Bifurcation behavior of hunting motion in high-speed rail vehicles under modal coupling

This paper presents a theoretical study of hunting bifurcation behavior in high-speed rail vehicles under modal coupling and compares it to the traditional uncoupled system. A dynamic simplified model that integrates the lateral and yaw motions of the rigid bogie and the lateral motion of the carbody is established to evaluate the modal coupled effect between the carbody and bogie. The stability and Hopf bifurcation of the trivial equilibrium are first analyzed qualitatively using the normal form theory. The linear stability analysis then reveals that modal coupling introduces a new unstable region known as carbody (primary) hunting, which is absent in the uncoupled system that only exhibits bogie (secondary) hunting. The double-parameter Hopf bifurcation analysis is further carried out, which considers the influence of suspension parameters on the bifurcation speed and stability region. Our findings indicate that the dynamical behavior of the coupled system can closely match that of the uncoupled system with suitable parameter configurations, effectively reducing primary hunting and enhancing the overall hunting stability of rail vehicles.