Research Of The Frequency Response Characteristics Of The Small Module Reducer Under The Condition Of High-and-Low Temperature

The project is derived from the National Natural Science Fund(Project Number: 51275538) and project funded from Spacecraft Mechanism Key Lab.(Project Number: SM2014D101). As the demands for high degree of accuracy and high reliability of gear device in the field of space is getting higher and higher, the backlash or seizure in gear pair caused by thermal deformation of gear device under the condition of high-and-low temperature is paid more and more attention. The clearance of gear device caused by high-and-low temperature has important influence on the dynamic transmission accuracy and frequency response characteristics of the device and how to calculate and evaluate the influence is of great significance. In this paper, the clearance non-linearity characteristics of small modules under the condition of high-and-low temperature in the field of space were studied.Lumped model of single-DOF gear pair in small modules reducer was built, in which clearance of gear system in the condition of high-and-low temperature? time-varying stiffness and synthetic meshing errors of gears are considered. The frequency response characteristics of the single-DOF gear pair in that reducer device were studied. The article can be divided into the following parts:(1) At the base of temperature characteristics in material coefficient of thermal expansion, the thermal deformation and clearance in gear pair were calculated.(2) Single-DOF gear pair dynamic model was built by the method of Lumped, and the model includes the factors of thermal deformation caused by high and low temperature?clearance?time-varying meshing stiffness and synthetic meshing errors of gears. The differential equations of the dynamic model were dimensional normalization so as to solving easily. The Harmonious Balance Method(HBM) based on describing function was used to solve the nonlinear differential equation of the single-DOF dynamic model in small modules reducer, and solving program of MATLAB was programmed to obtain the fundamental frequency steady-state response of the non-linear differential equations.(3) The thermal deformation of gear system under the condition high-and-low temperature?clearance?time-varying meshing stiffness and synthetic meshing errors were taken account to study the change rule of frequency response characteristics of the gear system. The results show that there are amplitudes jump and multi-valued solution in the drawing of frequency response characteristics during to the clearance varying caused by thermal deformation under the condition of high-and-low temperature. And the non-linearity was becoming stronger?the steady-state response becoming more complex as the increasing of clearance. For example, the system is linear and time-invariant as the clearance becoming zero under the condition of high temperature(102.4?);The system has typical nonlinear characteristics with more complex shock-state as the clearance increasing(to 0.1) under the condition of low temperature(-20?).