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Identification and assessment of a simplified model for vehicle ride simulation

M. Carpinelli1, G. Gatti

1, D.Mundo

1, M. Gubitosa

2, A.Toso

2

1 Department of Mechanical Engineering, University of Calabria

Ponte Pietro Bucci, 87036 Rende, Italy

e-mail: [email protected], [email protected], [email protected]

2 Simulation Division – LMS International

Interleuvenlaan 68, 3001 Leuven, Belgium

e-mail: [email protected], [email protected]

Abstract This paper proposes a procedure to identify the dynamic parameters of an eight degrees of freedom (8

DOFs) vehicle concept model. A high fidelity model for ride simulations implemented in the commercial

multibody code Virtual.Lab Motion has been considered as benchmark. The proposed simplified model is

implemented with the help of the multibody libraries in Mathworks\Simulink environment. In this latter,

suspension links are included in a trailing arm configuration in order to take into account the longitudinal

to vertical force coupling between the sprung and the unsprung masses during acceleration maneuvers. A

non linear least-squares method is used for the identification process with the aim of minimizing the

difference in the dynamic behavior between the high fidelity and the simplified vehicle model. The

proposed methodology can be used to create and calibrate reliable concept models based on ride

simulations or physical tests on predecessor models, thus enabling early concept-phase prediction and

optimization of ride performance of new vehicles.

1 Introduction

In the last decades, Computer-Aided Engineering (CAE) tools have been extensively used by engineers to

accelerate the development cycle of complex products. The number of expensive physical prototypes has

been greatly reduced by means of reliable virtual models used as predictive tools in any phases of the

design process of new products. Especially in the automotive industry, were a complex set of design

requirements and constraints must be fulfilled to ensure that a new product meets customer satisfaction

and approval by regulatory bodies, the need for efficient tools for performance prediction and optimization

in an early design stage is pushing researchers to develop new methodologies for vehicle concept design

[1-4]. The concept phase is a highly strategic step in the vehicle design process. Indeed a proper concept

design phase can lead to an improved initial CAD (Computer-Aided Design) model of the vehicle, which

is a basic requirement for a faster convergence of the development cycle towards an optimal final product.

Vehicle handling and ride performance are generally analyzed by means of high fidelity Multibody (MB)

models which allow an accurate prediction of the vehicle dynamic behavior thus enabling engineers to

adapt the design based on the output of virtual simulations. Detailed MB models are often composed by

more than 100 bodies and contain elastic and dissipative force elements with realistic nonlinear stiffness

and damping properties which are used to model real components such as shock absorbers and suspension

bushings. In order to create a detailed MB model, the center of gravity (CG) position of each body must be

known together with its mass and inertia properties. Moreover the positions of the suspension hard points

must be defined and the stiffness and damping properties of shock absorbers and suspension bushings

3695

must be assigned. At the beginning of the design process few data are generally available and the

description of a detailed MB model is not possible.

A different approach can then be used which is based on the definition of a simplified vehicle concept

model composed by few bodies and having a limited number of degrees of freedom (DOFs). Such a model

is ment to reproduce the dominant ride dynamic behavior of a real vehicle including the squat and dive

phenomena, which occur during acceleration and braking due to the longitudinal weight transfer. The

approach presented in this paper adopts such a simplified vehicle model. An identification procedure is

then presented which allows obtaining parameters needed to define the concept model using data coming

from ride simulations or physical tests on predecessor models. In particular, during the identification

phase, data coming from a virtual measurements campaign on a detailed MB model of a passenger car are

used to tune the concept model parameters.

The outline of the paper is as follows. Section 2 provides a brief overview of the simplified models

currently used to assess the vehicle ride behavior in the early phase of the design process. In the same

section the proposed vehicle concept model is described and the main differences with respect to the

classical models are highlighted. In Section 3 a detailed MB model of a passenger car is presented and a

virtual measurement campaign is defined in order to obtain data needed for the following parameter

identification process. In Section 4 the parameter identification process is presented while in Section 5

simulation results obtained with both the identified concept model and the detailed MB model are

compared in order to test the effectiveness of the identification process.

2 Development of a vehicle concept model for ride analysis

In this section a brief description of the full 7 DOF vehicle model generally used for ride analysis is first

presented. The issue of taking into account the squat phenomenon occurring during the acceleration phase

is then addressed and proper modifications are introduced into the classical model to achieve a reliable

ride behavior during the acceleration phase. The modeling process of the multibody system under study

within the Matlab/Simulink environment is then presented together with a brief description of the

underlying equations of motion.

2.1 Vehicle ride model and squat phenomenon

Several ride models have been proposed for the assessment of the vehicle ride behavior [5-8]. Figure 1

shows the model which is generally used to analyze the ride behavior of a passenger car with independent

suspensions [6, 8]. This model is composed by five bodies: the sprung mass, mainly representing the

vehicle body, and the four unsprung masses, including the inertia proprieties of suspension’s moving

elements. The seven DOFs adopted are the pitch, roll and bounce of the vehicle body and the vertical

displacements of the four unsprung masses. The system’s parameters are the mass and inertia properties of

the vehicle body and wheels, and the damping and stiffness properties of tires and shock absorbers. The 7

DOFs model can be implemented within a multibody software and then used to analyze the ride behavior

of the vehicle by means of a direct dynamic analysis once the vertical displacements at the 4 wheel-road

contact points are specified. In this simple model the road roughness is considered as the only excitation

source since vibrations transmitted from the engine to the vehicle body as well as vibrations due to mass

imbalances in the tire/wheel assembly are not taken into account. However this model is able to provide

useful estimation of the ride properties of the vehicle since road surface irregularities are usually one of

the major sources of excitation for the vehicle body in the low frequency range.

3696 PROCEEDINGS OF ISMA2012-USD2012

Figure 1: 7 DOFs Model for a passenger car

A drawback in the use of the 7 DOFs model is that it is not able to reproduce the longitudinal to vertical

force coupling between the unsprung and sprung masses occurring during acceleration or braking

maneuvers. Indeed, under acceleration, the vertical load on the rear wheels increases due to the

longitudinal weight transfer implying a jounce movement in the rear suspension and a rebound movement

in the front suspension [5,9]. This phenomenon, which in a rear drive vehicle is called “Power Squat”,

causes vehicle pitch during the acceleration phase. The amount of jounce and rebound of the rear and front

suspensions is determined by the percentage of load transfer which is directly carried by the suspension

links. In order to correctly model the power squat phenomenon the use of a different modeling of the

suspension linkages is thus needed. In the analysis of the vehicle longitudinal behavior all the relevant

suspension properties can be studied considering a lateral view of the vehicle as shown in Figure 2. It is

known that when considering the suspension behavior on a lateral plane normal to the ground and parallel

to the centerline of the car, any suspension system is functionally equivalent to a trailing arm pivoting to

the chassis at a point located at the lateral instant center of rotation (IC) and rigidly connected to the wheel

at the other extremity [5,9].

The position of the trailing arm’s IC is of crucial importance since it determines the amount of load

transfer which is carried out by the suspension links thus influencing the pitch angle and the vertical

motion of the vehicle body during the acceleration phase. The position of the pivot point for a certain

suspension can be specified by means of its longitudinal distance d from the wheel-road contact point and

by the angle Ф as shown in Figure 2. In order to take into account the power squat phenomenon, in the

proposed vehicle concept model the four suspensions are modeled in a trailing arm configuration, as

explained in the following paragraph.

Sprung Mass

Suspension Properties

Unsprung Masses

Tire Properties

VEHICLE CONCEPT MODELLING 3697

Figure 2: Trailing Arm Configuration

2.2 Vehicle concept model architecture

The kinematic scheme of the vehicle concept model is shown in Figure 3, where bodies, joints and force

elements are represented in different colors.

Figure 3: Full Car Concept Model

Similarly to the 7 DOFs model presented in the previous section, the proposed vehicle concept model is

composed by 5 rigid bodies: the chassis body and the 4 wheels. As previously anticipated, the wheels are

connected to the chassis in a trailing arm configuration. In particular each wheel is connected to the

chassis by means of a rotational joint whose axis is normal to the lateral plane parallel to the centerline of

the car. The intersection between this plane and the axis of the joint connecting the wheel and the chassis

defines the position of the trailing arm IC. While in a real vehicle the position of the suspension pivot

point in the lateral plane changes as the linkage moves, in the proposed vehicle model this point is held

fixed. The kinematic scheme of the trailing arm configuration used to model the suspension linkages is the

same of that shown in Figure 2. It is worth noting that the wheel and the trailing arm shown in Figure 2 are

modeled as a single rigid body. A translational joint is applied between the wheel center and the wheel-

road contact point allowing only the relative vertical displacements corresponding to the tire deflections.

FRONT

REAR

KTire CTire

KF CF

KR CR

KTOR_F

CTOR_F

KTOR_R CTOR_R

Φ

d Fx

Fz

wheel radius

unsprung mass

pivot point

trailing arm


Finally the wheel-road contact points are kinematically constrained as being equal to the road elevation,

excluding the possibility of contact separation. Since we are only interested in the longitudinal and vertical

dynamics it is possible to neglect yaw and lateral displacement of the chassis, assuming thereof straight

driving maneuvers. The considered model has thus 8 DOFs which are the vertical and longitudinal

displacements and the roll and pitch angles of the chassis, plus the relative rotations of the 4 wheel-trailing

arm bodies with respect to the chassis. Taking into account the longitudinal DOF of the chassis along the x

direction is one of the main differences between the proposed model and the classical 7 DOFs full car

model generally used for ride analysis.

Spring and damper force elements are also used to take into account system compliances and dissipative

effects. The wheel centers are connected to the chassis by means of 4 spring-damper force elements with

linear characteristics representing the suspension shock absorbers. Linear springs and dampers are also

inserted between each wheel center and the corresponding wheel-road contact point in order to model the

vertical tire properties. An equivalent concentrated torsional stiffness and damping element is introduced

to take the front and rear stabilizer bars into account. In particular, a rotational spring-damper force

element connects the trailing arms on the same axle introducing a relationship between their relative

rotations. In this way the vertical displacement and velocity of one wheel affects the vertical dynamics of

the other wheel on the same axle reproducing the coupling effect of a stabilizer bar.

In order to numerically define the model shown in Figure 3, several parameters have to be introduced. For

each body, the position of the center of gravity (CG) must be specified together with its mass and inertial

properties. The rotational joints representing the pivot points of the front and rear suspensions must be

also located in the corresponding lateral plane. Moreover the stiffness and damping properties related to

the shock absorbers, the stabilizer bars and the tires must be specified. The identification of fitting values

for these quantities will be discussed in Section 4.

2.3 Implementation of the multibody concept model

The multibody vehicle concept model described in section 2.2 was implemented within the Simulink

environment. Multibody equations of motion are formulated in Simulink using relative coordinates. This

approach minimizes the number of coordinates needed to represent the system configuration and allows

simulating the motion of serial multibody systems organized hence in an open kinematic chain

configuration, without specifying the constraint equations. When dealing with constrained mechanical

systems having a cyclic structure, as in the case of the vehicle concept model under study, the multibody

equations can be expressed in the following descriptor form:

vq

λqGvqfvqM ),(),,()( tt T

0qg ),( t (1)

where M is the mass matrix and q and v are the generalized coordinates and the corresponding velocity

variables respectively. Centrifugal, Coriolis and external forces are retained in the vector f while g and G

are the constraints vector and the constraint Jacobian respectively, and λ is the vector of Lagrange

multipliers associated with the constraint forces. Eq. 1 represents a system of index-3 Differential-

Algebraic-Equations (DAEs). In order to solve the system governing equations in Simulink, the index of

the DAEs in Eq.1 is reduced by differentiating twice the constraint equations with respect to time. The

obtained system of equations is then solved for λ and treated as an Ordinary Differential Equation (ODE)

system while proper approaches are used to solve the problem of numerical drift from the constraint

conditions due to the double differentiation of the constraint equations [10].

The implementation of the MB concept model in the Simulink environment was based on the scheme

reported in Figure 3. Several blocks representing bodies and joints were assembled in order to obtain the

desired kinematic structure [11]. Force elements were also inserted to represent shock absorbers, stabilizer


bars and tires. Displacement drivers along the vertical direction were applied to the four wheel-road

contact points in order to introduce the desired road profile. Proper drive torques acting on the rear trailing

arms and longitudinal forces applied to the wheel-road contact points were also inserted in order to control

the longitudinal motion of the vehicle as it will be explained in the next section.

2.4 Longitudinal motion and road excitation

As described in the preceding sections the longitudinal DOF has been retained in the proposed vehicle

concept model. In order to reproduce a typical driving maneuver (i.e an acceleration phase on a rough

road) the longitudinal law of motion must be assigned together with the road profile as functions of time.

In a real vehicle the acceleration ax of the chassis is due to the longitudinal forces arising at the wheel-road

contact patches. Also in the vehicle concept model the longitudinal motion of the chassis must be

determined by the longitudinal forces at the four wheel-road contact points. In particular for a rear drive

vehicle with independent suspensions on both front and rear axle, the drive torque is imposed to the rear

wheels by the differential through the halfshafts. Since the differential is mounted on the chassis, during

the acceleration phase the drive torque is exerted by the chassis on the rear trailing arms as shown in the

free body diagram of Figure 4a. The longitudinal traction force acting on the rear wheels can be

determined starting from the drive torque imposed by the halfshafts using the following formula [5]:

r

TF drive

rearx _ (2)

where r is the effective wheel radius. It is assumed here that a ride test is performed, in which, once the

vehicle has been accelerated to the desired longitudinal speed, the driver acts on the clutch pedal. In this

way during the deceleration phase the only excitation source is represented by the road irregularities since

the vibrations transmitted by the engine to the vehicle body through the engine mounts are negligible. In

order to simulate this test condition, during the deceleration phase the drive torque is not longer applied at

the rear wheels and the vehicle speed slows down as happens when the neutral gear is engaged (Fig.4b). A

longitudinal resistant force always acts on each wheel during both the acceleration and the deceleration

phase. This force is due to the tire rolling resistance and is proportional to the vertical load acting on each

wheel:

WfR rx (3)

The parameter fr in Eq.3 is the rolling resistance coefficients of the tire while W is the vertical force acting

on the wheel. Typical values of the rolling resistance coefficients relate to the vertical load in the

proportion of 0.01 [5].

Figure 4: Longitudinal Forces and Torques during acceleration (a) and deceleration (b)

Multibody models are typically used to carry out direct dynamic analyses which consist of determining the

motion of the system resulting from the application of external loads and kinematically driven DOFs. In

the automotive field direct dynamic analysis are extensively used to analyze the dynamic behavior of the

a)

Rx_front Rx_rear Fx_rear Rx_front Rx_rear

Tdrive

Mtot ax Mtot ax

b)


vehicle. For example, in the analysis of the vehicle ride behavior, the road profile is assigned together with

the traction torque at the drive wheels and the resulting motion of the vehicle is observed as schematically

shown in Figure 5.

Figure 5: Direct Dynamic Analysis Input

When performing a direct dynamic analysis on the vehicle concept model, the desired drive torque must

be assigned to the driving wheels (i.e. the rear wheels in the case under study) and the resulting

longitudinal forces acting on the rear tires can then be computed using Eq.2. The longitudinal forces due

to the tires rolling resistance can be estimated using Eq.3 once the vertical load acting on each wheel and

the tire properties are known.

A different approach must be adopted in order to specify the vehicle longitudinal motion during the

identification process. As it will be further explained in Section 4, the dynamic analysis on the vehicle

concept model performed during the parameter identification phase must be based on data coming from

experimental/virtual measurements. In a real maneuver, the drive torque as a function of time is not

directly available but it is possible to measure the longitudinal acceleration ax of the chassis. The

longitudinal acceleration can be used to estimate the longitudinal traction force acting on each rear wheel

during the acceleration phase with the following equation:

frontxrearxxtotrearx RRaMF ___2

1 (3)

here Mtot is the total vehicle mass and Rx_rear and Rx_front are the rolling resistance forces respectively on the

rear and front wheels which oppose to the vehicle motion. Eq.3 refers to the vehicle running on a road

with negligible slope. Moreover the aerodynamic force acting on the vehicle body is not taken into

account since it is negligible, if compared to the rolling resistance forces, at the speed reached during

maneuvers considered in the following sections [5]. Once the traction forces on the rear wheels are known

the drive torque can be easily estimated using the inverse of Eq.2 and the direct dynamic problem can be

solved since the drive torques and the correspondent traction forces have been determined.

In a typical direct dynamic analysis the road profile at the tire-road contact points is assigned in order to

study the corresponding vehicle response (Fig.5). However in a real ride test the displacements of some

points located on the suspension links or on the wheel rims are the quantities that can be effectively

measured. This measures must be used as input for the dynamic analysis during the identification

procedure in order to compare the response of the vehicle concept model and the measured response of the

real vehicle. In particular, as it will be described in the following sections, the vertical displacements

measured at the rim centers will be used as input for the direct dynamic analyses during the parameter

identification process as shown in Figure 6.

Vehicle Concept Model

Road Profile

Tdrive

Vehicle Dynamic Response


Figure 6: Direct Dynamic Analysis input during the identification process

3 Virtual measurement campaign

The goal of the vehicle concept model described in Section 2 is to make reliable indications about the

vehicle ride behavior available during the early phases of the suspension design process. Model

parameters should be tuned by means of an identification procedure using data coming from experimental

ride tests on a real predecessor vehicle or obtained by means of ride simulations performed with previous

developed MB models. In order to test the proposed methodology, a virtual measurement campaign has

been carried out on a detailed vehicle MB model within the LMS VirtuaLab.Motion simulation

environment. The identification process is addressed in Section 4 while in this section the detailed MB

vehicle model is presented together with the virtual tests performed to obtain a set of virtual output data

which are used in the following parameters identification procedure.

3.1 Detailed vehicle MB model

The vehicle under analysis is a rear wheel drive model mounting multilink rear suspension and a

McPherson type front suspension. The detailed multibody model of the vehicle shown in Figure 7 was

prepared starting from the industrial FEM of the full vehicle provided by a car manufacturer [4,12]. In

particular the mass and inertia properties of all rigid bodies, together with the location of the connection

points, were extracted from the full FEM. The bushing connections between suspension links, chassis and

subframe are modeled with non-linear stiffness and damping characteristics. Shock absorbers are inserted

with realistic non-linear stiffness and damping properties and provided with bump and rebound stops. The

front and rear stabilizer bars are modeled by means of concentrated rotational springs and a steering rack-

and-pinion system is also included into the model. The driveline subsystem and the exhaust pipe are both

inserted in order to provide the model with its complete mass and inertia properties. The obtained

multibody model has a total of 164 degrees of freedom and is composed by 81 bodies with a total

estimated mass of 1240 Kg. In order to accurately reproduce the tires behavior the Delft TNO-Tire model

was used [13,14]. Table 1 shows some parameters and settings used for the tire models adopted in the

simulations.

Tyre Characteristics Tire operational settings

Vertical Stiffness (KTire) 196261 [N/m] Contact Type used Smooth road / 2d road

Vertical Damping (CTire) 50 [N/m/s] Dynamics Non Linear Relaxation / Rigid Ring

Rolling Resistance Coefficient (fr) 0.01 Slip Forces Combined slip

Table 1: Tire model characteristics


Rim-Centers Vertical

Displacements

ax Chassis



Figure 7: Full Car Detailed MB Model

3.2 Ride simulations and measurements

The detailed MB model was used to reproduce several ride tests in order to collect significant data which

are needed during the parameter identification procedure. The test campaign was tailored to highlight the

vertical dynamic behavior of the vehicle and the force coupling between the sprung and the unsprung

masses during the acceleration phase. Since we are not interested in the vehicle lateral dynamics the

steering wheel is held fixed during all simulated maneuvers.

In order to simulate the road roughness, road profiles representing various types of real roads and runways

were obtained starting from their Power Spectral Density (PSD) [6]. The obtained road profiles were then

implemented in Virtual.Lab Motion through the introduction of spline-curves representing the road

profiles in correspondence of the tire contact points [15]. Figure 8 shows the degree of roughness in its

spatial deployment as well as its PSD for an average road which corresponds to the category C in the ISO

classification table [16].

0 0.5 1 1.5 2-8

-6

-4

-2

0

2

4

6x 10

-3

Spatial Coordinate x [m]

Road E

levation [

m]

Road Profile

Road ProfileLEFT

Road ProfileRIGHT

100

102

10-10

10-8

10-6

10-4

Spatial Frequency [CYCLE/m]

Power Spectral Density

PS

D [

m2/C

YC

LE

/m]

Figure 8: Portion of the road profile and its ISO 8608 classification by PSD


The longitudinal motion of the vehicle was imposed by means of a traction torque at the rear wheels

directly applied to the wheel hub joints. In each virtual test the traction torque starts acting on the rear

wheels after 5 seconds of simulation. At the end of the acceleration phase the traction torque on the rear

wheels is no longer applied and the vehicle speed slows down throughout the rest of the maneuver

simulating the deactivation of the clutch.

In Figure 9 the traction torque used to accelerate the vehicle from the rest condition to the speed of 15 m/s

in 5 seconds is reported together with the corresponding longitudinal speed of the chassis. The chassis

deceleration after the clutch deactivation is of about 0.01 g which is a typical deceleration value due to the

rolling resistance forces at the four wheels [5].

4 6 8 10 12 14 16 18 200

500

1000

t [sec]

a)

Drive T

orq

ue [

Nm

] Drive Torque at the rear wheels

4 6 8 10 12 14 16 18 200

10

20

t [sec]

b)

x s

peed [

m/s

]

Longitudinal Speed of the Chassis

Figure 9: Driving torque at the rear wheels (a) and longitudinal speed of the chassis (b)

Several simulations were performed using different combinations of road roughness and longitudinal laws

of motion in order to take into account different operating conditions. In particular two driving maneuvers

were selected to obtain data needed for the following parameter identification procedure as described in

Table 2. In the first maneuver the vehicle is accelerated from 0 to 15 m/s (54 Km/h) in 10 seconds. During

the acceleration phase the vehicle rides on a road with a degree of roughness classified as A within the

ISO table while during the deceleration phase the road profile corresponds to the B type. In the second

maneuver the vehicle undergoes a greater acceleration and rides on a C type road during the deceleration

phase.

# Maneuver Acceleration Phase ISO classification of road profile

Acceleration Deceleration

1 0-54 Km/h in 10 seconds A B

2 0-54 Km/h in 5 seconds A C

Table 2: Drive maneuvers simulated for the identification process

The selected maneuvers reproduce typical operating conditions, which highlight the vertical and

longitudinal behavior of the vehicle. In particular the squat phenomena occurring during the acceleration

phases can be observed in the first part of each maneuver, while the vehicle ride properties can be

analyzed during the deceleration phases, when the vehicle incurs in a road profile with a greater degree of

roughness.


When performing an experimental ride test, significant quantities such as the vertical displacements and

the roll and pitch angles of the chassis can be obtained from the outputs of accelerometers and string-

potentiometers mounted on the vehicle. In order to simulate a real experimental measurements campaign,

several virtual sensors were placed on the detailed vehicle MB model to measure the vertical displacement

of the chassis and its roll and pitch angles. These quantities will be compared with the vertical

displacement, roll and pitch angles obtained with the concept model during the parameter identification

process when computing the cost functions. As described in Section 2 the vertical displacements of the

four wheel centers were selected as the measured virtual quantities which must be given in input to the

concept model during the parameter identification process. These quantities can be actually measured in a

real ride test thus allowing the proposed procedure to be applied using experimental data. Figure 10 shows

the vertical displacements of the front left and rear left wheel centers measured during the second

maneuver. It is possible to notice how the vertical load transfer from the front axle to the rear axle causes

respectively an increase and a reduction in the deflections of the rear and front tires during the acceleration

phase.

4 6 8 10 12 14 16 18 20

-40

-30

-20

-10

t [sec]

z r

im c

ente

r [m

m]

Rim centers vertical displacements

Rear Left Wheel

Front Left Wheel

Figure 10: Vertical displacements of the Front Left and Rear Left wheel centers

4 Parameter Identification Process

The concept model must be provided with a proper set of parameters representing the suspension

characteristics [17,18]. This Section describes the identification process implemented in order to obtain

the unknown suspension parameters of the vehicle concept model. Before starting the parameter

estimation procedure, several data are needed to define the geometry and the mass and inertia properties of

the vehicle concept model. In particular the mass and the inertia tensor of the vehicle body (chassis and

engine) were extracted from the detailed MB model and then inserted into the concept model together with

the values of the wheel masses. Moreover the positions of the CGs of the vehicle body and of the 4 wheels

in the rest condition were measured on the detailed MB model and then used to define the positions of

bodies composing the vehicle concept model. Since during the estimation phase the displacements are

directly applied to the wheel centers there is no need to specify the vertical tire properties. However the

rolling resistance coefficient must be specified within the concept model in order to take into account the

longitudinal forces. Once the topology of the vehicle concept model and its mass and inertia properties

have been defined, it is possible to start the parameters identification procedure. The 12 parameters which

must be estimated are listed in Table 3.

Parameters Front Rear

Concentrated linear stiffness and damping of the shock-absorbers KF CF KR CR

Concentrated torsional linear stiffness of the stabilizer-bars Ktor_F Ctor_F Ktor_R Ctor_R

Trailing arms pivot point location in the lateral plane dF ФF dR ФR

Table 3: Identified Parameters of the Vehicle Concept Model


Figure 11: Scheme of the Identification Process

Figure 11 shows the workflow of the estimation process implemented in the present research work. The

first step was the selection of a proper set of virtual driving maneuvers in order to highlight the vertical

and the longitudinal dynamic behavior of the detailed vehicle MB model under study. The virtual

measures representing the vertical displacements of the wheel centers and the longitudinal acceleration of

the Chassis were then used as input for the concept model as described in section 2. The dynamic response

obtained with the concept model, together with the measured dynamic response of the detailed MB model,

were then given in input to the estimation algorithm. In particular the vertical displacements and the roll

and pitch angles of the chassis were selected as the output quantities describing the dynamic responses of

the two models. Optimization techniques were then used in order to estimate the set of parameters

minimizing the cost-function between the dynamic responses of the detailed MB model and of the concept

model in a least square sense. In particular the parameters estimation procedure was carried out using the

nonlinear least-squares method based on the trust-region algorithm.

5 Validation of vehicle concept model

Once the parameters of the concept model have been identified, a direct dynamic analysis can be

performed on the concept model using the same inputs specified for the detailed MB model, i.e. the road

profile at the wheel-road contact points and the drive torque on the rear wheels. The obtained responses

can then be compared to test the effectiveness of concept model. Since now the road input is applied at the

wheel-road contact points, the tire vertical stiffness and damping must be taken into account in the vehicle

concept model. The values of the tire vertical stiffness and damping reported in Tab.1 were thus inserted

into the vehicle concept model and the second maneuver described in Tab.2 was reproduced.

Road Profile

Tdrive

Rim-Centers Vertical Displacements

ax Chassis


Detailed MB Model


Identification Algorithm

Estimated Parameters

Virtual Measurements



4 6 8 10 12 14 16 18 20230

240

250

260

270

280

290

t [sec]

z [

mm

]Comparison z Chassis

Detailed MB Model

Concept Model

4 6 8 10 12 14 16 18 200.2

0.4

0.6

0.8

1

t [sec]

pitch [

deg]

Comparison pitch Chassis

4 6 8 10 12 14 16 18 20-0.3

-0.2

-0.1

0

0.1

0.2

t [sec]

roll

[deg]

Comparison roll Chassis

Figure 12: Maneuver 2, comparison of the dynamic responses

Figure 12 shows a comparison between the responses obtained with the concept model and the detailed

MB model. In particular the vertical displacements and the pitch and roll angles of the chassis are

compared. The identified concept model is able to accurately reproduce the dynamic response of the

detailed MB model during both the acceleration and the deceleration phases. During the acceleration

phase, which begins and ends after 5 and 10 seconds of simulation respectively, the pitch variations and

the vertical displacements of the chassis due to the squat phenomenon are correctly reproduced. The

concept model produces accurate results also during the deceleration phase when the vehicle incurs in a C

type road. The transition from an A type road during the acceleration phase to a C type road during the

deceleration phase is clearly visible in the third graph of Figure 12 where the roll angles are compared.


6 Conclusions

In this paper a simplified 8 DOFs vehicle concept model has been proposed which is able to accurately

reproduce both the ride vehicle behavior and the squat phenomenon occurring during the acceleration

phase. An identification process has been implemented to obtain the unknown parameters of the vehicle

concept model based on the output of experimental/virtual measurements on predecessor models. A virtual

measurements campaign has been carried out by means of a detailed Multibody model of a passenger car

in order to test the proposed methodology. Finally the effectiveness of the estimation process has been

ascertained comparing simulation results obtained with the identified concept model with those obtained

from the reference simulations of the detailed MB model for a typical ride maneuver.

The proposed methodology could be used to calibrate a reliable vehicle concept model which is able to

predict the chassis dynamics and the vibrational level of the body, thus allowing a first estimation of the

loads acting on the components connected to the chassis. Moreover the influence of new vehicle

configurations on the vibrational chassis response could be evaluated (i.e. new mass and inertia properties,

spring stiffness, damping coefficients), thus allowing a first design optimization. The analysis of the ride

dynamics during acceleration and braking could also furnish useful information for the suspension design

i.e. guiding the positioning of the lateral instant rotation centers of the suspension linkages.

Future developments of the presented work include the modeling of engine vibrations which contribute to

the ride behavior in the high frequency range. The low complexity level of the proposed concept model

makes it prone to be used in Real-Time (RT) simulations where the computational effort needed to run a

vehicle MB model has a crucial importance. Future researches will thus investigate the use of the

proposed concept model for Hardware-in-the-loop testing of active suspension systems.

Acknowledgements

The research leading to these results has received funding from the People Programme (Marie Curie

Actions) of the European’s Seventh Framework Programme FP7/2007-2013 under REA grant agreements

n. 213543 (ITN “VECOM”) and n. 285808 (IAPP “INTERACTIVE”).

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