This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with...This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with consideration on the factors including the time-varying system stiffness,the transmission error,the tooth backlash and the self-excited excitation of the wheel-set.The frequency-response equation of the system at super-harmonic resonance is obtained by the multiple scales method,and the stabilities of the system are analyzed using the perturbation theory.Complex nonlinear behaviors of the system including multi-valued solutions,jump phenomenon,hardening stiffness are found.The effects of the equivalent damping and the loads of the system under the stick-slip oscillation are analyzed.It shows that the change of the load can obviously influence the resonance frequency of the system and have little effect on the steady-state response amplitude of the system.The damping of the system has a negative effect,opposite to the load.The synthetic damping of the system composed of meshing damping and equivalent damping may be less than zero when the wheel-set has a large slippage,and the system loses its stability owing to the Hopf bifurcation.Analytical results are validated by numerical simulations.展开更多
基金Project(U1234208)supported by the National Natural Science Foundation of ChinaProject(2016YFB1200401)supported by the National Key Research and Development Program of China
文摘This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with consideration on the factors including the time-varying system stiffness,the transmission error,the tooth backlash and the self-excited excitation of the wheel-set.The frequency-response equation of the system at super-harmonic resonance is obtained by the multiple scales method,and the stabilities of the system are analyzed using the perturbation theory.Complex nonlinear behaviors of the system including multi-valued solutions,jump phenomenon,hardening stiffness are found.The effects of the equivalent damping and the loads of the system under the stick-slip oscillation are analyzed.It shows that the change of the load can obviously influence the resonance frequency of the system and have little effect on the steady-state response amplitude of the system.The damping of the system has a negative effect,opposite to the load.The synthetic damping of the system composed of meshing damping and equivalent damping may be less than zero when the wheel-set has a large slippage,and the system loses its stability owing to the Hopf bifurcation.Analytical results are validated by numerical simulations.
