Research On Nonlinear Dynamics Of Planetary Gear Transmission System Considering Nonsmooth Factors

For the study of nonlinear dynamics of planetary gear,most scholars only consider the basic nonlinear factors such as time-varying meshing stiffness,meshing damping,comprehensive error and backlash.With the progress of industrial technology and the development of gear dynamics,non-smooth factors have become an important factor that can not be ignored.The gear system contains typical non-smooth factors such as backlash and dry friction.Therefore,on the basis of considering the basic nonlinear factors,this paper takes the non-smooth factors including friction,lubrication and random backlash as the starting point to study the nonlinear dynamic characteristics of planetary gear system.The main contents of this paper are as follows:(1)The type and nature of the system's excitation are studied,and the equivalent stiffness and damping of the system are given based on the oil film.At the same time,the mathematical expressions of the comprehensive error,backlash,tooth surface friction and friction arm of the planetary gear system are also given.(2)The coordinate system of the planetary gear system is constructed.Based on the analysis of the excitation parameters of the system,the dynamic model considering the tooth friction is established.The dynamic differential equation of the system is deduced by Newton's second law,the relative linear displacement of the generalized coordinates is introduced,and the system equation is solved by Runge-Kutta numerical method.(3)The nonlinear analysis methods such as bifurcation diagram,Largest Lyapunov exponent diagram,phase diagram,Poincaré map diagram,time history diagram and FFT spectrum diagram are used to study the influence of the changes of excitation parameters such as excitation frequency,damping ratio,load,comprehensive error and meshing stiffness amplitude on the motion state of the system with or without friction.At the same time,the influence of friction on the bifurcation and chaos of the system is analyzed.(4)The lubrication factors are considered in the planetary gear dynamics model,and the behavior characteristics of friction force under different lubrication conditions are described.Under the coupling effects of friction and lubrication,the bifurcation and chaotic vibration characteristics of the system with excitation frequency,load,comprehensive error,and viscosity of the lubricant are analyzed,and the influence of lubrication factors on the system is also compared and analyzed.(5)The Monte Carlo algorithm and the central limit theorem are used to generate random numbers to simulate random gear backlash.Based on the coupling effects of friction and lubrication,the dynamic characteristics of the system with parameters such as excitation frequency,load,comprehensive error,and viscosity are analyzed under random gear backlash.In order to further study the influence of the disturbance of the backlash on the dynamic characteristics of the system,the bifurcation and chaos characteristics of the system with the internal backlash and the external backlash are studied.At the same time,the main path of the system to chaos and the impact of the increase of the magnitude of the gap disturbance on the system are analyzed.