Abstract: The three dimensional dynamic models of trailer car and motor car are set up, and then the train dynamic model for three train formation is constructed by considering the coupler devices between cars. Based on the first order approximation theory of the ordinary differential equations and Hopf bifurcation theory and Poincare map, the linear and nonlinear hunting stability of each car, and the whole train system are studied in the case of operating on straight and large radius curved track by numerical method. The numerical results show that there is little difference for the nonlinear critical speed between the train model and a single car model on straight track. The nonlinear critical speed on curved track is lower than on straight track. The type of train formation and the damping and stiffness values in the considered range has not much influence on the train critical speeds. Therefore, no matter the cars in the trainset have same parameters or not, the linear and nonlinear critical speeds of the train system can be approximately described by the car among the trainset with lowest linear and nonlinear critical speeds.

Key words: Critical speed, Hopf bifurcation, Hunting stability, Powered trainset