Bifurcation Characteristic and Energy Transfer of Vehicle Shimmy System Considering the Coupling of Vertical and Lateral Dynamics

Abstract Since the vehicle is a complex mechanical system with many subsystems, the influence of the dynamic coupling between the subsystems of the vehicle on shimmy should be taken seriously. Therefore, a 12 degrees-of-freedom dynamic model of vehicle shimmy system with consideration of the dynamic coupling between the vertical motion and the lateral motion of the vehicle is established. In particular, the influence of the vertical load of the tire on the nonlinear cornering force is also considered. Then, the dynamic stability of the shimmy system is discussed with the help of the system eigenvalues, and the influence of the damping of the front suspension on the dynamic stability is also examined from the viewpoint of the energy transfer. On this basis, the damping of the front suspension is selected as a bifurcation parameter, and the two-dimensional center manifold of the high dimensional shimmy system is obtained by means of the center manifold theory. Finally, the Hopf bifurcation characteristic of the shimmy system is analyzed, and the analytical solutions of the shimmy system are derived for different damping of the front suspension. The results show that the increase of the damping of the front suspension is beneficial to attenuate vehicle shimmy and improve the dynamic stability of the vehicle.