Dynamic modeling and behavior analysis of vehicle shimmy system considering the rubber bushing

Vehicle shimmy is a harmful vibration phenomenon that significantly affects vehicle stability and safety. Unlike previous studies that typically neglected the influence of suspension rubber bushings, this paper focuses on the rubber bushing at the connection between the suspension damper and the vehicle body, and systematically investigates its effect on the dynamic response of a vehicle shimmy system. A seven-degree-of-freedom (DOF) shimmy model is first established based on Lagrangian theory. The nonlinear system is then linearized to analyze the stability characteristics under variations in the axial stiffness of the rubber bushing. Furthermore, numerical simulations are conducted to examine the dynamic responses and bifurcation behavior of the nonlinear shimmy system under different parameter conditions. The results reveal that increasing the axial stiffness of the rubber bushing reduces both the unstable speed range and the steady-state shimmy amplitude. In summary, increasing the stiffness of rubber bushings offers a cost-effective and practically viable approach to suppress vehicle shimmy, providing both theoretical insights and practical guidance for the early-stage design and optimization of anti-shimmy strategies.