROAD SubroutineEach time Adams/Tire calls your TYRSUB, your TYRSUB must call the ROAD subroutine to ensure that the ROAD subroutine is initialized properly and can perform its work of calculating the tire-road contact point, the local road normal, and coefficient of friction.

Adams/Tire passes a pointer to the ROAD subroutine to your TYRSUB. Therefore, your TYRSUB declares ROAD as an external and never knows the exact subroutine that is called. This allows your TYRSUB to work with different road models without having to alter your TYRSUB.

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Calculating Tire Forces and MomentsWhen Adams/Tire calls your TYRSUB with JOBFLG = NORMAL (0) or DIFF (5), your TYRSUB should calculate and return tire forces and moments. To calculate tire forces and moments, typically your TYRSUB will:

• Call the ROAD subroutine.• Calculate tire kinematics.

• Calculate tire forces and moments at the tire contact patch.• Transfer the forces and moments from the contact patch to the wheel center in ISO-C axis system

for return to Adams/Tire.

Loading Results For PlottingWhen Adams/Tire calls your TYRSUB with JOBFLG = NORMAL(0) or DIFF (5), your TYRSUB should load results in the VARINF array. The specific results and their location in the VARINF array are defined in include file:

install_dir/solver/atire/usrsubs/abg_varptr.inc.

For example, abg_varptr.inc defines integer parameters giving the location of the lateral and longitudinal slips that you use, such as:

VARINF( slipi_ptr ) = alphaVARINF( slipx_ptr ) = kappa

Where alpha and kappa are the lateral and longitudinal slip, respectively, calculated by your TYRSUB.

Handling ErrorsAccording to TYDEX STI v1.4, a TYRSUB should not stop the execution of a simulation because of a fatal error. Instead, it should use the IERR argument to return a fatal error and use the TYRMOD argument to return an error message. The simulation code can then cleanly terminate execution. In Adams/Tire, however, you can call the Adams/Solver utility, ERRMES, from your TYRSUB to output a message to your screen and message file to terminate the Adams execution.

TYRSUB Arguments

Note: Adams/Tire provides utilities for calculating slip angle, inclination angle, longitudinal slip, and other quantities in SAE coordinates.

Note: Adams/Car and Adams/Chassis use the effective rolling radius returned in the VARINF array to calculate initial wheel rotational velocities. In addition, Adams/Driver examines the lateral and longitudinal slips returned in VARINF to determine how close a vehicle is to its limit of adhesion. So if you plan to use your TYRSUB with these products, you must load results in the VARINF array.


The following sections provide an overview of the arguments in TYRSUB based on their function, and then describes each argument in order of calling sequence:

• TYRSUB Calling Sequence

• TYRSUB Input Arguments

• TYRSUB Output Arguments

• TYRSUB Argument Descriptions

TYRSUB Calling SequenceThe following sample code shows the calling sequence for arguments in TYRSUB:

Subroutine TYRXXX( + NDEV, ISWTCH, JOBFLG, IDTYRE,+ TIME, DIS, TRAMAT, ANGTWC, VEL, OMEGA, OMEGAR,+ NDEQVR, DEQVAR, NTYPAR, TYPARR,+ NCHTDS, CHTDST, ROAD, IDROAD,+ NROPAR, ROPAR, NCHRDS, CHRDST,+ FORCES, TORQUE, DEQINI, DEQDER, TYRMOD,+ NVARS, VARINF, NWORK, WRKARR,+ NIWORK, IWRKAR, IERR)

TYRSUB Input ArgumentsThe types of input arguments are:

• Job Control

• States

• Tire Properties

Job ControlThere is only one job control argument: JOBFLG. The value of JOBFLG determines the task that TYRSUB performs, such as reading the tire property file or evaluating the tire forces and moments.


StatesThe tire states contain the displacement, orientation, and velocity information about the wheel and wheel carrier (hub). The state arguments are:

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Subroutine TYRXXX(+ NDEV, ISWTCH, JOBFLG, IDTYRE,+ TIME, DIS, TRAMAT, ANGTWC, VEL, OMEGA, OMEGAR,+ NDEQVR, DEQVAR, NTYPAR, TYPARR,+ NCHTDS, CHTDST, ROAD, IDROAD,+ NROPAR, ROPAR, NCHRDS, CHRDST,+ FORCES, TORQUE, DEQINI, DEQDER, TYRMOD,+ NVARS, VARINF, NWORK, WRKARR,+ NIWORK, IWRKAR, IERR)

Tire PropertiesThe tire properties arrays (TYPARR) contain the data that your TYRSUB reads from the tire property file during initialization and returns to Adams/Tire. Adams/Tire stores this array statically.

The integer NTYPAR is the size of the TYPARR array, which is currently limited to 300.


TYRSUB Output ArgumentsThe types of output arguments are:

• Forces and Moments

• Information

• Error Handling

Forces and MomentsThe arguments FORCES and TORQUE return the forces and moments on the wheel at the wheel center. TYRSUB returns the forces and moments in units of Newtons and Newton-meters, respectively, according to the TYDEX ISO-C coordinate system. For more information on the TYDEX axis systems, see Tire Axis Systems.

Subroutine TYRXXX(+ NDEV, ISWTCH, JOBFLG, IDTYRE,+ TIME, DIS, TRAMAT, ANGTWC, VEL, OMEGA, OMEGAR,+ NDEQVR, DEQVAR, NTYPAR, TYPARR,+ NCHTDS, CHTDST, ROAD, IDROAD,+ NROPAR, ROPAR, NCHRDS, CHRDST,+ FORCES, TORQUE, DEQINI, DEQDER, TYRMOD,+ NVARS, VARINF, NWORK, WRKARR,+ NIWORK, IWRKAR, IERR)


InformationTYDEX STI supports the output of tire information, such as contact patch forces and slip angle, through the variable information array (VARINF).


Error HandlingTYDEX STI states that the TYRSUB may not terminate execution of the calling program, but rather should return an error code (IERR) and message text (TYRMOD). Adams/Tire modifies the standard and allows TYRSUB to call the Adams/Solver utilities USRMES or ERRMES for purposes of error handling and stopping execution, if desired.


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TYRSUB Argument DescriptionsThe following TYRSUB argument descriptions are listed in order of calling sequence:

NDEVAn integer variable that contains the value of the logical output device number for error messages. We recommend calling the Adams/Solver utilities USRMES or ERRMES rather than writing directly to the NDEV device. This ensures proper handling of the error message. For more information, see USRMES and ERRMES in the Adams/Solver Subroutines online help.

ISWTCHAn integer variable that contains the value of the USE_MODE control switch. Adams/Tire sets the ISWTCH variable to zero in all cases except dynamic and quasi-static simulations (for example, Adams/Solver modes 4 and 6). For dynamic and quasi-static simulations, ISWTCH = TYPARR(1).

JOBFLG - (Job Control Flag)An integer variable whose value determines the action TYRSUB should take. Table 1 shows the values and meaning of JOBFLG

• NDEV

• ISWTCH

• JOBFLG

• IDTYRE

• TIME

• DIS

• TRAMAT

• ANGTWC

• VEL

• OMEGA

• OMEGAR

• NDEQVR

• DEQVR

• NTYPAR

• TYPARR

• NCHTDS

• CHTDST

• ROAD

• IDROAD

• NROPAR

• ROPAR

• NCHRDS

• CHRDST

• FORCE

• TORQUE

• DEQINI

• DEQDER

• TYRMOD

• NVARS

• VARINF

• NWORK

• WRKARR

• NIWORK

• IWRKAR

• IERR


JOBFLAG Values and Descriptions:

Each value is explained below.

• INITIALIZE (JOBFLG = 2) The first call to a TYRSUB always has JOBFLG=init=1. TYRSUB opens and reads any files necessary to process the tire data before the actual simulation begins.

• RESET (JOBFLG = 3) The TYRSUB is called with JOBFLG=reset=3 after the first initialization while IFLAG=true. You can ignore reset mode in Adams/Tire. This deviates from the TYDEX STI definition stating that the tire parameters array may have changed.

• INQUIRE (JOBFLG = 1) Currently, Adams/Tire does not support JOBFLG=inquire=1. TYDEX STI states that a TYRSUB when called with JOBFLG=inquire=1 should return the needed dimensions of the TYPAR, DEQVAR, VARINF, WORK, and IWRAR arrays. For example, a tire that requires 30 states integrated (30 modes) would set NDEQVAR=30 to give the needed dimension of the DEQVAR array. Currently, Adams/Tire limits the number of integrated states to two. These are usually used for relaxation length in the longitudinal and lateral direction. Therefore, this JOBFLG setting is not used in this release of Adams/Tire.

• END SIMULATION (JOBFLG = endsim = 99) The TYRSUB is called with JOBFLG=endsim=99 just before Adams/Solver is excited. The TYRSUB should close any open files and free any memory allocated. Message handling is not available at this point during execution. Therefore, calls to ERRMES or USRMES do not function.

• SUCCESSFUL INTEGRATION STEP (JOBFLG = sstep = 4)

Description: Value:Parameter in

ac_sti_jobflg.inc:INITIALIZE JOBFLG = 2 INITRESET JOBFLG = 3 RESETINQUIRE* JOBFLG = 1 INQUIREEND SIMULATION JOBFLG = ENDSIM =

99ENDSIM

SUCCESSFUL INTEGRATION STEP*

JOBFLG = SSTEP = 4 SSTEP

NORMAL EVALUATION

JOBFLG = NORMAL = 0

NORMAL

DERIVATIVE EVALUATION

JOBFLG = DIFF = 5 DIFF

* Indicates item is not supported in current version of Adams/Tire.

../../../utility/errmes.html

../../../utility/usrmes.html

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Currently, Adams/Tire does not support JOBFLG = sstep = 4 in its version of TYDEX STI. When JOBFLG = sstep = 4, the input states (such as displacement and velocity) are converged states.

• NORMAL EVALUATION (JOBFLG =normal = 0) When called with JOBFLG = normal = 0, TYRSUB returns the tire forces and torques based on the inputs.

• DERIVATIVE EVALUATION(JOBFLG = diff = 5) When called with JOBFLG = diff = 5, TYRSUB should return tire forces and torques based on the inputs. Adams/Solver uses the returned value to estimate the partial derivatives of the forces and torques with respect to the inputs.

IDTYREAn integer variable that provides the ID of the GFORCE statement that applies the tire forces and moments to the wheel.

TIMEA double-precision variable that provides the current simulation time.

DISA double-precision array of dimension three, which specifies the values of the wheel carrier translational displacement (x, y, z) at the wheel center with respect to the road reference marker expressed in the road reference marker's axis system in units of meters.

TRAMATA double-precision array of dimension 3 x 3, which specifies a transformation matrix used to transform data from the wheel carrier axis system to the road reference marker axis system.

ANGTWCA double-precision variable, which specifies the rotational angle of the wheel with respect to the wheel carrier in radians.

VELA double-precision array of dimension three, which specifies the values of the wheel carrier translational velocities (x, y, z) at the wheel center with respect to the road reference marker expressed in the wheel carrier (ISO-C) axis system in units of meters/second.

OMEGAA double-precision array of dimension three, which specifies the wheel carrier angular velocity at the wheel center with respect to the road reference marker expressed in the wheel carrier (ISO-C) axis system in units of radians/second.


OMEGARA double-precision variable that specifies the value of the rotational speed of the rim with respect to the wheel carrier about the wheel's (rim's) spin axis in radians/second.

NDEQVRAn integer variable the dimension of DEQVAR, default is two, which means that Adams/Tire supports tire models using two differential equations.

The number of states can be set by adding N_TIRE_STATES in the [MODEL] section of the tire property file:

[MODEL]N_TIRE_STATES = <number of required stated>

DEQVARA double-precision array that provides the values of the differential equations associated with the tire. Note that to determine the values in the DEQVAR array, Adams/Tire integrates the derivatives that the tire model returns in the DEQDER array.

NTYPARAn integer variable that represents the dimension of the tire parameters array (TYPARR). If NTYPAR equals zero, TYPARR contains no values.

TYPARRThe tire parameters array. A double-precision array of dimension NTYPAR that contains the values of the tire model parameters. If the PROPERTY_FILE_FORMATin the tire property file is set to 'USER', NTYPAR is set to zero and the tire property file name is passed to the STI in the CHTDSTstring. The maximum size of TYPARR is 300.

NCHTDSAn integer variable that gives the number of characters in the tire property file name (CHTDST).

CHTDSTThe tire property file name. A character variable of length 256 that provides the tire property file name and path (for example: "/usr/people/cjones/tire.tpf ").

ROADThe external symbol name that provides the road contact subroutine that TYRSUB calls to determine the local road normal and tire-road contact point.

IDROADAn integer that specifies the branch flag for the road contact model method. The value is set according to the contents of the road property file (.rdf). Reserved values are:

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900 BEDPLATE used for suspension analysis901 2D Handling (point follower) Contact method902 2D Durability Contact method903 3D Handling (point follower on a smooth road)904 3D Durability Contact method

For more information, see Creating Road Models.

NROPARAn integer variable that gives the dimension of ROPAR. If NROPAR equals zero, ROPAR contains no values.

ROPARThe road parameters array. A double-precision array of dimension NROPAR, which contains the values of the road contact model parameters. If the method is set to 'USER' in the [MODEL] block of the road property file, then NROPAR is set to zero, and the road property file name is passed to the STI in character variable CHRDST. For more information, see Creating Road Models.

NCHRDSAn integer variable that provides the number of characters (length) of the road property file name.

CHRDSTThe road property file name. A character variable of length 256 that holds the road property file name and path, for example: /usr/people/cjones/road.dat.

FORCEThe tire force vector. A double-precision array of dimension three, that TYRSUB outputs. It provides tire forces at the wheel center in Newtons expressed in the TYDEX-C (ISO-C) axis system.

TORQUEThe tire moment vector. A double-precision array of dimension three that the TYRSUB outputs. It provides the tire moments at the wheel center in Newton-Meters expressed in the TYDEX-C (ISO-C) axis system.

DEQINIA double-precision array of dimension NDEQVR. It specifies the initial values of the differential equations (DEQVAR) associated with the tire. When JOBFLG = inquire = 1, TYRSUB returns the initial values of the differential equations. For other values of JOBFLG, the values returned in DEQINI are ignored. Currently, Adams/Tire does not use values returned in DEQINI. The initial values of differential equations are always set to zero.

../../tire/tire_road.htm


DEQDERA double-precision array of dimension NDEQVR. It provides the time derivative of the differential equations (DEQVAR) associated with the tire. When JOBFLG = normal = 0 or JOBFLG = diff = 5, TRYSUB must return values for DEQDER. For other values of JOBFLG, any values returned in DEQINI are ignored.

TYRMODA character variable of length 256 containing a descriptive error message. Adams/Tire outputs the message to the screen and message file (.msg) when the value of IERR is not equal to zero.

NVARSAn integer parameter giving the maximum size, currently 40, of the VARINF array. A TYRSUB must not assign a value to NVARS.

VARINFThe tire-variable information array. A double-precision array of dimension NVARS for outputting information, such as tire contact patch forces and slip angle, which the simulation does not use directly. TYDEX STI specifies that the first six values of the VARINF array should hold the contact patch forces and moments in the TYDEX-H (ISO-W) axis system.

NWORKAn integer parameter giving the dimension of the working array (WRKARR), currently one. A TYRSUB must not assign a value to NWORK.

WRKARRThe working array. A static double-precision array of dimension NWORK the tire model may use as desired. Currently, the working array is limited to a dimension of one. Adams/Tire stores these values for each tire between calls to TYRSUB.

NIWORKAn integer parameter giving the dimension of the integer working array (IWRKAR), currently one. A TYRSUB must not assign a value to NIWORK. As specified in TYDEX STI, when Adams/Tire adds support for the JOBFLG = inquire = 1, TYRSUB can return the actual dimension of IWRKAR using NIWORK.

IWRKARThe integer working array. A static integer array of dimension NIWORK, which is currently limited to one, that TYRSUB can use as needed. Adams/Tire stores these values for each tire between calls to the TYRSUB.

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IERRThe integer variable giving an error value. Valid values are:

• 0 No error • 1 Warning: Calling program should print message contained in TYRMOD • 2 Error: Calling program must not use the outputs • 3 Fatal Error: Calling program should stop execution.


Defining and Reading Tire Property FilesLearn more about creating tire property files:

• About Tire Property Files

• Example Tire Property File

• Required Blocks

About Tire Property Files When you create your own user tire model, you must also define your own tire property file. At a minimum, this file instructs Adams/Tire to call your tire model to compute tire forces and moments during a simulation and supplies to Adams/Tire required information about the tire.

Adams/Tire requires every tire property file to supply:

• Tire model to be used (for example, a reference that causes Adams/Tire to call your TYRSUB). • Units of the data contained in the file.• Dimensions of the tire: unloaded radius, width, and aspect ratio.• Tire vertical stiffness and damping.

Because Adams/Tire reads the above information from every tire property file, you must provide it in the form shown in the next sections.

Besides the required data, your property file can contain any information in any form you want. If you choose to structure the data in TeimOrbit format, MSC supplies a set of utilities for reading the data from your file. These utilities include routines to obtain unit conversion factors so you can convert data to SI units. For more information, see Utilities for Reading Property Files.

Example Tire Property File$-----------------------------------------------------------MDI_HEADER[MDI_HEADER]FILE_TYPE

= 'tir'FILE_VERSION

= 2.0FILE_FORMAT

= 'ASCII'(COMMENTS){comment_string}'Tire

- XXXXXX''Pressure

- XXXXXX''Test Date

- XXXXXX''Test tire''New File Format v2.1'

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$----------------------------------------------------------------units[UNITS]LENGTH

= 'mm'FORCE

= 'newton'ANGLE

= 'degree'MASS

= 'kg'TIME

= 'sec'$----------------------------------------------------------------model[MODEL]! use mode

12

! --------------------------------- ! smoothing

X !PROPERTY_FILE_FORMAT

= 'USER'FUNCTION_NAME

= 'TYR501'USE_MODE

= 2.0$------------------------------------------------------------dimension[DIMENSION]UNLOADED_RADIUS

= 309.9WIDTH

= 235.0ASPECT_RATIO

= 0.45$-----------------------------------------------------------parameter[PARAMETER]VERTICAL_STIFFNESS

= 310.0VERTICAL_DAMPING

= 3.1ROLLING_RESISTANCE

= 0.0CSLI

= 1000.0CALPHA

= 800.0CGAMMA

= 0.0UMIN

= 0.9


UMAX= 1.0

RELAXATION_LENGTH= 0.0

$---------------------------------------------------------------shape[SHAPE]{radial width}1.0

0.01.0

0.21.0

0.41.0

0.51.0

0.61.0

0.71.0

0.81.0

0.851.0

0.90.9

1.0

Required BlocksYour tire property file must contain a specific set of blocks that Adams/Tire expects. These blocks can appear in any order, and your tire property file can contain other blocks that you define. The blocks that your tire property file must contain are:

• [MODEL] Block • [UNITS] Block

• [DIMENSION] Block

• [PARAMETER] Block

[MODEL] BlockThe [MODEL] block specifies the tire model that Adams/Tire will use. For your tire model, specify a property file format of “USER”and a function name that is the entry point to the tire functions, such as:

[MODEL] PROPERTY_FILE_FORMAT = “USER”FUNCTION_NAME = “TYR501”

In the example above, Adams/Tire calls subroutine TYR501 to read the tire property file and to evaluate the tire forces and moments.

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[UNITS] BlockA [UNITS] block specifies the units of the data in the tire property file. This enables Adams/Tire to convert any data it reads from the tire property file to SI units (meters kilograms, Newtons, seconds, radians). Any data your TYRSUB reads from the tire property file should also be converted to SI units, as the example TYRSUB illustrates.

An example [UNITS] block is shown below:

[UNITS] LENGTH

= 'mm' FORCE

= 'newton' ANGLE

= 'radians' MASS

= 'kg' TIME

= 'sec'

The allowed values for unit strings are:

[DIMENSION] BlockThe [DIMENSION] block specifies the tire's unloaded radius, width, and aspect ratio. Adams/Tire uses these values to size wheel and tire graphics.

[DIMENSION] UNLOADED_RADIUS = real_value > 0

WIDTH = real_value > 0ASPECT_RATIO = 1 > real_value > 0

FORCE: FORCE : 'KG_FORCE', 'NEWTON', 'KNEWTON','POUND_FORCE', 'KPOUND_FORCE', 'DYNE', 'OUNCE_FORCE'

MASS: 'KG', 'GRAM', 'POUND_MASS', 'KPOUND_MASS', 'SLUG', 'OUNCE_MASS'

LENGTH: 'KM', 'METER', ' CM', 'MM', 'MILE', 'FOOT', 'INCH'TIME: 'MILLISECOND', 'SEC', 'MINUTE', 'HOUR' ANGLE: 'DEGREE', 'RADIAN'

Note: You can use the utility subroutine ATRTOU to read the [UNITS] block from a tire property file and then use the utility subroutine ACUNFN to obtain unit conversion factors.


[PARAMETER] BlockThe [PARAMETER] block specifies the vertical stiffness and damping of the tire. Adams/Tire makes this information available to Adams/Car and Adams/Chassis during suspension analysis by incorporating a test-rig tire.

[PARAMETER] VERTICAL_STIFFNESS = real_value > 0 VERTICAL_DAMPING = real_value >= 0

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Creating Road ModelsYou create a road model by writing a road evaluation function that tire models call to determine tire-road contact points, local road normal, and coefficient of friction. Learn about:

• Instructing Adams/Tire to Use Your Road Function

• Tasks Your Road Function Must Perform

• Skeletal Road Function Example

• Road Function Subroutine Calling Sequence

• Road Function Input Arguments

• Road Function Output Arguments

Instructing Adams/Tire to Use Your Road FunctionYou instruct Adams/Tire to use your road function by defining a road property file that specifies METHOD="USER" and contains a user function name that matches your road function. For example, Adams/Tire uses function ARC501 if the road property file contains:

[MODEL]METHOD = 'USER'USER_SUB_ID = 501

Then, during a simulation Adams/Tire passes the address of your road function in the ROAD argument to TYRSUB. TYRSUB then calls your road function to calculate the tire-road contact point, local road normal, and coefficient of friction.

From Adams/Tire, TYRSUB passes to your road function the name of the road property file so your road function can open and read data from the file.

Tasks Your Road Function Must PerformAll road functions must perform these tasks:

1. Read any data it requires from the road property file.2. Calculate the tire-road contact point, local road normal, and road coefficient of friction.3. Handle errors. For example, report when needed data is missing from the road property file.

The value integer argument JOBFLG governs how and when your ARCSUB performs these tasks. The skeletal road function example, shown next, shows which tasks the road function performs based on JOBFLG. The arguments and their declarations are omitted here for brevity. For information on the ARCSUB arguments, see Road Function Input Arguments.

Skeletal Road Function ExampleSUBROUTINE ARC501(....)

include 'ac_sti_jobflg.inc'


IF ( JOBFLG .EQ. INIT .OR.. JOBFLG .EQ. RESET ) THEN

c Read Road Property File

ENDIF

IF ( JOBFLG .EQ. NORMAL .OR.. JOBFLG .EQ. DIFF ) THEN

c Calculate Tire-Road Contact Point, Road Normal, andc Coefficient of Friction.

ENDIF

c Handle Errors

RETURNEND

Road Function Subroutine Calling SequenceSUBROUTINE ARC501(JOBFLG, IDTYRE,& TIME, DIS, TRAMAT,& IDROAD, NROPAR, ROPAR, NCHRDS, CHRDST,& NSHAPE, SHAPE, UNLDRD, WIDTH,& NROAD, EFFVOL, EFFPEN, RCP,& RNORM, SURFAC, IERR, ERRMSG )

Road Function Input ArgumentsThe input arguments are explained below in calling sequence order:

• JOBFLG

• IDTYRE

• TIME

• DIS

• TRAMAT

• IDROAD

• NROPAR

• ROPAR

• NCHRDS • CHRDST

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• NSHAPE

• SHAPE

• UNLDRD

• WIDTH

JOBFLGAn integer variable that contains the value of the initialization flag. JOBFLG takes the value:

• 0 - Normal mode • 1 - Subroutine must return the actual dimensions of NTYPAR, NDEQVR, NVARS, NIWORK,

NWORK(Not used in Adams/Tire) • 2 - First initialization • 3 - Re-initialization during simulation • 4 - Successful step (not used in Adams/Tire) • 5 - Adams/Solver is differencing (unique to Adams/Tire) • 99 - Final simulation step (not used in Adams/Tire)

IDTYREAn ID of the GFORCE statement that applies the tire forces and moments to the wheel.

TIMEA double-precision variable that contains the value of the current simulation time.

DISA double-precision array of dimension 3, which specifies the values of the wheel carrier translational displacement (x, y, z) at the wheel center with respect to the road reference marker.

TRAMATA double-precision array of dimension 3 x 3, which specifies a transformation matrix used to transform data from the wheel carrier coordinate system to the coordinate system of the road reference marker.

IDROADAn integer that specifies the road model method (for example, 900 for ARC900).

NROPARAn integer variable that represents the dimension of ROPAR. If NROPAR is equal to zero, ROPAR contains no available values.


ROPARA double-precision array of dimension NROPAR, which contains the values of the road model parameters. If [MODEL] -> METHOD in the road property file is set to 'USER', NROPAR is set to zero and the road property file name is passed to the STI in the CHRDST string.

NCHRDSAn integer that represents the dimension of CHRDST.

CHRDSTA character string of dimension NCHRDS, which contains the name of the road property file. The CHRDST string contains the full path of the file up to a maximum of 256 characters.

NSHAPEAn integer that represents the dimension of SHAPE. If NSHAPE = 0, then the cross section defaults to a cylindrical shape.

SHAPEA double-precision array of dimension (2,NSHAPE) representing the shape of the tire carcass cross-section:

• 1 = Radius [%] • 2 = Width [%]

Legal values for radius and length are:

• 1.0 £ Radius £ 0.0 • 0.0 £ Width £ 1.0

For example, the following shows how data is stored in the SHAPE array:

Shape (1) = First fractional radiusShape (2) = First fractional widthShape (3) = Second fractional radiusShape (4) = Second fractional radius

Note: 1.0 = 1/2 width

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NSHAPEAn integer that represents the dimension of SHAPE. If NSHAPE = 0, then the cross section defaults to a cylindrical shape.

SHAPEA double-precision array of dimension (2,NSHAPE) representing the shape of the tire carcass cross-section:

• 1 = Radius [%] • 2 = Width [%]

Legal values for radius and length are:

• 1.0 £ Radius £ 0.0 • 0.0 £ Width £ 1.0

UNLDRDA double-precision variable that specifies the unloaded radius.

WIDTHA double-precision variable that specifies the total width of the tire.

Road Function Output ArgumentsThe output arguments are listed below in calling sequence order:

• NROAD

• EFFVOL

• EFFPEN

• RCP

• RNORM

• SURFAC

• IERR

• ERRMSG

NROADAn integer value that is used to define the surface type. NROAD takes the following values:

• 0 - No road data • 1 - In contact with the road


EFFVOLA double-precision variable that contains the value of the effective penetrated volume between the tire carcass and the road.

EFFPENA double-precision variable that contains the value of the effective penetration between the tire carcass and the road.

RCPA double-precision array of dimension three, which contains the values of the contact point location relative to the road reference marker.

RNORMA double-precision array of dimension three, which contains the road normal vector. This vector is directed out (upward) from the road surface.

SURFACA double-precision variable that contains the value of the average surface friction.

IERRAn integer variable giving the error status of the road contact subroutine. IERR takes the following values:

• 0 = No error • 1 = Warning • 2 = Error - Do not use the results • 3 = Fatal Error

ERRMSGA character string of dimension 80 that contains descriptive error messaging that is passed to the main tire calling routine through TYRMOD.

Note: Inside the road model, STOP statements are not allowed.

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Utilities for Reading Property FilesWriting code to read a file can be a tedious task when creating a user tire or road model. If you already have an existing tire or road property file format and reader, you may need only to modify the format and reader to accommodate the blocks and parameters that Adams/Tire requires. If you do not have an existing property file reader, then Adams/Tire provides a set of utilities for reading TeimOrbit format files that you can use to read property files.

The following sections describe the TeimOrbit format, outlines how to use the utilities that Adams/Tire provides, and documents the calling sequence of the utilities. In addition, it describes the calling sequence of utilities you call to obtain unit conversion factors.

Learn about:

• About TeimOrbit Format

• Using Read TeimOrbit (RTO) Utilities

• Utilities for Reading TeimOrbit Format Property Files

About TeimOrbit FormatAll the standard Adams/Tire tire and road property files employ the TeimOrbit format. TeimOrbit formatting is a way of organizing data into:

• Blocks denoted by brackets "[", "]"• Subblocks denoted by parenthesis "(", ")"• Tables denoted by braces "{", "}"

A subblock is always the child of a block. A table can be a child of either a block or a subblock.

For example, a TeimOrbit file might contain the following blocks and subblocks:

[BLOCK_1]PARAMETER_1 = 1.0(SUB-BLOCK_1)PARAMETER_2 = 2.0{TABLE_1}1.0 2.02.0 3.0[BLOCK_2]PARAMETER_2 = 'TWO'{TABLE_2}1.0 2.02.0 3.0(SUB-BLOCK_2)PARAMETER_1 = 'ONE'

Parameters and tables are located for reading according to the block and/or subblock in which they reside. Therefore, PARAMETER_2 in BLOCK_2 is not confused with PARAMETER_2 in BLOCK_1. This example, which uses realistic names, illustrates where parameter are placed:

[VERTICAL_DATA]STIFFNESS = 310.0DAMPING = 14.3


[LATERAL_DATA]STIFFNESS = 232.0DAMPING = 11.2

Any strings beginning with a dollar sign "$" are ignored and, therefore, are used as comments. Before you create your own property file, we recommend that you review some existing files to learn how they are structured.

Using Read TeimOrbit (RTO) UtilitiesThe process of reading a property file using the RTO utilities is:

1. Open the file using subroutine RTO_OPEN_FILE_F2C.2. Read the [UNITS] block using subroutine ATRTOU.3. Obtain unit conversion factors from Adams/Solver using subroutine ACUNFN.4. Read the desired data from the file and convert the data to SI units using various read TeimOrbit

utilities as explained in ACUNFN.5. Close the file using subroutine RTO_CLOSE_FILE_F2C.

Utilities for Reading TeimOrbit Format Property FilesYou can use the following utilities to read data from TeimOrbit format files:

• ACUNFN

• ACUNFN_F2C

• ACUNMP

• ATRTOU

• RTO_OPEN_FILE_F2C

• RTO_CLOSE_FILE_F2C

• RTO_READ_QUOTED_STRING_F2C

• RTO_READ_SUBBLOCK_STRING_F2C

• RTO_READ_INTEGER_F2C

• RTO_READ_SUBBLOCK_INTEGER_F2C

• RTO_READ_REAL_F2C

• RTO_READ_SUBBLOCK_REAL_F2C

• RTO_READ_TABLE_LINE_F2C

• RTO_START_TABLE_READ_F2C

• RTO_START_SUBBLOCK_TABLE_READ_F2C

ACUNFN

Calling SequenceSubroutine ACUNFN ( UNITS, CV2MDL, CV2SI )

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DescriptionGiven unit strings read from a property file, ACUNFN returns conversion factors from property file units to model and SI units. Generally, you proceed a call to ACUNFN by a call to ATRTOU to read the [UNITS] block from a property file.

You use the unit conversion factors that ACUNFN returns to convert data read from a property file to either model or SI units (Newtons, kilograms, meters, seconds, radians). For example, if you read a damping coefficient from a property file that has units of force*time/length and you need to convert that value to model units, then you might do the following:

damp_coeff = damp_coeff*CV2MDL(1)*CV2MDL(4)/CV2MDL(3)


Arguments

Argument: Type*: Storage: Use* and Description:UNITS

• UNITS(1): force • UNITS (2): mass • UNITS (3): length • UNITS (4): time • UNITS (5): angle

CA 12x5 R Array of five 12-character strings read from the property file containing the unit names.

CV2MDL

• CV2MDL(1)Force conversion

• CV2MDL(2)Mass conversion

• CV2MDL(3) Length conversion

• CV2MDL(4)Time conversion

• CV2MDL(5)Angle conversion

DA 5 E Conversion factor from property file units to model (dataset) units.

CV2SI

• CV2SI(1)Force conversion

• CV2SI(2)Mass conversion

• CV2SI(3)Length conversion

• CV2SI(4)Time conversion

• CV2SI(5)Angle conversion

DA 5 E Conversion factor from property file units to SI units. SI units are Newtons, kilograms, meters, seconds, and radians.

*Key:

Type: A = array; C = character; D = double precision; I = integer (for example, DA indicates double-precision array).

Use: R = referenced, but not set; E = evaluated (for example, the subroutine sets the value of this argument).

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ACUNFN_F2C

Calling SequenceSubroutine ACUNFN_F2C ( FORCE, MASS, LENGTH, TIME, ANGLE, CV2MDL, CV2SI)

DescriptionProvides an entry point to ACUNFN from C-language routines.

Arguments

Argument: Type*: Storage: Use* and Description:FORCE C 12 R Force string from property

file [UNITS] block.MASS C 12 R Mass string from property

file [UNITS] block.LENGTH C 12 R Length string from property

file [UNITS] block.TIME C 12 R Time string from property

file [UNITS] block.ANGLE C 12 R Angle string from property

file [UNITS] block.


ACUNMP

Calling SequenceSubroutine ACUNMP ( UN_IN, UN_OUT )

DescriptionMaps standard property file (Adams/View) unit strings to Adams/Solver unit strings.

CV2MDL

• CV2MDL(2)Mass conversion

• CV2MDL(3)Length conversion

• CV2MDL(4)Time conversion

• CV2MDL(5)Angle conversion

DA 5 E Conversion factor from property file units to model (dataset) units.

CV2SI

• CV2SI(1)Force conversion

• CV2SI(2)Mass conversion

• CV2SI(3)Length conversion

• CV2SI(4)Time conversion

• CV2SI(5)Angle conversion

DA 5 E Conversion factor from property file units to SI units. SI units are Newtons, kilograms, meters, seconds, and radians.

*Key:


Use: R = referenced, but not set; E = evaluated (the subroutine sets the value of this argument).

Argument: Type*: Storage: Use* and Description:

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Arguments

ATRTOU

Calling SequenceSubroutineATRTOU (ID, UNITS)

DescriptionReads the [UNITS] block from a property file and returns a character array containing the unit strings for force, mass, length, time, and angle. Use ATRTOU with ACUNFNto obtain conversion factors from property file units to model units or SI units.

Before calling ATRTOU, you must call RTO_OPEN_FILE_F2C to open the property file for reading. If the [UNITS] block is not found in the file or there is a problem reading one of the unit strings, ARTOU writes a message to the message file and terminates Adams/Solver execution.

Argument: Type: Storage: Use* and Description:UN_IN

• UN_IN(1): force • UN_IN(2): mass • UN_IN(3): length • UN_IN(4): time • UN_IN(5): angle

CA 12x5 R Array of five 12-character strings read from the property file containing the unit names.

UN_OUT CA 2x5 E Array of five two-character strings containing the Adams/Solver unit string corresponding to the unit strings read from the property file.

*Key:




Arguments

RTO_CLOSE_FILE_F2C

Calling SequenceSubroutine RTO_CLOSE_FILE_F2C (FileName, FileNameLen, Success)

DescriptionCloses a previously opened file.

Argument: Type*: Storage: Use* and Description:ID I - R Identifier of the Adams dataset

statement associated with the property file being read (for example, the ID of the tire GFORCE statement when reading a tire property file). Identifies the statement when an error occurs.

UNITS

• UNITS(1): force • UNITS(2): mass • UNITS(3): length • UNITS(4): time • UNITS(5): angle

C.A. 12x5 E Array of five 12-character strings read from the tire property file containing the unit names.

*Key:


Use: R = referenced, but not set; E = evaluated (for example, the subroutine sets the value of this argument).

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Arguments

RTO_OPEN_FILE_F2C

Calling SequenceSubroutine RTO_OPEN_FILE_F2C (FileName, FileNameLen, Success)

DescriptionOpens a file for reading by the TeimOrbit utilities.

Arguments

Argument: Type*: Storage: Use* and description:FileName C 256 R File name with full pathFileNameLen I - R Number of characters in the file name (not

the length of the FileName array).Success I - E • If the file was found and closed,

success is returned as one (1).• If the file was not found or could

not be closed, success is returned as zero (0).

*Key:



Note: Before using any of the other RTO utilities, you must first open a file using this subroutine.

Argument: Type*: Storage: Use* and description:FileName C 256 R File name with full path (for example,

'/usr/people/smith/tire.tir')


RTO_READ_INTEGER_F2C

Calling SequenceSubroutine RTO_READ_INTEGER_F2C (BlockName, BlockNameLen,AttributeName, AttribNameLen,Value, Success )

DescriptionReads an integer value assigned to an attribute in a block in the open file. For example, the call:

CALL RTO_READ_INTEGER_F2C( 'GEAR_RATIOS', 11,+ 'N_GEARS', 7, Value, Success)

will read this from an open file:

[GEAR_RATIOS]N_GEARS = 5

On return, the integer variable Value is 5 and Success is 1.

Arguments

FileNameLen I - R Number of characters in the file name (not the length of the FileName array).

Success I - E • If the file was found and opened, success is returned as one (1).

• If the file was not previously opened, success is returned as zero (0).

*Key:



Argument: Type*: Storage: Use* and Description:BlockName C 256 R Block name in file containing the desired

subblock.BlockNameLen I - R Number of characters in the block name.Attribute Name C 256 R The name of the attribute sought in the file.Attribute NameLen I - R Number of characters in the attribute name.

Argument: Type*: Storage: Use* and description:

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RTO_READ_QUOTED_STRING_F2C

Calling SequenceSubroutine RTO_READ_QUOTED_STRING_F2C ( BlockName, BlockNameLen,AttributeName, AttribNameLen,Value, ValueLen, Success )

DescriptionReads the string associated with an attribute in a block of a file. For example, the call:

CALL RTO_READ_QUOTED_STRING_F2C( 'MYBLOCK', 7, 'MYSTRING',+ 8, Value, ValueLen, Success)

reads the data:

[MYBLOCK]MYSTRING = 'heretofore'

On return:

• The character array Value holds ‘heretofore’ • The integer ValueLen is 10 • Success is 1

Value I - E On return, the string value of the attribute.Success I - E • If the value is read, success is

returned as one (1).• If the read fails, success is returned as

zero (0). *Key:



Argument: Type*: Storage: Use* and Description:


Arguments

RTO_READ_REAL_F2C

Calling SequenceSubroutine RTO_READ_REAL_F2C (BlockName, BlockNameLen,AttributeName, AttribNameLen,Value, Success)

DescriptionReads a real value assigned to an attribute in a block in the open file. For example, the call:

CALL RTO_READ_INTEGER_F2C('GEAR_RATIOS', 11,+ 'FINAL_DRIVE', 11, Value, Success)

reads this data from an open file:

[GEAR_RATIOS]FINAL_DRIVE = 4.11

On return, the variable Value is 4.11 and Success is 1.

Argument: Type*: Storage: Use* and description:BlockName C 256 R Block name in file containing the desired

attribute.BlockNameLen I - R Number of characters in the file name (not

the length of the FileName array).AttributeName CI - R Name of attribute sought in the file.AttributeName Len I - R Number of characters in attribute name.Value C 256 E On return the string value of the attribute.ValueLen I - E Number of characters in value.Success I - E • If a value is read, success is

returned as one (1).• If the read fails, success is

returned as zero (0). *Key:



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Arguments

RTO_READ_SUBBLOCK_INTEGER_F2C

Calling SequenceSubroutine RTO_READ_SUBBLOCK_INTEGER_F2C (BlockName, BlockNameLen,SubBlockName, SubBlockNameLen,AttributeName, AttribNameLen,Value, Success)

DescriptionReads an integer value assigned to an attribute in a subblock of a block in the open file. For example, the call:

CALL RTO_READ_SUBBLOCK_INTEGER_F2C( 'TIRE_DATA', 9,+ 'LATERAL_FORCE', 13, 'N_SLIP_ANGLES', 13,+ Value, Success )

reads this data from the file:

[TIRE_DATA](LATERAL_FORCE)N_SLIP_ANGLES = 6

On return, the integer variable Value is 6 and Success is 1.

Argument: Type*: Storage: Use* and Description:BlockName C 256 R Block name in file containing the desired subblock.BlockNameLen I - R Number of characters in the block name.Attribute Name C 256 R The name of the attribute sought in the file.Attribute NameLen I - R Number of characters in the attribute name.Value D - E On return, the value of the attribute.Success I - E • If the value is read, success is returned as

one (1).• If the read fails, success is returned as zero

(0). *Key:




Arguments

RTO_READ_SUBBLOCK_REAL_F2C

Calling SequenceSubroutine RTO_READ_SUBBLOCK_REAL_F2C (BlockName, BlockNameLen, SubBlockName, SubBlockNameLen,AttributeName, AttribNameLen, Value, Success)

DescriptionReads a real value assigned to an attribute in a subblock of a block in the open file. For example, the call:

CALL RTO_READ_SUBBLOCK_REAL_F2C( 'FORCES', 6, 'FY', 2,+ 'DAMPING_COEFF', 13, Value, Success )

reads this data from an open file:


subblock.BlockNameLen I - R Number of characters in the block name.SubBlockName C 256 R Name of subblock in file containing the

desired attribute.SubBlockNameLen I - R Number of characters in the subblock

name.Attribute Name C 256 R The name of the attribute sought in the

file.Attribute NameLen I - R Number of characters in the attribute

name.Value I - E On return the value of the attribute.Success I - E • If the value is read, success is





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[FORCES](FY)DAMPING_COEFF = 1.72

On return, the variable Value is 1.72 and Success is 1.

Arguments

RTO_READ_SUBBLOCK_STRING_F2C

Calling SequenceSubroutine RTO_READ_SUBBLOCK_STRING_F2C (BlockName, BlockNameLen,SubBlockName, SubBlockNameLen,AttributeName, AttribNameLen,Value, ValueLen, Success )

DescriptionReads a string assigned to an attribute in a subblock of a block in the open file. For example, the call:

Argument: Type*: Storage: Use* and Description:BlockName C 256 R Block name in file containing the

desired subblock.BlockNameLen I - R Number of characters in the block

name.SubBlockName C 256 R Name of subblock in file containing

the desired attribute.SubBlockNameLen I - R Number of characters in the subblock



name.Value D - E On return the value of the attribute.Success I - E • If the value is read, success is






CALL RTO_READ_SUBBLOCK_STRING_F2C( 'FORCES', 6, 'FY',+ 2, 'DAMPING', 7, Value, ValueLen, Success )

reads the data:

[FORCES](FY)DAMPING = 'on'

On return:

• Character array Value holds ‘on’• The integer ValueLen is 2• Success is 1

Arguments



desired attributeSubBlockNameLen I - R Number of characters in the subblock



name.Value C 256 E On return the string value of attribute.ValueLen I - E Number of characters in value.Success I - E • If the value is read, success is





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RTO_READ_TABLE_LINE_F2C

Calling SequenceSubroutine RTO_READ_TABLE_LINE_F2C (Value, ValueLen, Success)

DescriptionReads a single line from a table. Use RTO_READ_TABLE_LINE_F2C after first locating the start of table using either RTO_START_TABLE_READ_F2C or RTO_START_SUBBLOCK_TABLE_READ_F2C. Typically, you use RTO_READ_TABLE_LINE_F2C in a while loop to read an entire table. For example, to read this table:

[MYBLOCK]{ X Y }0.0 0.240.1 0.480.3 0.96

Use code, such as the following:

c --- Locate the start of the table ---CALL RTO_START_TABLE_READ_F2C( 'MYBLOCK', 7,+ Format, FormatLen, Success )IF ( Success .eq. 0 ) THENc --- Table Not Found ---ELSE10 CONTINUECALL RTO_READ_TABLE_LINE_F2C( Value, ValueLen, Success )IF ( Success .eq. 0 ) thenc --- End of table found ---GOTO 20ELSEc --- Parse string in Value To retrieve values, then goc get another line of the table.cc The first time through this loop Value holdsc " 0.0 0.24/n"cc The third time through this loop Value holdsc " 0.3 0.96/n"c ---GOTO 10ENDIFENDIF20 CONTINUE


Arguments

RTO_START_SUBBLOCK_TABLE_READ_F2C

Calling SequenceSubroutine RTO_START_SUBBLOCK_TABLE_READ_F2C (BlockName, BlockNameLen, SubBlockName, SubBlockNameLen,Format, FormatLen, Success )

DescriptionLocates the start of a table in a subblock of a block in a file before calling RTO_READ_TABLE_LINE_F2C. There can be only one table per subblock. The start of a table is denoted by braces {" and "}. For example, the call:

CALL RTO_START_SUBBLOCK_TABLE_READ_F2C( 'MYBLOCK', 7,+ 'MYSUBBLOCK', Format, FormatLen, Success)

Searches for this data in the open file:

[MYBLOCK](MYSUBBLOCK){ S FX FY }0.0 1.15 -2.130.1 2.15 -2.130.2 1.48 -2.13

On return:

• Format contains the string, “ _S_FX_FY” • FormatLen contains the integer 9 • Success contains the integer 1

Argument: Type*: Storage: Use* and Description:Value C 256 E On return the nth line of a table.ValueLen I - R Number of characters in value.Success I - E • If the value is read from the table, success is

returned as one (1).• If the end of the table is found, success is




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Arguments

RTO_START_TABLE_READ_F2C

Calling SequenceSubroutine RTO_START_TABLE_READ_F2C (BlockName, BlockNameLen, Format, FormatLen, Success)

DescriptionLocates the start of table in a block in a file before calling RTO_READ_TABLE_LINE_F2C. There can be only one table per block. The start of a table is denoted by braces {" and "}. For example, the call:

CALL RTO_START_TABLE_READ_F2C( 'MYBLOCK', 7, Format,+ FormatLen, Success)

Searches for this data in the open file:

[MYBLOCK]{ X Y }0.0 0.240.1 0.480.3 0.96



desired attribute.SubBlockNameLen I - R Number of characters in the subblock

name.Format C 256 E The string containing the table column

headings.FormatLen I - E The number of characters in the Format

string.Success I - E • If the value is read, success is






On return:

• Format contains the string, " XY" • FormatLen contains the integer 6 • Success contains the integer 1

Arguments


subblock.BlockNameLen I - R Number of characters in the block name.Format C 256 E The string containing the table column

headings.FormatLen I - E The number of characters in the Format string.Success I - E • If the value is read, success is returned

as one (1).• If the read fails, success is returned as

zero (0). *Key:



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Utilities for Calculating Tire Forces and MomentsAdams/Tire provides a set of utility subroutines you can use in your user tire model to calculate tire kinematics and vertical forces and to transfer tire forces and moments from the contact path to the wheel center. Learn about the utilities:

• ACTCLC

• ACTFZ

• XCP2HB

ACTCLC

Calling SequenceSUBROUTINE ACTCLC(TRAMAT, VEL, OMEGA, OMEGAR, RADIUS, RNORM,VLON, VCPLON, VCPLAT, VCPVRT,ALPHA, GAMMA, KAPPA,URAD, CPMTX)

DescriptionGiven the wheel/tire's orientation (TRAMAT) and velocity (VEL, OMEGA, OMEGAR) relative to the road and the local road normal (RNORM), ACTCLC computes tire kinematics in the SAE axis system. The tire kinematics are:

• Contact-patch velocities • Slip angle (ALPHA) • Inclination angle (GAMMA) • Longitudinal slip (KAPPA) • SAE contact-patch axis system (CPMTX) • Unit vector directed from the wheel center to the contact patch (URAD)

Arguments

Argument: Type:* Storage: Use* and Description:TRAMAT DA 3,3 R Transformation from ISO wheel carrier

(TYDEX ISO-C system) axis system to road (earth) axis system.

VEL DA 3 R Translational velocity of wheel carrier in ISO wheel carrier axis system.

OMEGA DA 3 R Rotational velocity of wheel carrier in ISO wheel carrier axis system.

OMEGAR DS 1 R Rotational speed of the rim (wheel) with respect to the wheel carrier about the +y axis of the ISO wheel carrier axis system.


ACTFZ

Calling SequenceSUBROUTINE ACTFZ (VCPVRT, RADIUS, TIREK, TIREC, UNLRAD,FRCRAD, ERRMSG, IERR)

DescriptionACTFZ uses the contact-patch vertical velocity in the SAE coordinate system to compute the radial damping. It replaces PNTFRC for calculating tire vertical force.

RADIUS DS 1 R The loaded tire radius (for example, distance from the wheel center to the road surface in the plane of the wheel).

RNORM DA 3 R Unit vector giving the local road normal in the road (earth) axis system. The road normal must be directed upward from the road surface.

VLON DS 1 E The longitudinal velocity of the tire in TYDEX ISO-C axis system.

VCPLON DS 1 E The SAE contact-patch longitudinal velocity.VCPLAT DS 1 E The SAE contact-patch lateral velocity.VCPRVT DS 1 E The SAE contact-patch vertical velocity.ALPHA DS 1 E Slip angle in SAE axis system.GAMMA DS 1 E Inclination (camber) angle.KAPPA DS 1 E Longitudinal slip ratio.URAD DA 3 E Unit vector directed from wheel center to

contact patch expressed in road (earth) reference marker axis system.

CPMTX DA 3,3 E Transformation matrix from the SAE contact-patch axis system to the road (earth) reference marker axis system.

*Key:



Argument: Type:* Storage: Use* and Description:

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Arguments

XCP2HB

Calling SequenceSUBROUTINE XCP2HB(FCP, TCP, RAD, TRNMTX, FORCES, TORQUE)

DescriptionXCP2HB transforms the contact-patch forces and torques to hub forces and torques expressed in the road reference marker axis system:

forces = [cpmtx]fcptorque = rad X ([cpmtx]fcp) + [cpmtx]tcp

Arguments

Argument: Type:* Storage: Use* and Description:VCPVRT DS - R Vertical contact-patch velocity in SAE

coordinates (+z is downward)RADIUS DS - R Loaded tire radiusTIREK DS - R Tire stiffness <n/m>TIREC DS - R Tire damping <n*s/m>UNLRAD DS - R Unloaded tire radius <m>FRCRAD DS - E Radial (vertical) force <n>ERRMSG CA 80 E Error messageIERR IS - E Error code:

IERR = 0, normal executionIERR = 3, problem calling IMPACT function

*Key:



Argument: Type:* Storage: Use* and description:FCP DA 3 R Contact patch forces expressed in SAE axis system

(+z is downward).TCP DA 3 R Contact patch torques expressed in SAE axis system

(+z is downward).RAD DA 3 R Radius vector from wheel center to contact patch

expressed in the road reference marker axis system.


CPMTX DA 3,3 R Transformation matrix from SAE contact-patch axis system to the road reference marker axis system.

FORCE DA 3 E Hub forces expressed in the road reference marker axis system.

TORQUE DA 3 E Hub torques expressed in the road reference marker axis system.

*Key:



Argument: Type:* Storage: Use* and description:

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User written tire plug-in: Using a tire demand loaded libraryNext to linking a user written tire model to the solver, another option is possible: creating a user dynamic library with the user written code (mdi cr-u) and use the tire plug-in to load the user tire dynamic library.

The tire model dynamic library should be built using with the mdi script option 'Adams User-DLL' or 'User Adams/Solver library'.

In the tire property file the [MODEL] section should contain following statements:

[MODEL]PROPERTY_FILE_FORMAT ='USER'FUNCTION_NAME ='<tiruserlibname>::TYR<number>'

Similar demand loaded library functionality is available for user-written roads:

[MODEL]PROPERTY_FILE_FORMAT ='USER'FUNCTION_NAME ='<roaduserlibname>::ARC<number>'

Documents

Adams Tire Mdr3 Help-152