Hunting motion and bifurcation behavior of six-axle locomotive based on continuation method

A six-axle locomotive with simple nonlinearities was taken as the study object.The creep forces and the flange forces between wheels and rails in rolling contact were decided by the Vermeulen-Johnson creep force laws and piecewise function respectively.The hunting motion and bifurcation behavior of the locomotive running on ideal straight and perfect track were analyzed in detail.Based on tangent predictor, Newton iteration corrector and computing the entire solution branches step by step, a continuation algorithm was presented to calculate and track the limit cycles in the locomotive system.It is pointed out that an unstable periodic solution is bifurcated from a stable stationary solution when vehicle speed reaches 53.700 m·s-1, while the unstable periodic solution remains its stability when the speed reduces to 50.855 m·s-1.In the processes, the subcritical Hopf bifurcation can cause the jump and hysteretic phenomena of the oscillating amplitude.The result indicates that such nonlinear phenomena as the coexistence of some oscillations may appear in some either low or high speed range of the locomotive.