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
A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomou...A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.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.
基金Supported by the National Natural Science Foundation of China(No.11172199)the Key Project of Tianjin Municipal Natural Science Foundation(No.11JCZDJC25400)
文摘A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.
