Abstract
This paper presents the analytical investigation of Hopf bifurcation in a rail wheelset system. The nonlinearity taken into account is nonlinear damping force in a longitudinal yaw damper. The bifurcation can be subcritical or supercritical, depending on the system parameters. It is found that softening nonlinear damping will lead to a subcritical Hopf bifurcation, which means that even below the linear critical speed, an unstable limit cycle may occur and lead the wheelset to unstable hunting. Furthermore, our investigation shows that hardening nonlinear damping will introduce a supercritical Hopf bifurcation. The stability of the bifurcated limit cycle is determined. It is found that increasing damping will decrease the amplitude of the hunting vibration and increase the linear critical speed. Based on the results, a method to control the bifurcation mode is suggested.
