Research Papers

A Hybrid Physical-Dynamic Tire/Road Friction Model

[+] Author and Article Information
Jingliang Li

e-mail: lijingliang@bit.edu.cn

Yizhai Zhang

e-mail: yzzhang@eden.rutgers.edu

Jingang Yi

e-mail: jgyi@rutgers.edu
Department of Mechanical and Aerospace Engineering,
Rutgers University,
Piscataway, NJ 08854

1Present address: School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081, P. R. China.

2Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 6, 2011; final manuscript received April 24, 2012; published online October 30, 2012. Assoc. Editor: Xubin Song.

J. Dyn. Sys., Meas., Control 135(1), 011007 (Oct 30, 2012) (11 pages) Paper No: DS-11-1173; doi: 10.1115/1.4006887 History: Received June 06, 2011; Revised April 24, 2012

We present a hybrid physical-dynamic tire/road friction model for applications of vehicle motion simulation and control. We extend the LuGre dynamic friction model by considering the physical model-based adhesion/sliding partition of the tire/road contact patch. Comparison and model parameters relationship are presented between the physical and the LuGre dynamic friction models. We show that the LuGre dynamic friction model predicts the nonlinear and normal load-dependent rubber deformation and stress distributions on the contact patch. We also present the physical interpretation of the LuGre model parameters and their relationship with the physical model parameters. The analysis of the new hybrid model's properties resolves unrealistic nonzero bristle deformation and stress at the trailing edge of the contact patch that is predicted by the existing LuGre tire/road friction models. We further demonstrate the use of the hybrid model to simulate and study an aggressive pendulum-turn vehicle maneuver. The CARSIM simulation results by using the new hybrid friction model show high agreements with experiments that are performed by a professional racing car driver.

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Fig. 1

A schematic diagram of the tire motion kinematics and contact patch geometry

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Fig. 2

A schematic of stress distribution across the contact patch

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Fig. 3

Steady-state bristle deformation under various slip values

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Fig. 4

Comparison results of the longitudinal force Fx of the hybrid physical-dynamic model with the Pacejka “magic” formula under various normal loads

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Fig. 5

A vehicle trajectory of a pendulum-turn maneuver from racing driving experiments

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Fig. 6

Testing data at four tires. (a) Longitudinal friction forces Fx. (b) Lateral friction forces Fy. (c) Normal loads Fz. (d) Tire slip ratios λ. (e) Tire slip angles α and vehicle side-slip angle β. (f) Vehicle pitch and roll angles.

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Fig. 7

Racing car driver input data. (a) Steering angle δ and yaw rate ωψ. (b) Normalized throttle/braking actuation.

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Fig. 8

Comparison of simulation results and testing data. (a) Longitudinal/lateral velocity vGx/vGy. (b) Longitudinal/lateral acceleration aGx/aGy. (c) Yaw rate ωψ. (d) Vehicle side-slip angle β.



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