stand still model

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A New Wheel Model For Vehicle Dynamic Simulation

Hai Chenguang.State Key Laboratory of Automobile Dynamics

Simulation, Jilin University

Changchun,130025,China

[email protected]

Ji Peng.State Key Laboratory of Automobile Dynamics

Simulation, Jilin University

Changchun,130025,China

[email protected]

Abstract - A new wheel model was established to simulate

stand-still and starting condition which can’t be accurately

described by previous tire model. In this new model, the wheel

is simplified into two parts: wheel-rim and contact patch,

which were connected by spring-dampers. Contact patch

dynamic system was established, so tire slip ratio can be

calculate more accurately. By introducing stick-slip friction

algorithm, vehicle model can simulate stand-still and starting

condition properly. Through simulation, the new wheel model

was verified well.

Keywords - Wheel model; Stand-still; Stick-slip friction;

I. INTRODUCTION

The previously established tire model has twoshortcomings. (1) Previous tire model use wheel-spin

velocity, longitudinal and lateral velocity of wheel center to

estimate tire slip velocity, so it is inevitable to introduce

large errors, as shown in Figure 1. (2) Because previous tire

model use relaxation length method to handle zero speed of

the vehicle[1] [2]

.it bring about instability and micro

vibration of the vehicle in parking.

Tire mechanical properties largely determine the

movement of the vehicle, so it is important to establish a

more accurate wheel model.

wx x

R V S

R

ω

ω

⋅ −=

⋅

(1)

wxV

ω

R

Figure 1 the estimate of the tire slip ratio

According to shortage of previous model, this paper

presents a new wheel model. The new wheel model builds

the completely dynamical system including contact patch

and elastic tire carcass, and it furthermore establish thecompletely dynamical differential equation of contact patch,

so we can use the movement of wheel-rim to accurately

calculate the tire slip velocity. Stick-slip separation friction

model was used to calculate the friction between contact

patch and road so the force of vehicle was truly calculated

at zero speed and we can simulate stand-still parking

properly.

II. ESTABLISHMENT OF THE NEW WHEEL MODEL

A. Introduction of new wheel model

In order to accurately describe the dynamic mechanicalcharacteristics of tire, the new model simplify the wheel

into two parts: wheel-rim and contact patch, spring-dampers

which represent elasticity of carcass were used in the model

to connect wheel rim and contact patch, as shown in theFigure 2.

Figure 2 wheel model

The new wheel model has three components:

The contact patch transient model

The UniTire steady-state model

The stick-slip separation friction model between

road and contact patch

B. Coordinate system definition[3]

1 Earth-Fixed Coordinate System (XE, YE, ZE) A

coordinate system fixed in the inertial reference. The XE

and YE axes are parallel to the ground plane. The ZE axis is

aligned with the gravitational vector. The positive ZE axis

points upward. The orientation of the XE, and YE axes is

arbitrary and should be based on the needs of the analysis or

test. The location of the origin is generally an arbitrarypoint defined by the user.

2 Wheel Coordinate System(XW,YW,ZW) A

coordinate system whose XW and ZW axes are parallel to the

wheel plane, whose YW axis is parallel to the wheel-spin

axis, and whose XW is parallel to the local road plane. The

V6-71978-1-4244-6349-7/10/$26.00 c2010 IEEE



positive ZW axis points to upward. The origin is fixed at

the wheel center.

3 Tire Coordinate System(XT,YT,ZT) A coordinate

system whose XT and YT axes are parallel to the local road

plane, with the ZT axis normal to the local road plane. The

orientation of the XT axis is defined by the intersection ofthe wheel plane and the road plane. The positive ZT points

upward. The origin is fixed at the contact center.

OT

X

T Z

T Y

C

E X

E Y

E Z

W Z

W X

W Y

Figure 3 coordinate system

C. contact patch transient model

In contact patch transient model, the completely

dynamical differential equation of contact patch was

established and we use it to calculate the tire slip velocity.

Spring-dampers were used in the model to connect wheel

rim and contact patch. Because spring-damper represent the

elasticity of the tire carcass and describe the relaxation

effect of the tire, the new model can more accurately

calculate the tire slip velocity. At the same time the elastic

deformation of the tire carcass can self-adaptively adjust the

position relationship of parts[4] [5]

. As shown in formula(2)-(4).

Figure 4 contact patch transient model

cxsxbcycxc F F V V m −=− )( ψ && (2)

cysybcxcyc F F V V m −=+ )( ψ && (3)

czszbc M M I −=ψ & (4)

Fsx, Fsy, Msz represent the force and moment road

acting on contact patch, Fcx, Fcy Mcz represent the force

and moment spring-damper acting on contact patch, Vcx,

Vcy represent tire longitudinal and lateral slip velocity[6]

.

D. UniTire steady-state model

After obtain the tire slip velocity, we use UniTiresteady-state model to calculate tire force between road and

tire. UniTire steady-state model can deal with complex tire

movement input, including large tire slip angle, large

longitudinal slip ratio, large camber angle and large vertical

load.

The advantages of UniTire steady-state model:

UniTire is based on generalized theory model, so it can

satisfy higher-order theory boundary conditions; UniTire

model construct semi-empirical formula based on

exponential function, so it has high identification accuracy

in nonlinear large-slip regional.

E. The stick-slip separation friction model between road

and contact patch

The interaction between tire and road surface can beviewed as a class of contact friction problem. When there is

a relative slip velocity between two objects in contact with

each other, the friction force will be produced to resist therelative movement and the friction force is the function of

the relative slip velocity. When the relative slip velocity is

close to zero, two objects will glue together, until there is a

sufficiently large external force to break this bond. At this

stage, because the relative velocity between two objects is

close to zero, the interaction force can not self-identify and

must dependent on outside forces.

Friction model algorithm: when there is a relative slip

velocity between tire and road, we use UniTire steady-state

model to calculate the friction force between tire and road;

when the slip velocity is very small and close to zero, the

friction model is considered to enter static friction state, the

friction force between tire and road balance with theexternal force, which is the elastic force of the equivalenttire carcass; when elastic force of tire carcass is larger than

maximum static friction force provided by road face,

friction model Re-enter the sliding friction state.

Static friction model introduces stability margins in

longitudinal, lateral, yaw direction and improve the stability

of the vehicle model, so the model able to generate enough

resistance effect when subject to small perturbations. At thesame time, the introduction of the static friction model

make the vehicle model can simulate stand-still (zero

speed) truly and solve the problem of the previous model.

III. THE SIMULATION AND ANALYSIS OF THE NEW WHEELMODEL.

ADAMS software is widely used within the

automotive industry. By programming the subroutine of the

new wheel model, we embed the wheel model into

V6-72 2010 2nd International Conference on Computer Engineering and Technology [Volume 6]



ADAMS and carry out the simulation of the vehicle

stand-still and vehicle starting [7]

.

A. The simulation of stand-still (Static equilibrium)

max_ µ F −

max_ µ F

Figure 5 friction model

Static equilibrium: parking without interference of

the external force. Simulation results are shown in Figure

6-7.

0 1 2 3 4 5

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

l o n g i t u d i n a l v e l o c i t y ( k m / h )

Time

new wheel model

PAC89

Figure 6 longitudinal velocity of vehicle CG

0 1 2 3 4 5

-1.50

-1.49

-1.48

-1.47

-1.46

-1.45

l o n g i t u d i n a l d i s p l a c e m e n t ( m )

time(s)

new wheel model

PAC89

Figure 7 longitudinal displacement of vehicle CG

From simulation results we can see:

When we use PAC89 tire model to simulate

stand-still (static equilibrium), the vehicle will have largeresidual velocity and zero-drift phenomenon will happen.

When we use the new wheel model, the vehicle can

enter static equilibrium state immediately and almost not

have residual velocity, so the new wheel model can makethe vehicle model simulate stand-still (zero speed) truly.

B. The simulation of vehicle starting

Vehicle starting: driving torque is exerted on thefront wheel, Simulation results are shown in Figure 8-9.

0 1 2 3 4

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

l o n g i t u d i n a l a c c e l e r a t i o n ( m / s 2 )

time (s)

new wheel model

PAC89

Figure 8 longitudinal acceleration of vehicle CG

0 1 2 3 4

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

l o

n g i t u d i n a l v e l o c i t y ( k m / h )

A

new wheel model

PAC89

Figure 9 longitudinal velocity of vehicle CG

From simulation results we can see:

The new wheel model has the ability to resist thesmall driving force. Although driving force is exerted on

the wheels, if the driving force does not exceed the

maximum static friction force provided by road, at this

time vehicle dose not start. When the driving force is

larger than maximum static friction force provided byroad, vehicle begins to start.

The PAC89 tire model does not have the ability to

resist the small driving force. As long as the small driving

force is exerted on the wheels, vehicle will begin to startimmediately. This is inconsistent with the actual.

IV. CONCLUSION

[Volume 6] 2010 2nd International Conference on Computer Engineering and Technology V6-73



This paper represents a new wheel model. The new

wheel model simplifies the wheel into two parts:

wheel-rim and contact patch, spring-dampers which

represent elasticity of carcass were used to connect wheel

rim and contact patch; the new wheel model builds the

completely dynamical system including contact patch and

elastic tire carcass; Stick-slip separation friction model

between tire and road is introduced and the determination

method of static friction force is found; the subroutine ofthe new wheel model is programmed and it is carried out

in ADAMS software.

Simulation results show that: (1) by contact patch

dynamic, the model can calculate out the tire slip ratio

more accurately, furthermore to calculate out the more

accurate tire force. (2) By introducing stick-slip

separation friction model between road and tire, the

vehicle model can simulate stand-still (zero speed) and

starting properly, so it overcomes the shortcomings of

previous models. (3) The new wheel model introduces

stability margins in longitudinal, lateral, yaw direction

and improves the stability of the vehicle model, so the

model able to generate enough resistance effect when

subject to small perturbations

V. ACKNOWLEDGMENT

The authors wish to thank Prof. Guan Xin and

Prof. Zhan Jun, of State key Laboratory of Automotive

Dynamic Simulation Jilin University, for their support

in my development.

REFERENCES

[1] I.J.M. Besselink, H.B.Pacejka. The SWIFT tyre model: overviewand application[J]. AVEC, 2004:525-530

[2] Konghui Guo, Lei Ren. A Non-steady and Non-linear Tire Model

Under Large Lateral Slip Condition[J]. SAE paper, 2000-01-0358.[3] SAE J670

[4] Konghui Guo, Ye Zhuang. Friction Coefficient Switching In Tire

Semi-empirical Model [J], Automobile technology. 2004

[5] Zhongcheng Yuan. Study of UniTire Steady State Tire Model [D].

Changchun, Jilin University, 2006.

[6] Hans B.Pacejka. Tyre and Vehicle Dynamics[M]. Oxford:

Butterworth-Heinemann, 2002.

[7] ADAMS2005. Help document. Solver

V6-74 2010 2nd International Conference on Computer Engineering and Technology [Volume 6]

stand still model

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