Analysis And Modeling Of Nonlinear Dynamics Of Gear-pair

With the development of high speed mechanical transmission, the demand of the dynamic behavior for gear transmission is enhanced increasingly. In fact, the gear transmission system is nonlinear, and it's significant to study its vibration characteristic in detail and analyze the influent factors. Nowadays, the research on reduction of vibration and noise and improvement of dynamic characteristic has become a hot topic. We can have an overall understanding of the influence of parameters on gear transmission system by creating the analytical model of gear system. Therefore, this paper studies the backlash nonlinear vibration problem for a gear pair and designs the gear profile modification to improve the dynamic characteristic of gear system.The gear system is a parameter self-excitation vibration system, and the noise is cause from vibration. There are some influent factors causing of vibration: dynamic excitation produced by tooth meshing in system itself, vibration of motor, vibration of operating structure and the variable load. Especially, the dynamic excitation produced by tooth meshing in system itself is the main factor causing of noise. The dynamic meshing excitation includes mesh loading and error loading. The mesh loading is cause by the variable mesh stiffness. The error loading is cause by processing errors and installation errors which make the tooth depart from the theory profile and change the instantaneous transmission ratio, which will cause impact between tooth and then produces error loading.Generally, the tooth contact ratio is not an integer, which makes the number of the engagement tooth change periodic. In addition, the elastic deformations are different from tooth root to addendum. These factors cause the tooth stiffness vary. The time-varying meshing stiffness plays an important role in dynamic characteristic of system. In view of this, this paper studies the time-varying meshing stiffness firstly, and creates an elastic contact FEA model of a pair of spur gear engaged to calculate the mesh stiffness.The research on backlash nonlinear dynamics of gear transmission system is that study the dynamic characteristics of gears with backlash. There are three kinds of solution methods for solving dynamic equations of backlash nonlinear system: numerical method, analytic method and experiment method. Generally the numerical method is adopted by researcher because of nonlinear property of backlash problem, which has advantage of gain the overall dynamic response. Runge-Kutta numerical solutions are always adopted, of which the main issue is to determine the integration step, or we can adopt the Runge-Kutta with variable step size. The study of dynamic response of backlash nonlinear gear system mainly deals with response in time domain and response in frequency domain. This paper solves the system response by means of numerical and analyzes the influence of each nonlinear factor on system vibration combining with the time evolution, spectrogram and phase portraits.Profile modification of involute gear includes profile modification along the tooth depth and axial modification along the tooth width. Profile modification includes three points: maximal tip relief, relief length and relief curve. Generally, the tip relief can be totally distributed on the pinion tooth or gear tooth, or distributed on both of pinion and gear. This paper adopts the method that modify addendum of pinion and gear respectively, and improve the dynamic property of gear system.This thesis comprises a total of six chapters. Chapter 1 presents the background and significance of this research work. A general statement of the development of nonlinear vibration theories of gear is given. Finally the main coverage of the study is described. Chapter 2 discusses the mechanism of vibration production of gear transmission, points out that the main factor caused of vibration is internal excitation, and introduce the transmission errors. Chapter 3 introduces the mesh deformation and mesh stiffness. Calculate the mesh stiffness by means of elastic contact finite element. Make a program with APDL language in ANSYS for calculating the mesh stiffness and transmission errors. Finally, the mesh stiffness is transform into Fourier pattern, providing data foundation for analysis of gear vibration. Chapter 4 creates a single degree analytical model of gear system with backlash, considering the backlash, mesh stiffness and transmission errors. Then solve the vibration equations by programming in MATLAB and analyze influences of the parameters on gear system. Chapter 5 discusses the basic principle and method of profile modification, and determines the modification curves. Analyze the modification effect and prove the correctness of the modification curves proposed. Chapter 6 summarizes the conclusions of the thesis and presents the defaults and improvement of the thesis.