Research On Nonlinear Dynamics Of Ring Planetary Gear Transmission With Small Tooth Number Difference

Ring planetary gear transmission with small tooth number difference is a drive which is composed of linkage mechanism and gear mechanism. It has simple structure, large speed-reduction ratio, high load capability. But Vibration, loud noise and severe fever are the outstanding problems, and they restrict its further extension and application in some degree. The present research on dynamics is restricted in linear model, but this transmission inevitably exist nonlinear factor such as clearance on movement pair, gear pair, bearing and so on. This factor will have nonlinear characteristic on this transmission. In order to fully reflect the dynamic behavior of this transmission, it is necessary to further study on the dynamics of such kind of system. The research purpose of this dissertation is to solve the problems of nonlinear dynamics on ring planetary gear transmission with small tooth number difference in order to improve the dynamic properties. The main contents are as follows: Three-ring transmission being widely used is taken as research object, Subsystem synthesis is adopted and the system is divided into four subsystem including input shaft, supporting shaft, internal gear board, output gear and shaft. On the premise of considering time-varying mesh stiffness, gear meshing errors and gear backlash, Lumped mass method is adopted and a coupling nonlinear vibration model of three-ring transmission is established. The factors including the elasticity of all shaft, the elasticity of planetary bearing on all shaft, the elasticity of bearing on output shaft, horizontal and vertical on internal board and output shaft are considered. The rigid body movement is eliminated by use of suitable coordinate transformation, and the equations are convenient to be solved by use of dimensionless process. This model is applied to other ring planetary gear transmission with small tooth number difference.Parameter vibration of the three-ring transmission system is researched. Multiple scale method is used to research the primary properties, ultraharmonic resonance properties, combination resonance properties and stabilities. The first-order stationary solutions are obtained under every condition respectively. The stability conditions of the stationary solutions are given at the same time in this dissertation.Harmonic balance method is used to solve the stable response of the three-ring transmission system.The influence of gear meshing errors and time varying mesh stiffness on nonlinear frequency domain characteristic of the three-ring transmission system is analyzed. Runge-Kutta numerical integration algorithm and MATLAB has been employed to simulate the dynamic responses on the different exciting frequency. A period doubling bifurcation route to chaos, and quasi-periodic bifurcation route to chaos have been identified. Various types of response such as Single-periodic, multi-periodic, quasi-periodic and chaotic response is analyzed and compared by use of phase plane plots, Poincare maps an so on.The experimental researches on the dynamic properties of the three-ring transmission are made. The test of natural frequency and dynamic response are made in order to verify the rationality of the theoretical studies.According to the principle of parallel gear, A new kind of internal parallel moving gears transmission with completely dynamic balance is designed. The stress of external toothed plate is carried out by ANSYS software, and the result shows that it can meet the requirement of strength. Dynamic analysis is researched and the natural frequency and dynamic load on main spare parts are obtained. The result shows that the load variation of amplitude is small and the transmission is relatively stable.