Mathematical Modeling and Dynamic Analysis of Planetary Gears System with Time-Varying Parameters

Planetary gears are widely used in automobiles, helicopters, heavy machinery, etc., due to the high speed reductions in compact spaces; however, the gear fault and early damage induced by the vibration of planetary gears remains a key concern. The time-varying parameters have a vital influence on dynamic performance and reliability of the gearbox. An analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness, and then the dynamical model of the planetary gears with time-varying parameters is established. The natural characteristics of the transmission system are calculated, and the dynamic responses of transmission components, as well as dynamic meshing force of each pair of gear are investigated based on varying internal excitations induced by time-varying parameters and tooth root crack. The effects of gear tooth root crack size on the planetary gear dynamics are simulated, and the mapping rules between damage degree and gear dynamics are revealed. In order to verify the theoretical model and simulation results, the planetary gear test rig was built by assembling faulty and healthy gear separately. The failure mechanism and dynamic characteristics of the planetary gears with tooth root crack are clarified by comparing the analytical results and experimental data.