Influence of nonlinear motor suspension parameters on Hopf bifurcation characteristics of high-speed bogie

A dynamic model of the bogie was established to investigate the influence of the elastic suspension of the motor and some nonlinear terms on the stability of vehicle hunting motion. Linear analysis was conducted based on the root locus method and other methods, and the influence of the elastic suspension of the motor on the linear critical speed was studied. Then, based on research on linear stability, the impact of the first Lyapunov coefficient of the model on the Hopf bifurcation type was analyzed. Subsequently, the influence of the stiffness and damping cubic terms in the motor suspension on the first Lyapunov coefficient was studied, and the possibility of controlling the Hopf bifurcation type by changing the stiffness and damping cubic terms in the motor suspension was analyzed, and relevant research was conducted. The results show that the increase of the cubic term of stiffness increased the corresponding speed when the amplitude of the limit cycle was 8 mm by about 3.4 km/h, and the increase of the cubic term of damping increased the corresponding speed when the amplitude of the limit cycle was 8 mm by about 8.9 km/h. Finally, a time-domain diagram corresponding to systems with different motor suspension stiffness and damping cubic terms was presented, further explaining the role of the motor suspension cubic terms and conducting relevant validation, providing reference opinions for the design of the motor elastic suspension of multiple units.