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    2 copyright LMS International - 2005

    Tire Force Element

    Models a vehicle tire interacting with a road profile.

    No bodies or constraints added by this element

    Forces calculated in the tire/ground plane

    Transformed to the global coordinate system when applied to the tire body

    Three components of force are calculated:

    normal

    longitudinal

    lateral

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    Tire Components

    Steer Angle

    Camber Angle

    Aligning Coefficient

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    Ride & Handling Definitions

    Ride analysis

    Vehicle analysis wherein the forces generated on vehicle components, and in

    particular on the passenger, are of primary importance.

    Handling analysis

    Vehicle analysis wherein the overall performance of the vehicle (directional

    response, lateral acceleration, etc.) is of primary importance.

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    Tire Models

    4 different models available with the Standard Tire license

    Simple Tire

    Complex Tire

    STI Tire

    Magic Tire

    6 Different versions of the TNO Tire, separately licensed

    TNO MF-Tyre Express, Standard, Supreme

    TNO MF-Swift Express, Standard, Supreme CD Tire, separately licensed

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    Simple Tire

    Road is fixed to global origin (no Road.Body)

    Minimal number of parameters needed

    Longitudinal forces calculated from simple curve only

    Lateral forces calculated from cornering stiffness only

    Longitudinal forces calculated by friction coef.

    Constant vertical damping only

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    Complex Tire

    Curve Damping

    Entry should include the name of the curve that defines the tire normal damping

    rate as a function of the chassis fore/aft speed.

    Trans.Damp.Defl

    When non-zero this value is used to attenuate the normal damping force for

    small tire deflections. If a value of zero is entered the nominal damping rate is

    used

    Rolling.Radius

    This value is found by dividing the distance traveled during one rotation by 2. Ifa value of zero is entered, the deflected radius found in the tire normal force

    calculation will be used.

    Carcass effects

    2nd order effects due to the tire carcass can be included in the vertical, lateral,

    and longitudinal directions

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    STI Tire

    Standard Tire Interface to bring in users tire code in standard format

    Values to be defined within the STI formfill:

    File .STI : File containing input information describing the STI tire

    IDROAD : Road type identification number

    File.ROAD: File containing information describing the STI road

    ISWTCH : Set to 0 for static analysis, 1 for dynamic analysis

    NOTE: Setting ISWTCH = -1 in the STI menu will cause DADS to automatically

    set the ISWTCH flag to 0 or 1 depending on the type of analysis encountered

    by DADS3D

    WRKARR 1-10: These are real work array values

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    Magic Tire

    Based on The Magic Formula Tyre Model by Hans Pacejka & Egbert Bakker, 1991

    This version of the Pacejka formulation is very good for motorcycle tires

    File.Magic

    Curve-fitted test results consistent with the Magic Formula formulation

    Describe the lateral force, aligning moment, and/or longitudinal force.

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    Three Tire Types Simple & Complex

    BASIC

    Ignores the rotational inertia of the wheel

    Tire body must be constrained to the chassis so no rotation occurs

    Steer angle is defined directly as a user input

    Camber is assumed to be zero

    INTERMEDIATE

    Ignores the rotational inertia of the wheel

    Tire body must be constrained to the knuckle so no rotation occurs

    Steer and camber angles calculated from the model

    FULL - Recommended

    Steer and camber angles calculated from the model

    Accounts for the rotational inertia of the wheel

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    Tire Connection Information

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    Tire Connection Information

    Tire Body and Chassis Body must be defined

    These can be the same for BASIC and INTERMEDIATE.

    Axi s on Chass is Body

    X-axis defines the vehicle direction of travel

    Z-axis defines up for the vehicle

    Axi s on Tir e Body

    origin at the center of the tire circle

    Z-axis along axis of rotation

    Z-axis should point in same quadrant as Chassis Y-axis

    Axi s on Road Body

    Used to assign road to moving body

    Vehicle on shaker platform

    Vehicle on trailer

    Used as option to position/orient road profile

    Surface is defined as height (z) versus x (spline curve) or x

    and y (spline surface)

    If no Road.Body, the road profile is assumed to be defined

    with respect to the global origin.

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    Normal Force Calculation Methods

    Point contact

    Valid if radius of curvature of road profile feature is much larger that tire radius

    Normal ForceX

    Z

    Road Reference

    Frame

    1) Road height and tangent line to roadsurface based on x, y coordinates oftire center in road reference frame.

    2) Perpendicular distance from wheelcenter to road tangent line definesdirection, point of application andtire deflection12

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    Normal Force Calculation Methods

    Distributed contact

    Tire divided into a user-defined number of vertical slices

    Each area of intersection is found

    Equivalent normal deflection, d, is found by equating the intersected area with

    that for the tire on a flat surface

    The point of application of the tire force, Cp, is found through a weighted

    average of the centroids of the partial intersected areas

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    Normal Force Calculation Methods

    Distributed contact continued

    The direction of the force is found through a weighted average of the terrain gradient

    vectors, gi, associated with the partial intersected areas

    Includes adjustments to account for sharp features

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    Road Profile

    4 Different Options

    Define in ROAD element

    Can be 2-D or 3-D

    If the same profile or surface is sufficient for all tires

    Define in the TIRE element

    If different profiles or exist for some or all tires

    Will override curve in ROAD element if both defined

    In ROAD.F user-defined subroutine

    User-defined analytic or tabular surfaces

    Otherwise, the road is assumed flat in the global X-Y plane and located at Z=0

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    Longitudinal and lateral forces are computed and act in this plane

    Normal Force act perpendicular to this plane

    Z-axis of the terrain tangent plane coordinate system is normal to thetangent plane, directed upwards

    X-axis is the intersection of the terrain tangent plane and the plane of

    the tire disk

    The Y-axis is in the terrain tangentplane, perpendicular to the X-axis

    Terrain Tangent Plane

    Plane tangent to the terrain profile at the point of contactPlane tangent to the terrain profile at the point of contact

    between tire and terrainbetween tire and terrain

    Resulting coordinate system of Terrain Tangent PlaneResulting coordinate system of Terrain Tangent Plane

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    Normal Force Effects

    Vertical.stiff

    When tire normal force is a linear function of displacement.

    Overridden when Curve.vertical is used.

    Curve.vertical

    When tire normal force is a non-linear function of displacement.

    Damping.coeff

    When normal force damping constant is independent of forward speed.

    Overridden when Curve.damping is used.

    Curve.damping

    When normal force damping coefficient is a function of chassis forward speed, NOT

    VERTICAL VELOCITY.

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    Normal Force Effects

    Num.Divisions

    Used with distributed contact normal force model

    Number of vertical slices into which the tire is divided.

    Zero for simple point-contact normal force model

    Use distributed contact model when road profile contains abrupt changes.

    Set high enough so that each slice is smaller than the smallest road profile feature.

    Trans.Damp.Defl

    When normal damping force is to be attenuated for small tire deflections. Avoids slap of damping force after lift-off

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    Longitudinal Calculation Methods

    Rolling resistance

    For any type (Basic, Intermediate, or Full)

    Parasitic longitudinal force due to carcass deformation losses, bearing friction, etc.

    Approximated as constant fraction of the normal force

    Crr = Coefficient of Rolling Resistance

    Fn = normal force

    Vclong = wheel center forward velocity

    Applied directly at wheel center, not tire patch

    )sign(VF-CFlongcnrrrr=

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    For Type BASIC or INTERM, the longitudinal force is computed from an explicit torque. If

    a torque is specified (Curve.torque), the longitudinal force is simply:

    T = Time based torque curve (Curve.torque)

    Rd = Deflected radius

    Longitudinal Calculation Methods

    dlong

    R

    TF =

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    For type FULL, the ratio of the longitudinal force to the normal force (the longitudinal force

    coefficient) is normally a function of rotational slip, S:

    Equation for Longitudinal Force

    Choice of 5 approaches for long

    Longitudinal Calculation Methods

    )sign(VVV-S pc

    p

    long

    =

    sign(S)FF nlonglong =

    Vp = Tire patch forward velocity

    Vclong = Wheel center forwardvelocity

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    Longitudinal Calculation Methods

    The 5 approaches for long to choose from are:

    Set Soil type to SIMPLE, the following curve of long vs. S applies

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    Longitudinal Calculation Methods

    The 5 approaches for long continued Set Soil type to HARD, the following equation applies

    Set Soil type to SOFT, the following equations apply

    rr

    SFbdk-

    long Ce-1 n +

    =

    k = rubber hardness = 60psi

    b = tire section width

    d = tire section diameter

    = Friction coefficient

    ( ) rr-7.5S-0.1Blong Ce-1e-1 n += = friction coefficientCI = Cone Index

    b = tire section width

    d = tire section diameterh = tire section carcass height

    +

    +

    =

    d

    b31h

    51

    F

    dbCIB

    n

    n

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    Longitudinal Calculation Methods

    The 5 approaches for long continued

    (S) User defined non-linear curve as function of longitudinal slip

    (Vp) User defined non-linear curve as function of tire patch forward velocity

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    Soil Types

    Determines long Surface.type - SIMPLE

    When operating on hard surfaces, where longitudinal friction coefficient is to be

    based upon a simple function of rotational slip. Surface.type - HARD

    When operating on hard surfaces, where longitudinal friction coefficient is based

    upon rotational slip, rubber hardness, tire undeflected radius, and section width.

    The equations governing hard surface tire forces are detailed in ASAE publication

    No. 79-1046

    Surface.type - SOIL

    When operating on soft soils. The equations governing soil surface tire forces are

    detailed in ASAE publication No. 87-1622.

    27 copyright LMS International - 2005

    Soil Parameters

    Cone.index

    Required when Surface.type HARD or SOIL is used. Otherwise unused. With

    Surface.type SOIL, this variable represents the cone index; with Surface.type

    HARD, it represents rubber hardness.

    Section.height

    Required when Surface.type SOIL is used. Otherwise unused.

    Section.width Required when Surface.type HARD or SOIL is used. Otherwise unused.

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    Alternatively, the longitudinal force may be generated by a longitudinal spring-

    damper force

    Rr is the rolling radius of the tire

    plong is the longitudinal position of the tire center

    plong0 represents the equilibrium position of the spring

    plong0 is kept constant until such time as the longitudinal force generated by the

    spring-damper is greater than that available through friction, at which time plong0slides until such time as the spring-damper force is less than the friction force

    Note & Warnings

    This method is only recommended for types of analysis where the vehicle is

    stationary

    If carcass effects are activated, this method is over ridden

    Longitudinal Calculation Methods

    plonglong0longrlonglong VC)pp(RKF ++=

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    Longitudinal Force Effects

    Rolling.Radius

    Defines constant radius for the tire force application point.

    If zero, the rolling radius is calculated dynamically based upon the undeflected radius and

    the tire deflection.

    Insures that x = Rrolling *

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    Longitudinal Force Effects

    Long.Stiff

    If carcass effects are not activated, used by longitudinal spring damper model in

    previous slide

    If carcass force model activated, used by the carcass force calculation

    Long.Damp

    Used when the Long.Stiff variable is used.

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    Function of the normal force and slip angle

    Analogous to the longitudinal force with rotational slip

    Slip angle is the angle between the tire center heading vector and the tire velocity vector

    projection in the terrain tangent plane.

    Lateral Force Calculation Methods

    ( )latccc1

    VsignV

    V

    tanlong

    lat

    =

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    Lateral Force Calculation Methods

    Lateral force typically varies with both the normal force and slip angle.

    Data can be entered through:

    Table.Lateral variable (Used primarily in handling analysis.)

    Where no carpet plot data exists, the relationship is approximated by a cubic

    polynomial determined from the following boundary conditions:

    C= cornering stiffness

    Flat = maximum lateral side force coefficient

    n = saturated steer angle generally approximated by:

    ( ) 00Flat = ( )

    C0d

    Flat = ( ) maxlat FF =n ( ) 0d

    Flat =n

    C

    F2.5 nn=

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    A third type of lateral force: lateral spring-damper

    Function of lateral translational displacement

    Define horizontal line which intersects the center of the tire patch, and is

    parallel to the forward velocity vector or Terrain Tangent plane X-axis.

    Displacement & Velocity is the perpendicular distance from the tire patch to this

    line

    Reference line remains in the same place until the lateral force is greater thanthat available through friction, line slides until force is less than the friction

    force. Used if Lateral.Stiff is not zero and carcass effects not activated

    Note: This method is only recommended for types of analysis where the vehicle is

    stationary

    Lateral Force Calculation Methods

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    Lateral Force Effects

    Cornering.stiff

    Used to approximate the lateral force carpet plot when Table.lateral is set to

    NONE.

    Expressed as (lateral force) divided by (sideslip angle).

    Used primarily in handling analysis.

    Roll.moment

    If the roll moment generated by the tire normal force combined with the lateral

    displacement of the tire patch is important, this flag should be set to TRUE.

    Relax.length

    When lateral force and aligning moment change abruptly, this parameter allows

    a more realistic (attenuated) tracking of the actual lateral force and aligning

    moment, due to carcass deformation

    35 copyright LMS International - 2005

    Lateral Force Effects

    Lateral.stiff

    If carcass effects are not activated, used by lateral spring damper model in previous

    slide

    If carcass force model activated, used by the carcass force calculation

    Units are lateral force divided by distance.

    Lateral.damp

    Used When the Lateral.stiff is used to generate lateral force.

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    Carcass Effects

    State equations added to improve tire response compared to test data from a customer

    VD=&

    carcass

    patch

    m

    CVKDF )(V

    +=&

    D is the displacement of the tire patch in the direction of interest

    V is the velocity of the tire patch in the direction of interest

    Fpatch is the force applied to the tire patch by the road surface in the

    direction of interest

    K is the tire carcass stiffness in the direction of interestC is the tire carcass damping constant in the direction of interest

    Mcarcass is the mass fo the deflected portion of the tire carcass

    37 copyright LMS International - 2005

    Carcass Effect Starting values

    Carcass mass of about 5% of the total tire+wheel mass.

    For the vertical carcass effect, it just use the vertical stiffness value

    For the longitudinal & lateral stiffness, start with a value equal to the vertical stiffness.

    Transient data from a pulse steer or something like that, can give a starting point for trying

    to tune the lateral stiffness.

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    Other Tire Parameters

    Steer.angle

    Used with BASIC tires when steer angle of tire is constant.

    Curve.Steer Used with BASIC tires when the steer angle of the tire is known as a function of

    time.

    Align.Coeff

    Represents the fore-aft displacement of the tire patch

    Use if the yaw moment from the tire lateral force combined with the fore-aft

    displacement of the tire patch is important

    Curve.Utility

    Used to access curve data inside user-modified tire routine.

    39 copyright LMS International - 2005

    Modeling tips for tires

    If there is unusual behavior at start of analysis, check:

    Vertical stiffness

    Set gravity to 0.0 (scale.gravity.coeff in System.data element) if tires are above

    ground initially. Vehicle should stay at rest above ground

    Only use the longitudinal & lateral spring damper models for stationary analysis

    Use of basic and intermediate types not recommended

    Table.Lateral most accurate for lateral force if data exists

    Typical Values on next slide is minimum amount of data to generate vertical, longitudinal& lateral forces

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    Typical Values

    Dry Pavement: 0.8-1.0

    Wet Pavement: 0.5-0.8

    Friction Coefficient

    0.005-0.04Rolling Resistance

    Car: 80-200 lb/deg

    Truck: 200-800 lb/deg

    Car: 350-900 N/deg

    Truck: 900-3500 N/deg

    Cornering Stiffness

    Car: 6-20 lb*s/in

    Truck: 10-85 lb*s/in

    (10% critical damping)

    Car: 1000-3500 N*s/m

    Truck: 1700-15000 N*s/m

    (10% critical damping)

    Vertical Damping

    Car: 850-1700 lb/in

    Truck: 850-6000 lb/in

    Car: 150K-300K N/m

    Truck: 150K-1000K N/m

    Vertical Stiffness

    Typical Values (English)Typical Values (SI)Variable

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    Lab Session: Complex Tire and RoadPage 1

    Virtual.Lab Motion Advanced Training

    Lab Session: Complex Tire and Road

    IntroductionThis tutorial illustrates the overall procedures in defining the Complex Tire andRoad elements. It also reviews the procedures of creating a spline curve andbushing element. This tutorial is intended to increase you familiarity with addingtires and road elements to models.

    Getting StartedTo open the model,

    1. Open Complex_Tire.CATAnalysis.

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    Lab Session: Complex Tire and RoadPage 2

    Virtual.Lab Motion Advanced Training

    Create the User Parameters

    Environment Settings

    There are specific settings that must be activated within the environment window

    to allow for the visualization of the defined parameters within the SpecificationTree.

    From the Main Menu, select ToolsOptions.

    1. Since all of our parameters will be defined within the Analysis document,Select the Motionbranch of the Options Tree and activate the selectionsShow parametersand Show relations.

    2. Click OKto close the Options dialog box.

    Defining Parameters

    1. Click the Formula button from the bottom toolbar.

    2. Within the Formulas dialog, Click on the Importbutton.

    3. From the File Selection dialog, select the file parameters.xls from thecomplex_tire directory. Click Open to close the dialog.

    4. An Import Result dialog box will open showing all the parameters that werepreviously defined in the Excel worksheet, Click the OKbutton.

    5. Click OKto close the Formulas dialog box. A new Parameters branch shouldnow appear in the Specification Tree below the Analysis Model branch of theSpecification Tree.

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    Lab Session: Complex Tire and RoadPage 3

    Virtual.Lab Motion Advanced Training

    Insert a Road Element (Flat Road)

    1. Click the black down arrow next to the Vehicle button on the MechanismDesign Workbench. This will display the Vehicle Suspension toolbar.

    2. Click the Road button from the Vehicle Suspension toolbar. This willbring up the Road dialog.

    3. Change the Namefield entry to read Fl at Road.

    4. Left and then Right-click in the Curve Namefield entry and select Newfromthe resulting menu. This will bring up a second Function dialog.

    5. Change the Namefield entry to Fl at Road Funct i on.

    6. Select SPLI NE. CURVEfrom the Function Typedrop-down menu.

    7. Left and then Right-click in the Curvefield entry and select Newfrom thecontextual menu. This will bring up a third Spline Curve dialog.

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    Lab Session: Complex Tire and RoadPage 4

    Virtual.Lab Motion Advanced Training

    8. Change the NameField Entry to Fl at Road Cur ve.

    9. In the Curve Datasection of the dialog, click theAddbutton to add a defaultvalue of (0,0) to the X Length and Z Length lists.

    10. In the field below the X Length list, enter 1.

    11. Click theAddbutton again to add a value of (1,0).

    12. Set the InterpolationField Entry to LI NEAR.

    13. Click OKto close the Spline Curve dialog.

    14. Click OKto close the LengthLength Function dialog.

    15. Click OKto close the Road dialog box.

    Insert a Bushing ElementA bushing element is inserted to the interface between the carrier and the shock

    bodies to reduce swing and vibration.

    1. Click the Bushingbutton from the Forces toolbar.

    2. The Bushing Force element requires that two axes be selected. In theSpecification Tree under Product1_Rootshock (shock.1)shockAxisSystems, select the Bushing Carrier_Shock Axis branch, this will populatethe Body 1Field Entry.

    3. In the Specification Tree under Product1_Root carrier (carrier.1)carrierAxis Systems, select theAbsolute Axis Systembranch as the Body 2Field Entry.

    4. Right-click the Spring Conical X field and choose Edit formula from thecontextual menu.

    5. In the blank field, enter the value (RSTI FF * 5. 7295779513082e+001) *1Nxm_rad. (You may click RSTIFF from the Parameter branch of theSpecification Tree instead of typing RSTIFF.)

    6. Click OKto close the Formula Editor dialog.

    7. Repeat steps 5-7 for Spring Conical Y and Spring Torsional.

    8. Right-click in the Damping Conical Xfield and select Edit formulafrom thecontextual menu.

    9. Enter the value ( RDAMP *5. 7295779513082e+001) * 1m2kg_s_r ad

    10. Repeat step 9-11 for Damping Conical Y and Damping Torsional fields

    11. Click OKin the Standard Bushing dialog box.

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    Lab Session: Complex Tire and RoadPage 5

    Virtual.Lab Motion Advanced Training

    Insert a Tire Element

    1. Click the black down arrow next to the Bushingbutton to display theForces toolbar.

    2. Click the Complex Tirebutton .

    3. Under the Product1_ROOT tire (tire.1)tireAxis System branch of theSpecification Tree, select theAbsolute Axis Systemas the Tire BodyFieldEntry.

    4. Under the Product1_ROOT carrier (carrier.1)carrierAxis Systembranch of the Specification Tree, select theAbsolute Axis Systemas theChassis Bodyfield entry.

    5. Right-click in the Radius field and choose Edit formula from the contextualmenu.

    6. Under the Analysis Model branch of the Specification Tree, selectParametersRADIUSfrom the Specification Tree. Click OK to close theFormula dialog.

    7. Follow the same basic steps (6 & 7) for the Vertical Stiffnessand Dampingfields using the VSTIFF and VDAMP parameters respectively.

    8. At the bottom of the Parameters section of the Complex Tire dialog, togglethe Typeradio button to Full.

    The dialog should look similar to the following picture.

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    Lab Session: Complex Tire and RoadPage 6

    Virtual.Lab Motion Advanced Training

    9. Click the OKbutton to save the values and close the dialog.

    Solve the Model1. Double-Click the Solution Setbranch from the Specification Tree, and

    change the solution EndingTimeto 5s. Select OKto close the dialog.

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    Lab Session: Complex Tire and RoadPage 7

    Virtual.Lab Motion Advanced Training

    2. Click the Compute Solution button .

    3. Once the Solution has completed successfully, click the Close Windowbutton in the Computing dialog box.

    Animate the Model1. Select Solution Set from the Specification Tree.

    2. Click theAnimatebutton from the Mechanism Design Workbench. This willbring up the Animation Toolbar.

    3. Click the Play Forwardbutton from this toolbar to display the animation.

    Selecting a new Road Profile

    1. Within the model Specification Tree under Product1_Root, Right-Click on theroad (road.1) branch and Select Hide/Show from the resulting menu.

    2. Within the model Specification Tree under Product1_Root, Right-Click on theroad.1 (road.2) branch and Select Hide/Show from the resulting menu. Asurface profile with two bumps should now appear.

    3. Double-Click the Analysis Model branch of the Specification Tree to activatethe Mechanism Design workbench. Double-Click the PostProcessingSuspension Road.1 branch to open the Road definition dialog. Left andthen Right-Click in the Elements/CurveField Entry. Select Newfrom theresulting Menu. Change the name of the new function to Bumpy Road

    Function.

    4. Left and then Right-Click in the CurveField Entry. Select Newfrom the

    resulting menu. Change the NameField Entry to Bumpy Road Cur ve.Toggle the Reference External Data option, and select the file road.txt fromthe project folder. Click OKto close the Spline Curve dialog. Click OKtoclose the Function dialog. Click OKto close the Road definition dialog.

    Solve the Model

    1. Select the Solution Setbranch from the Specification Tree.

    2. Click the Compute Solution button .

    Once the Solution has completed successfully, click the Close Windowbutton inthe Computing dialog box.

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    Lab Session: Complex Tire and RoadPage 8

    Virtual.Lab Motion Advanced Training

    Animate the Model1. Select Solution Set from the Specification Tree.

    2. Click theAnimatebutton from the Mechanism Design Workbench. This willbring up the Animation Toolbar.

    Click the Play Forwardbutton from this toolbar to display the animation.

    ConclusionCongratulations, this completes the Virtual.Lab Motion Complex Tire and RoadLab.

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    Lab Session: Post-Processing TrainingPage 1

    Virtual.Lab Motion Advanced Training

    Tire with Spline Surface & Post-Processing

    Objective

    The objective of this Lab is to create tire force elements that reference a splinesurface element (carpet plot) and learning about the post-processing capabilitiesin Virtual.Lab.

    Lab Agenda

    1. Create the fourth tire element and spline surface element.

    2. Associate the pre-existing three tire force elements with the spline surface

    element.3. Solving and post-processing the model.

    4. Using post-processing tools in Virtual.Lab on the results obtained duringstep 3.

    Create fourth tire element and splinesurface element

    SelectFile

    Open

    car.CATAnalysisfile from the Virtual.Lab Main Menubar. This file should be found in the Postprocessing_Lab folder. Under theAnalysis ModelForces branch of the model Specification tree, three tireelements called tireone, tiretwo and tirethree have already been defined. Thegoal in this part of the lab is to create a spline surface element that is referencedby all the tires and create a fourth tire element.

    Creating fourth tire element

    1. Click the black arrow to the right of the Bushing Button , this will displaythe Forces Toolbar. To create the fourth tire element click on the Complex

    Tirebutton in the Forces toolbar. This will bring up the following window.

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    Lab Session: Post-Processing TrainingPage 2

    Virtual.Lab Motion Advanced Training

    2. For the Tire BodyField Entry, Select the Product1_ROOT tire4 (tire4.1)tire4 Axis System tiret4 branch of the model Specification Tree. For theChassis BodySelect the Product1_ROOT chassis (chassis.1) chassis

    Axis Systems chasscenter branch of the model Specification Tree. Forthe Road BodyField Product1_ROOT ground (ground.1) ground AxisSystems ground_default_ref branch of the model Specification Tree.

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    3. For the RoadField Entry under the Elements section of the dialog, Left andthen Right-Click in the Field Entry and select New. This will bring up thefollowing window.

    Change the Function Typeto SPLI NE. SURFACEand under the Elementssection right click in the Surface Field Entry and select new to create Spl i neSur f ace. 1element

    1. For the X, Y and Z MagnitudeField Entries pick Di mensi onl essfrom thedrop-down list.

    2. Toggle the Reference external data file radio button. Now click the Browse

    button and pick the pi t _cr v3. t xt file.

    3. Change the InterpolationField Entry to LI NEARby picking it from the drop-down list. Now click the OKbutton to create the spline surface element calledSpl i ne Sur f ace. 1.

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    4. For all the other required parameters please fill the Field Entries from thefollowing image of a completed Complex Tire dialog window.

    4. Notice that a formula has been applied to the Cornering Stiffness Field Entry.To apply this formula, Left and then Right-Click in the Field Entry box. SelectEdit Formula from the resulting menu. This will bring up the Formula Editorwindow.

    5. Within the Formula Editor, the following formula will be entered:

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    ( cor ner * 5. 7296e001) *1mxkg_s2_r ad

    Mathematical operators, such as parentheses and multiplication symbols can beentered by select the symbol from the Operators list. To activate this list, selectOperatorsfrom the first column of the dialog labeled Dictionary.

    To find the parameter cor ner , Select Parametersfrom the Dictionarycolumn,Realfrom the Member of Parameterscolumn, and scroll to the bottom of theMembers of Allcolumn to find the listing of parameters. Double-Click the

    cor ner parameter to enter it into the formula.

    Click OKin the Formula Editor once the formula is complete, this will return theresulting value back to the tire dialog.

    6. Click OK in the tire dialog once complete.

    Associate the pre-existing three tireforce elements with the spline surfaceelements1. To associate the pre-existing tireone tire-force element to the spline surface

    element, Double-Click on the Forces tireonebranch of the SpecificationTree.

    2. Left-click in the RoadField Entry in each dialog and select LengthLengthFunction.1 from the modeling tree.

    3. Repeat steps 1-4 for elements tiretwo and tirethree.

    Solving model to get results for post-processing

    Select and highlight the Solution Set under the car_AnalysisCase branch of theSpecification Tree.

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    Now click the Compute Solution button to solve the model.

    Using post-processing tools in

    Virtual.LabPost-processing tools in Virtual.Lab can be divided into two groups Plotting and

    Animation tools.

    Plotting tools

    Plotting sample results from the LMSMotionResults file

    1. From the Mechanism Design Workbench, Click the Open Motion Graph

    Window button . This will bring up the plot creation window.

    2. The simulation time is automatically plotted on the X-axis. Under the Y-axisselection at the top of the Define Plots section of the Motion Graph Windowselect Revolute under Type next to Element.

    3. Under the Y-axis select the rev:fz1, rev:fx1,and rev:fy1.

    4. To finish the definition of a plot, make sure both the X and Y-axis selections

    are highlighted and then click the CreatePlotsbutton . A new branchshould appear on the right side of the screen below the car_AnalysisCase

    branch of the tree.

    Creating a Motion Display to display the plot

    1. To open the graphing window, Click the New Display button . This willbring up the New Function Display wizard. Accept the setting of MotionDisplay by clicking the Next button. Accept the XY Plot setting by clicking theFinish button in the wizard window.

    2. To place the previously defined plot in the Motion Display window, Right-Clickand then pick the Select Dataoption. Within the Default Data Selection

    window highlight the ***car_AnalysisCase*** SYSTEM:Time_rev1:fz1option and then click the Display button in the Default Data Selection dialog.

    3. Now you can change the title of the plot and the axes titles as required.Double-click on the title of the X-axis, this will bring up the following window.

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    Click the Title tab as shown above and select the Custom radio button. Now acustom title can be defined, for example, Si mul at i on Ti me ( sec) . In asimilar manner, the title of the Y-axis can be changed to Z- di rect i onReact i on For ce f or Rev1 .

    4. To change the title of the graph, double-click on the graph title, Graph1 () inthis case, in the top-left corner of the white plotting space. This will bring upthe Edit Graph window as shown below.

    5. Click on the Titletab and modify the title as desired, in this case input Post -process i ng Trai ni ng Pl ot . Picking one of the options in the Positiondrop-down list can modify the position of the title, for instanceTop- Cent er .

    6. The plots for fx1 and fy1 vs. Simulation Time (sec) can be modified in asimilar manner.

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    Using the Graphing Tools to create Computed Plots

    The Graphing Tools toolbar is shown at the top of the Motion Graph Window.This toolbar contains read and write operations, arithmetic operations, calculus

    operations, scaling, smoothing and create FFT operations. This section will dealwith performing some of these operations on the plots.

    1. To add two plots, clicking on the Add Curves button will bring up thefollowing window

    2. Clicking on a plot under the car_AnalysisCase branch of tree shown on theright of the screen selects a curve to be added. In this case pick the

    SYSTEM: Ti me__r ev1: f x1and SYSTEM: Ti me__r ev1: f y1plots.

    3. Once the plots are selected, Click the OKbutton. This will create a branchlabeled AddCurves. 1 under the GraphComputed Plots branch.

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    4. To open the Motion Display, Double-click the Function DisplaysMotionDisplay - XY-Plot branch.

    5. Right-click in the white plotting space and the following menu will be

    displayed.

    Click on the Select Databutton and the Default Data Selection window will belaunched.

    6. From the Default Data Selection window select the computed plotAddCurves. 1and then Click the Display button from the Default DataSelection dialog.

    7. Close the Motion Display window when all plotting procedures have beencompleted.

    Animation Tools

    Selecting the car_AnalysisCaseSolution Set branch of the Specification Treefollowed by the Animate button from the Mechanism Design workbench, providesa basic animation of the mechanism model. The Animation Tools toolbar has

    more advanced tools like camera follow, interference, animation trace, scaledmotion, point trace and animation vectors.

    Camera Follow Animation

    This animation tool allows the user to attach a camera to a body in the model andthen view the animation from the point of view of that body.

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    1. Right-click the Analysis Model Animation Scenes branch of theSpecification Tree. Select New Animation Scene from the resulting menu, thiswill create an animation scene in the Specification Tree labeled Scene.1 asshown below.

    2. Click and highlight the Scene. 1branch in the specification tree and click the

    Camera Follow button of the Animation Tools toolbar, this will bring upthe following window.

    3. For the Look FromField Entry select the axis system called Axi s . Syst em. 1under the Links Manager Link.1chassis_csys(chassis_csys.1) chassispart document branch of the Specification Tree.

    4. For the Look ToField Entry select the axis system called chassi s_cgunderthe chassis part branch. Change the View AngleField Entry to 25and Clickthe OKbutton in the Camera dialog.

    5. To activate the Camera Follow animation scene, using the Control key, selectthe car_AnalysisCaseSolution Set branch and the Animation Scenes Scene.1 Camera.1 branch of the Specification Tree.

    6. Click theAnimate button in the Motion Animation toolbar. This willanimate the model with the Cameras point of view.

    Multi-case Animation

    Multi-case animation allows for two different results to be animatedsimultaneously for a given model. This means the same model may be solved

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    two different times with different parameters and the resulting motion can beanimated together.

    1. Select Insert from the Virtual.Lab Motion Main Menu Bar and Select the NewAnalysis Case option. This will create an analysis case with the nameAnalysisCase.1 in the Specification Tree.

    2. Now click the One Body Initial Condition button in the Initial Conditionstoolbar. This will bring up the following window.

    3. For the Attachments point selection pick the origin of the chassi s_cgAxissystem under the chassis part. Enter 20m_sin the Time DerivativeFieldEntry and Click the OKbutton.

    4. Now double-click on each of the LengthLengthFunction elements associatedwith the tire force elements. This will bring up a window similar to thefollowing window.

    In each case change the Function Type to SPLI NE. CURVE. Now click in theCurve Field Entry and pick the hi l l s_cr vspline curve element from thespecification tree.

    5. Select the AnalysisCase that you just insertedSolution Set branch of the

    Specification Tree and Click the Compute Solution button.

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    6. For multi-case animation, press and hold down the Control key and select thecar_AnalysisCase Solution Set and AnalysisCase.1Solution Set

    branches. Now Click theAnimate button and watch the animation ofboth cases simulataneously.