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.
The adhesion coefficients of a bisectional road have significant coupled influences on the shimmy characteristics of the front wheels of a vehicle. A four-degree-of-freedom model for a representative sport utility vehicle was established. This model considered the adhesion coefficients of a bisectional road and the friction of the steering system of the suspension. The existence and stability of the system’s limit cycles were qualitatively determined using the Hopf bifurcation theorem and the centre manifold theory based on the model. The influences of the adhesion coefficients on the Hopf bifurcation characteristics of the system were calculated using a numerical method. The results showed that the road adhesion coefficient μ1 of the left front wheel and the road coefficient μ2 of the right front wheel significantly affected the vehicle shimmy and coupling relationship when different. Keeping μ1 at a certain value, the swing angles and the angular velocities of the two front wheels consistently decreased when μ2 decreased. The phenomenon repeatedly occurred when the difference Δ μ between the adhesion coefficients increased. Moreover, the discrepancy between the amplitude of the left front wheel and the amplitude of the right front wheel is much more apparent when both the adhesion coefficients are larger. Good agreement between the shimmy characteristics of the two wheels was also found when comparing the results using the centre manifold reduced-dimensions method with the numerical method. Furthermore, a higher reduced order caused the reduced system to be closer to the original system.
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