Study On Nonlinear Dynamics Characteristics Of Planetary Gear Train

Planetary gear train transmission can complete the decomposition and synthesis of motion and has the advantages of strong carrying capacity and high power,and has been widely used in wind power equipment,aircraft,vehicles and ships.Since the planetary gear system is affected by a variety of internal and external excitations and clearances,it belongs to a strong nonlinear system,and the dynamic response of the system parameter changes complex,and it is prone to fatigue,failure and broken teeth,which reduces the reliability and stability of the system.Therefore,studying the influence of the change of medium parameters of the planetary gear train on the dynamic characteristics of the system can grasp the state and transmission mechanism of the planetary gear system in actual work,and can provide a reference for its design improvement,parameter selection and smooth operation.In this paper,the effects of time-varying meshing stiffness,meshing frequency,comprehensive meshing error and meshing damping on the dynamic response and bifurcation characteristics of different systems are studied under certain parameters,and the differences and connections of similar nonlinear factors on the dynamic response and bifurcation characteristics of different systems are studied under certain parameters.Firstly,considering many nonlinear factors in the gear system,taking the single-degree-of-freedom gear pair torsional nonlinear dynamic model as the theoretical basis,the relationship between the amplitude and the dimensionless frequency is solved by the harmonic balance method.The differential equation of gear pair system is numerically solved by the variable-step 4th-order Runge-Kutta method and Matlab,and the bifurcation diagram of the system displacement with the change of meshing frequency,stiffness amplitude,error amplitude and damping ratio is obtained.When analyzing the influence of different parameter changes on their dynamic characteristics by bifurcation diagram,it is found that the dynamic characteristics of the gear pair system are relatively simple,and they mainly enter the chaos by doubling the bifurcation.Secondly,considering a variety of tooth side clearances,a 2K-H planetary gear system vibration dynamics model with N+2 degrees of freedom is established,and the bifurcation diagram under different parameters is obtained by the control parameter method,and combined with the analysis of time history,phase plane,Poincaré section and FTT spectrogram,it is found that the system has rich bifurcation characteristics and variable dynamic response.When the meshing stiffness and error parameters change,not only the double period bifurcation and the Naimark-sacker bifurcation enter the chaos,but also the co-dimensional bifurcation enters the chaotic motion through the phase-lock.When the meshing frequency changes,the system mainly doubles the bifurcation into the chaotic motion,and mainly takes the periodic motion and the chaotic motion.The damping ratio and stiffness have a great influence on the system,while smaller stiffness and increased damping ratio are beneficial to the system.Finally,the nonlinear dynamic model of multistage gear transmission system including planetary gear train is established,and the numerical simulation of its motion differential equation is dimensionality reduced and dimensionless,and it is found that compared with gear pair and 2K-H planetary gear train,the motion form and bifurcation of the multistage gear system including planetary gear train are changeable and complex,including general periodic motion,periodic motion,chaotic motion,cataclysm,mutation,Hopf bifurcation and double period bifurcation.The influence trend of meshing damping on hybrid multistage gear system is similar to that of 2K-H planetary gear train and single-degree-of-freedom gear pair system.When analyzing the dynamic response of the system by taking the stiffness amplitude ratio and error as the bifurcation parameters,it is found that the change of parameters makes the system enter the approximate period or chaotic motion with Hopf bifurcation as the mainstay.With the help of Poincaré section and bifurcation diagram,the evolution process of the system from periodic motion to chaos through bifurcation is analyzed.