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Establishment and Simulation Analysis of 18 DOF Unified Dynamics Model of Automobile Chassis

  • Control Theory and Applications
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Abstract

The unified dynamics modeling of automobile chassis is the foundation of the chassis integrated control. Previous researches mainly focused on one or two subsystems, which could not fully reflect the dynamics characteristics of automobile chassis. In this paper, a unified dynamics mathematical model involving 18 degrees of freedom (DOF) of a two-axle vehicle is established to evaluate the ride comfort and handling stability of the vehicle, based on the coupling relationship of vehicle longitudinal, lateral and vertical dynamics. In order to verify the correctness of the 18-DOF unified dynamics model, the following three methods are used: 1) comparison with other four submodels, 2) experimental verification and 3) co-simulation test. Both simulation and test results indicate that the unified dynamics mathematical model can be used to evaluate the comprehensive dynamics performance of automobile chassis, and it is beneficial for the subsequent research of chassis integrated control system.

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Abbreviations

M :

Mass of the car model

M s :

Mass of the sprung mass

m u1j (j = l, r):

Mass of each front unsprung mass

m u2j (j = l, r):

Mass of each rear unsprung mass

L 1 :

Distance of the body center of gravity to the front axle

L 2 :

Distance of the body center of gravity to the rear axle

h :

mass center of gravity to roll axis

Iyy :

Pitch moment of inertia of sprung mass

I xx :

Roll moment of inertia of sprung mass

I zz :

Yaw moment of inertia of sprung mass

I xz :

Xz product of the inertia of sprung mass

K s1j (j = l, r):

Front suspension stiffness coefficient

C s1j (j = l, r):

Front suspension damping coefficient

K s2j (j = l, r):

Rear suspension stiffness coefficient

C s2j (j = l, r):

rear suspension damping coefficient

K t1j (j = l, r):

Front tire vertical stiffness coefficient

K t2j (j = l, r):

Rear tire vertical stiffness coefficient

K α1j (j = l, r):

Front tire lateral stiffness coefficient for linear tire

K α2j (j = l, r):

Rear tire lateral stiffness coefficient for linear tire

d :

Track width

φ :

Roll angle of sprung mass

u 1j (j = l, r):

Active control force of front suspension

u 2j (j = l, r):

Active control force of rear suspension

F y :

Lateral force

o l :

Roll center position of sprung mass

C :

Gravity position of sprung mass

α 1j (j = l, r):

Front tire sideslip angle

α 2j (j = l, r):

Rear tire sideslip angle

δ :

Steering angle of the tire

V :

Absolute velocity of the car

β:

Sideslip angle of the car

r :

Yaw rate

Ψ:

Heading angle

ψ :

Angle between the absolute velocity and the Xa axis

θ :

Pitch angle of sprung mass

w 1j (j = l, r):

Uneven road input of front tire

w 2j (j = l, r):

Uneven road input of rear tire

zs1j (j = l, r):

Vertical position of front corner of sprung mass

z s2j (j = l, r):

Vertical position of rear corner of sprung mass

zu1j (j = l, r):

Vertical position of front corner of unsprung mass

zu2j (j = l, r):

Vertical position of rear corner of unsprung mass

z s :

Vertical position of gravity of sprung mass

g:

Acceleration of gravity

ω :

Wheel rotation speed

v x :

Longitudinal velocity

v y :

Lateral velocity

a x :

Longitudinal acceleration

a y :

Lateral acceleration

X :

Longitudinal displacement

Y :

Lateral displacement

T b :

Braking torque

V ω :

Forward velocity of the tire

R :

Rolling radius

μ 0 :

Peak friction coefficient of tire to road

Tω :

Nominal tread width

T p :

Tire pressure

A0, A1, A2, A3, A4, B1, B3, B4, C1, C2, C3, C4 :

Coefficients for the Calspan tire

CS/F z :

Calspan coefficient for the slope of the normalized longitudinal force vs longitudinal slip curve at zero longitudinal slip

k A :

The proportion that the tread length ap0 changes with Fx

k α :

Lateral stiffness coefficient of the tire

k c :

Longitudinal stiffness coefficient of the tire

a p :

Tire contact patch length

a p0 :

Tread length with zero longitudinal force

Y γ :

Camber thrust stiffness

F z :

Instantaneous value of normal load on the tire

F x :

Instantaneous value of longitudinal force on the tire

F zt :

The tire design load at the operating tire pressure

s :

Longitudinal slip

α :

tire side slip angle

μ nom :

Nominal adhesion coefficient of tire to road

1:

front

2:

rear

l :

left

r :

right

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacture Technology for Automobile Parts, Ministry of Education, Chongqing University of Technology, 69 Hongguang Avenue, Banan District, Chongqing, 400054, China

    Fei Lai & Cheng-Yue Jiang

Authors
  1. Fei Lai
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  2. Cheng-Yue Jiang
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Corresponding author

Correspondence to Fei Lai.

Additional information

This work is supported by the Scientific Research Foundation of Chongqing University of Technology (2019ZD31), the Scientific Research Project of Vehicle Engineering College (CL2019-02), the Science and Technology Talent Project of Chongqing Banan District (2020TJZ017), and the Science and Technology Research Program of Chongqing Education Commission of China (KJQN202001102).

Fei Lai is an associate professor in Chongqing University of Technology. He received his Ph.D. degree in mechanical engineering from Chongqing University in 2010. His research interests include vehicle dynamics and control.

Cheng-Yue Jiang is a professor in Chongqing University of Technology. He received his Ph.D. degree in mechanical engineering from University of Birmingham in 2009. His research interests include vehicle active and passive safety.

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Lai, F., Jiang, CY. Establishment and Simulation Analysis of 18 DOF Unified Dynamics Model of Automobile Chassis. Int. J. Control Autom. Syst. 19, 2323–2342 (2021). https://doi.org/10.1007/s12555-019-0750-9

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  • DOI: https://doi.org/10.1007/s12555-019-0750-9

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