Study On The Hopf Bifurcation Characteristics Of Dual-axle Heavy-duty Vehicles Shimmy System

Shimmy was ubiquitous in modern automotive suspension and steering system and was affected by stiffness of suspension mechanism and steering mechanism, lateral characteristics of tires, dry friction and so on. The shimmy system showed different motion characteristics of limit cycles when motivated by different initial excitation. The shimmy phenomenon of single-axle steering system has been studied deeply, their achievements have been widely applied in automotive design and improvement process. Compared with the single-axle steering system commonly used in passenger cars, the structure of dual-front axle steering system used in heavy-duty vehicles was more complex, and was required to bear a greater load from all directions, which made its shimmy characteristics different with the single-axle steering system. However, the shimmy characteristics study of heavy vehicles on the dual-front axle steering system was still rare currently. With the increase importance of heavy-duty vehicles in the vehicle market, the shimmy characteristics research of its steering system should be strengthened in order to improve the design for heavy-duty vehicles.In order to study the shimmy characteristics of heavy-duty vehicles’dual-front axle steering system the roll and yaw phenomenon caused shimmy, theory and numerical simulation method were both took to analyze the limit cycles induced by dry friction in a single wheel shimmy system. Based on the foregoing analysis, a multi-degree of freedom shimmy system for dual-front axle steering system was built. The main contents are as follows:(1) Analyze the multi-limit cycles characteristics induced by dry friction of a single wheel shimmy system with qualitative theory method and then verify the results by numerical simulation method. The influence of system parameters on the bifurcation structure characteristics was also discussed.(2) A nine degrees of freedom model of dual-front axle steering system was established. Theory and numerical simulation method were both took to analyze the Hopf bifurcation characteristics. The influence of some parameters had on the multiple limit cycles shimmy were found.(3) A new model considered the roll and yaw degree was established based on the previous nine degrees of freedom model to analyze the roll and yaw of heavy-duty vehicles caused by shimy.It showed that dry friction hysteresis effect may generated degenerate Hopf bifurcation and then induce multiple limit cycles responses within a certain range in vehicle shimmy system. The bifurcation of dual-front axle steering shimmy system belonged to Hopf bifurcation and the shimmy of the steering system can cause the roll and yaw of the heavy-duty vehicles. The caster angle, the angular stiffness between the front wheel and the middle rock arm, the dry friction torque can be designed properly to weaken the strength of shimmy.