Dynamic shimmy behavior and bifurcation analysis of driver–vehicle–road system

Abstract Based on the stretched string tyre model, the constraint equation with consideration of the dynamic coupling between the front wheel shimmy and plane motion of the vehicle is derived. On this basis, a novel dynamic shimmy model of driver-vehicle-road system is proposed. The root loci of the dynamic system are analyzed and two critical vehicle speeds are obtained by solving the Jacobian matrix. For two critical vehicle speeds, the centre manifold theory is applied to reduce the dynamic system and examine the stability of the limit cycle. The system stability region for different system parameters and road adhesion coefficients is also analyzed. Furthermore, the saddle node (SN) bifurcation and Hopf bifurcation characteristics of the dynamic system considering the steering input are studied with the help of the complexification-averaging (CA) method. Then, the mathematical expression of the periodic solution is obtained, and the effects of system parameters and vehicle driving conditions on the bifurcation characteristics are also investigated. According to the numerical and analytical results, measures to suppress vehicle shimmy are proposed. Finally, the experimental data verify the reliability of the shimmy model.