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Modified Tire-Slip-Angle Model for Chaotic Vehicle Steering Motion

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Abstract

The 5-DOF vehicle model employs the classical tire-slip-angle model to elicit the stability characteristics in vehicle handling during chaotic motion. However, the energy is not conserved, and the simulation results do not match actual behavior in that the vehicle should stop having lost balance. We have analyzed the limitations of the classical tire-slip-angle equation, and developed another model, which can be applied to all conditions. To ensure the correct use of the Pacejka’s magic formula for vehicle dynamics, we discuss the differences in tire axis systems between the ISO and adapted SAE (Pacejka), and propose a transformation method relating the two different tire axis systems. Finally, simulations are described that are performed in accordance with the established 5-DOF vehicle system dynamics model. The simulation results show that all states returned to the stable region after the vehicle had lost balance. The process involved energy dissipation, and approaches the response actually experienced. The limitations of the classical tire-slip-angle model are fully displayed and the effectiveness of the proposed slip angle model is demonstrated in unsteady vehicle states.

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Abbreviations

DOF:

Degree of freedom

ISO:

International Standardization Organization

SAE:

Society of Automotive Engineers

MF:

Magic formula

CG:

Center of gravity of vehicle

\(v_\mathrm{x} ,v_\mathrm{y} \) :

Longitudinal and lateral velocity at the CG, respectively.

\(v_\mathrm{x1} ,v_\mathrm{y1} ,v_\mathrm{x2} ,v_\mathrm{y2}\) :

Longitudinal and lateral velocity of front and rear tires under the vehicle coordinate system respectively.

\(v_\mathrm{xf} ,v_\mathrm{yf} ,v_\mathrm{xr} ,v_\mathrm{yr}\) :

Longitudinal and lateral velocity of front and rear tires under the wheel coordinate system respectively.

\(\delta _\mathrm{f}\) :

Front wheel steering angle

a, b :

Distance from CG to front and rear axles, respectively.

\(\alpha _\mathrm{f} ,\alpha _\mathrm{r}\) :

Slip angle at front and rear tires respectively.

\(\omega \) :

Yaw rate of vehicle

k :

Tire slip ratio

\(\omega _\mathrm{w}\) :

Angular speed of wheel

\(R_\mathrm{e} \) :

Rolling radius of wheel

\(v_\mathrm{wx}\) :

Longitudinal velocity of wheel center in wheel plane

m :

Mass of the vehicle

\(I_\mathrm{z} \) :

Moment of inertia of vehicle

\(F_\mathrm{yf} ,F_\mathrm{yr}\) :

Lateral force at front and rear tires, respectively.

\(F_\mathrm{xf} ,F_\mathrm{xr}\) :

Longitudinal tire force at front and rear tires respectively.

\(\omega _\mathrm{f} ,\omega _\mathrm{r}\) :

Angular velocity of front and rear tires respectively.

\(T_\mathrm{bf} ,T_\mathrm{br}\) :

Braking torque on front and rear respectively.

\(T_\mathrm{d}\) :

Torque to driving wheels

J :

Wheel moment of inertia

\(C_\mathrm{x}\) :

Drag coefficient

\(A_\mathrm{Lx}\) :

Frontal area of the vehicle

\(\rho \) :

Mass density of air

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Acknowledgements

This research is supported by the project of National Science Foundation China (Grant No. 51475199).

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Authors and Affiliations

  1. College of Transportation, Jilin University, Changchun, 130000, China

    Yu Mu, Ling Li & Shuming Shi

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  1. Yu Mu
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  2. Ling Li
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  3. Shuming Shi
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Correspondence to Shuming Shi.

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Mu, Y., Li, L. & Shi, S. Modified Tire-Slip-Angle Model for Chaotic Vehicle Steering Motion. Automot. Innov. 1, 177–186 (2018). https://doi.org/10.1007/s42154-018-0019-7

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