Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction

Daogao Wei,Yibin Jiang,Changhe Chen,Fugeng Zhou,Ke Xu,Wenjing Zhao

doi:10.1155/2015/839801

Daogao Wei, Yibin Jiang + Show 4 more

Open Access

https://doi.org/10.1155/2015/839801

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Abstract

Multiaxle steering is widely used in commercial vehicles. However, the mechanism of the self-excited shimmy produced by the multiaxle steering system is not clear until now. This study takes a dual-front axle heavy truck as sample vehicle and considers the influences of mid-shift transmission and dry friction to develop a 9 DOF dynamics model based on Lagrange’s equation. Based on the Hopf bifurcation theorem and center manifold theory, the study shows that dual-front axle shimmy is a self-excited vibration produced from Hopf bifurcation. The numerical method is adopted to determine how the size of dry friction torque influences the Hopf bifurcation characteristics of the system and to analyze the speed range of limit cycles and numerical characteristics of the shimmy system. The consistency of results of the qualitative and numerical methods shows that qualitative methods can predict the bifurcation characteristics of shimmy systems. The influences of the main system parameters on the shimmy system are also discussed. Improving the steering transition rod stiffness and dry friction torque and selecting a smaller pneumatic trail and caster angle can reduce the self-excited shimmy, reduce tire wear, and improve the driving stability of vehicles.

Highlights

In recent years, with the rapid development of the transportation industry, high-speed and multiaxle heavy trucks with dual-front axles have become widely used for their load capacity, high performance-price ratio, adaptability, and high horsepower
The shimmy problem in its dual-front axle steering system leads to abnormal tire wear, off-tracking, and shaking of the steering wheel [1,2,3]
To obtain the manifold for the system in two-dimensional space, we reduced the dimension of the differential equations of state using center manifold theory and found the Hopf paradigm in the polar coordinates with the use of normative theory so that the Hopf bifurcation characteristics of the shimmy system of the dual-front axles can be fully analyzed

Summary

Introduction

With the rapid development of the transportation industry, high-speed and multiaxle heavy trucks with dual-front axles have become widely used for their load capacity, high performance-price ratio, adaptability, and high horsepower. Liao [18] and Li et al [19] explored the application of multirigid body theory in the dynamic simulation of a dual-front axle steering system and proposed the condition under which tires bear heavy load in a dual-front axle vehicle They built a spatial model for the dual-front axle based on ADAMS and conducted a simulation analysis. Using TruckSim, a dynamics analysis software for vehicles, Li [20] studied how to determine and describe the seven characteristic parameters of a heavy truck steering system, namely, axle and suspension, transmission, tire, body, brake system, and aerodynamics, and laid down a solid foundation for the study of multiaxle steering technology and the improvement of its handling stability. The contribution of this study is the finding that the selfexcited shimmy phenomenon of the dual-front axle of a heavy truck is generated by Hopf bifurcation

Dynamics Model for a Dual-Front Axle Shimmy System

Hopf Bifurcation Qualitative Analysis of the Shimmy System

Calculation and Analysis of the Hopf Bifurcation in the Shimmy System

Conclusions