Research On Nonlinear Vibration Of Flexible Wheel Of Electromagnetic Harmonic Movable Teeth Transmission System

The electromagnetic harmonic movable teeth transmission system is a new type of decelerating transmission system which involves electromagnetic field,harmonic transmission and movable teeth transmission technology.The system can output large torque at low speed,and it has the characteristics of quick response,small moment of inertia,simple structure,controllable current,high transmission efficiency and accuracy.In order to optimize the design parameters of the transmission system and effectively evaluate and control the dynamic performance of the system,it is necessary to study the nonlinear vibration characteristics of the system,establish a nonlinear dynamic model,and analyze the internal resonance,dynamic stability,bifurcation and chaos.The purpose of this paper is to study the nonlinear vibration characteristics of flexible wheels in the transmission components of the system.According to the nonlinear properties of the flexible wheel,the nonlinear vibration differential equation of the flexible wheel is firstly established in this paper.The Galerkin principle is used to split the vibration differential equation,and the multi-scale method is used to solve the nonlinear response of the radial vibration mode of the flexible wheel cylindrical shell.The 1:1 internal resonance,the energy conversion process and the vibration mode of the system under the change of various parameters are studied.Based on the nonlinear vibration differential equation of flexible wheel,Lyapunov stability theory,Hopf bifurcation theory and saddle node bifurcation theory,the stability and bifurcation behavior of flexible wheel vibration are studied.Then,the Duffing equation of flexible wheel chaotic vibration is obtained by using Donnell-Kármán large deflection thin-walled cylindrical shell theory,Bubnov-Galerkin principle and Melnikov function,and the bifurcation diagram and phase plane diagram of flexible wheel vibration system are drawn,displacement time history curve and Poincaré map are used to analyze the chaotic behavior of the flexible wheel vibration when the initial value of the system changes and the conditions for entering into the chaotic motion.According to the chaotic motion of the flexible wheel,the OGY(Ott,Grebogi,Yorke)feedback control method is used to control the chaotic motion of the flexible wheel vibration,and the MATLAB analysis software is used to simulate the chaos control to verify its effectiveness.Finally,the natural frequency of the flexible wheel is simulated by ANSYS software to verify the correctness of the system dynamic equation.