Bifurcation analysis in hunting dynamical behavior in a railway bogie: Using novel exact equivalent functions for discontinuous nonlinearities

This paper presents an investigation on bifurcation of railway bogie behavior in the presence of nonlinearities which are yaw damping forces in longitudinal suspension system and the friction creepage model of the wheel/rail contact including clearance. Through Routh–Hurwitz stability criterion and a more accurate model than Yang and Ahmadian, the analytical expression of critical speed is achieved as well as the limit cycle frequency. Then, by Averaging method and analytical critical speed, the amplitude of the limit cycle is determined while the wheel/rail clearance is taken into account. To solve the nonlinear equations analytically, both dead zone discontinuity and yaw dampers must be formulated properly. In this direction, a suitable and novel exact equivalent functions (EF) is introduced. Furthermore, 2D and 3D bifurcation diagrams are depicted to show the mechanism creation of Hopf bifurcation which is employed in the design of stable wheelset systems. Finally, the accuracy of one-axle model results for the prediction of critical speed is evaluated in contrast with two-axle bogie model.