Frequency Domain Identification Method For Nonlinear Coupling Dynamics Of Planetary Gear Train Based On Volterra Series Theory

The planetary gearbox plays an important role in a wide range of applications in mechanical transmissions.When a pair of gears are engaged in a planetary gear train,due to changes in speed and load,there are unavoidable errors in pitch and tooth shape.During the operation,meshing impact occurs accelerating the material fatigue on the meshing gear surface,causing the occurrence and evolution of gear meshing surface cracks,and eventually lead to more serious shocks,vibrations or abnormal operating noises between tooth surfaces.In this paper,it is difficult to identify the early weak fault features of the sun gear and planetary gear cracks in the star gear train and their crack damage.Using Volterra series nonlinear system model theory.The fault diagnosis method of the crack and damage degree of the sun gear and the planetary gear in the planetary gear train based on Volterra series is studied.This article mainly studies several aspects:(1)First introduce the background knowledge of Volterra series.The time domain and frequency domain expressions of the Volterra series are analyzed.Explain the basic properties of Volterra series and the generalized frequency response function.Finally,the basic idea of the Volterra series model in fault diagnosis is described.(2)For the solution of Volterra kernel function,the least squares and neural network solution method of classical Volterra kernel function is studied.The characteristics and scope of application of least squares method and BP neural network method are summarized.In order to optimize the BP neural network algorithm to fall into the local minimum problem,this paper uses the genetic algorithm to optimize the BP neural network Volterra kernel identification algorithm.The method firstly uses the input and output vibration signals of the system to determine the Volterra model.Secondly,the BP neural network method optimized by genetic algorithm effectively solves the Volterra series.Finally,the simulation analysis of complex nonlinear systems is carried out to verify the feasibility of the genetic algorithm-optimized BP neural network to identify the Volterra series kernel method,and the anti-noise analysis and experiments are carried out to verify that the Volterra series kernel has good noise immunity.(3)Use the planetary gearbox to measure the speed and vibration signals as well as the load and vibration time domain signals as the original reference.According to the least squares solving method,the neural network solving method and the genetic algorithm optimized BP neural network method for comparative analysis,Verify the accuracy and adaptability of the proposed method.At the same time,the influence of the order and memory length of Volterra series on the identification accuracy is discussed.(4)In the experimental part,this paper uses the planetary gearbox fault loading test rig to complete the data collection work.Normal and different degrees of crack experimental data of the sun gear and the planetary gear in the planetary gear train were collected.The Volterra experimental model is established by the measured data,and the generalized frequency response of each order kernel function is compared and analyzed.The ability to distinguish the degree of crack failure of each order kernel function and the range of adaptation are discussed.The influence of changing the order of kernel function on the identification result is verified.(5)The final experimental results show that:(1)Using the BP neural network optimized by genetic algorithm to identify the Volterra kernel function has good precision;(2)Volterra series model the third-order kernel is more intuitive and more detailed to describe the strong nonlinear system model under multi-factor coupling conditions.(3)The generalized frequency response of the third-order kernel of the Volterra series model can effectively distinguish the weak faults with different degrees.