Vehicle parameter design based on nonlinear bifurcation analysis of hunting motion of a wheelset

This paper deals with a nonlinear hunting motion of a railway wheelset. A hunting motion has characteristics of Hopf bifurcation. Hopf bifurcation is classified with sub critical Hopf bifurcation and super critical Hopf bifurcation. In case a sub critical Hopf bifurcation, an amplitude of a limit cycle of a hunting motion exists under a critical speed of a railway vehicle. Therefore, if a railway vehicle has bogie parameters of a sub critical Hopf bifurcation characteristics, a hunting motion of the vehicle might occur by some disturbance under a critical speed. In this paper, the characteristics of a sub critical Hopf bifurcation of hunting motion is considered. Using center manifold theory, equations of motion are reduced to differential equations of normal form. Moreover, an amplitude of a limit cycle is considered from the differential equations of normal form.