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

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.

Hopf Bifurcation Characteristics of the Vehicle with Rear Axle Compliance Steering

“…Bifurcation in a shimmy analysis is frequently called Hopf bifurcation, which creates limit cycles from an equilibrium point as a bifurcation parameter crosses a critical value [22]. Hopf bifurcation is a local bifurcation in which a xed point of the dynamical system loses stability [23]. In Figure 3, Hopf bifurcation of the compliance steering angle leads to the shimmy of the compliance steering Figure 4 shows the time history of compliance steering angle and yaw rate, respectively.…”

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

“…It is assumed that a 0.01 rad angular displacement is exerted on the front-left wheel as initial excitation. Based on equations (10)- (17) and the parameters listed in Tables 1 and 2 (for choice of parameters in Table 2, see Wei et al [14] and Mi et al [18]), numerical simulation can be carried out. e dynamic responses of front wheels' shimmy, pitman arm's swing, and front wheel axes' lateral swing in two systems at the velocity of 10 m/s are shown as Figures 4-6, where the time history response and steadystate phase portrait of each DoF are drawn on.…”

“…Ran et al [13] studied the effects of the nonlinearities in tire on the stability of vehicle shimmy by the energy flow method. Wei et al [14] developed a nine-degrees-of-freedom (DoF) dynamic model to study the shimmy of a dual front axle heavy truck. Lu et al [15][16][17] performed a comprehensive study on vehicle shimmy in which the clearance in mechanism structure, such as in the steering linkage mechanism, the steering handling mechanism, and the cross shaft type universal joint, is taken into account, and the effect of the roll motion of vehicle body to vehicle shimmy is also considered.…”

Dynamic Analysis of a Planar Hydraulic Rock‐Breaker Mechanism with Multiple Clearance Joints

“…Lu et al analyzed the dynamics of the steering mechanism and vehicle shimmy system with multiple clearance joints [32,33]. Wei et al studied the 9-DOF dynamics of a vehicle shimmy model based on Lagrange's equation [34]. A series of factors have been considered in the literature to decrease the vibration dynamics due to clearances, such as the effect of flexible linkages and fluid lubricant on the mechanisms with clearances [35,36].…”