Modeling and Analysis of Vehicle Shimmy with Consideration of the Coupling Effects of Vehicle Body

Xiaogao Li,Nan Chen,Ning Zhang,Xianjian Jin

doi:10.1155/2019/3707416

Xiaogao Li, Nan Chen + Show 2 more

Open Access

https://doi.org/10.1155/2019/3707416

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Abstract

Based on the Lagrange equation, a 9-degrees-of-freedom shimmy model with consideration of the coupling effects between the motions of vehicle body and the shimmy of front wheels and a 5-degrees-of-freedom shimmy model ignoring these coupling effects for a vehicle with double-wishbone independent front suspensions are presented here to study the problem of vehicle shimmy. According to the eigenvalue loci of system’s Jacobian matrix plotted on the complex plane, the Hopf bifurcation characteristics of nonlinear shimmy are studied and the conditions for the generation of limit cycle are analyzed. Numerical calculation and simulation are used to study the dynamic behavior of vehicle shimmy. By comparing the dynamic responses of two different shimmy models, the coupling effects of vehicle body on vehicle shimmy are studied. Finally, the relationship between the amplitude of each DoF and vehicle velocity and the influences of vehicle parameters such as the mass of vehicle body, the longitudinal position of the center of gravity of vehicle body, and the inclination angle of front suspension on shimmy are studied.

Highlights

Shimmy phenomenon, which widely exists in vehicles, motorcycle and landing gear of airplane, is a problem of nonlinear dynamics [1,2,3]
Vehicle shimmy is a sustained oscillation of the steering wheels around the kingpin, combined with the lateral yaw motion caused by the interaction between the tire and the dynamic behavior of steering system
Recent research studies indicate that the main factors which affect vehicle shimmy are (a) the dynamic response of tires, (b) the parameters of suspensions and steering system, and (c) the clearance and friction in mechanical structures

Summary

Introduction

Shimmy phenomenon, which widely exists in vehicles, motorcycle and landing gear of airplane, is a problem of nonlinear dynamics [1,2,3]. Recent research studies indicate that the main factors which affect vehicle shimmy are (a) the dynamic response of tires, (b) the parameters of suspensions and steering system, and (c) the clearance and friction in mechanical structures. Pacejka et al [6, 7] did a more comprehensive study on the problem of wheel shimmy, especially on constructing the mathematical model of tire, and developed the famous Magic Formula [8]. Erefore, there are coupling effects between the shimmy of the front wheels and the motions of the vehicle body It is still not clear how the motions of vehicle body affect the dynamic behavior of vehicle shimmy. Based on the numerical analysis, the coupling effects between vehicle shimmy and the motions of vehicle body are discussed with the time history response and the phase portrait of each DoF of vehicle shimmy.

Vehicle Shimmy Model

Existence Analysis of Hopf Bifurcation

Numerical Simulation