Nonlinear shimmy and dynamic bifurcation in vehicle system with driver steering input

Based on the dynamic coupling analysis of the front wheel shimmy and vehicle plane motion, a three degrees of freedom (DOF) nonlinear shimmy model considering driver steering input is established. Firstly, when the driver steering input is not considered, the modal properties and dynamic stability of the system are investigated by solving the Jacobian matrix. Then, the nonlinear shimmy behavior considering the driver steering input is discussed by means of numerical calculations. The slow flow equations of the vehicle system considering the driver steering input are derived based on the complexification-averaging (CA) method. According to the nonlinear dynamics theory, the saddle node (SN) and Hopf bifurcation characteristics of the system are analyzed, the analytical solution of the front wheel shimmy angle is also obtained. Finally, with the help of the understeer gradient, the influence of the linear cornering stiffness of the front wheel on the nonlinear shimmy motion is discussed. It is summarized that the SN and Hopf bifurcation are more likely to occur in the shimmy system for an oversteered vehicle. The relevant conclusions are useful for the early anti-shimmy design of vehicles.