Nonlinear dynamics of planetary gear transmission by harmonic balance method based on DFT

Gear transmission is bound to have some backlash (clearance), which may be designed to provide better lubrication due to manufacturing errors and wear, while nonlinear dynamics studies on planetary gear system subjected to clearances are very limited. A lateral-torsional coupled nonlinear dynamic model of a planetary gear system with multiple backlash, time-varying mesh stiffness, error excitation and sun-gear shaft compliance is constructed. To solve the resulted equations, a numerical harmonic balance method is developed based on discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT). This method is applicable for general periodic steady responses of time-varying periodic systems with multiple harmonic, even superharmonic and subharmonic solutions. As an example, nonlinear frequency response characteristics of a 2K-H planetary gear system are obtained by employing the developed method. Some typical nonlinear phenomena, such as jump discontinuities and multi-valued solutions, are observed. The study yields some guidelines to be instrumental to further nonlinear studies of planetary transmission.