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 ofnonlinearities which are yaw damping forces in longitudinal suspension system and the friction creepagemodel of the wheel/rail contact including clearance. through routhhurwitz stability criterion and a moreaccurate model than yang and ahmadian, the analytical expression of critical speed is achieved as wellas the limit cycle frequency. then, by averaging method and analytical critical speed, the amplitude ofthe limit cycle is determined while the wheel/rail clearance is taken into account. to solve the nonlinearequations analytically, both dead zone discontinuity and yaw dampers must be formulated properly. inthis direction, a suitable and novel exact equivalent functions (ef) is introduced. furthermore, 2d and 3dbifurcation diagrams are depicted to show the mechanism creation of hopf bifurcation which is employedin the design of stable wheelset systems. finally, the accuracy of one-axle model results for the predictionof critical speed is evaluated in contrast with two-axle bogie model.