Dynamic analysis of a planetary gear system with multiple nonlinear parameters

Considering time-varying meshing stiffness, comprehensive gear error and piece-wise backlash nonlinearities, a torsional nonlinear dynamic model of multistage gear of planetary gear system is established. By using Runge-Kutta numerical integration method, the dynamic responses are solved, analyzed and illustrated with the bifurcation parameters variation including excitation frequency, gear backlash and damping. The motions of the planetary gear system and diverse nonlinear dynamics characteristics are identified through global bifurcation diagram, FFT spectra, Poincaré map, the phase diagram and the largest Lyapunov exponent (LLE). The numerical results expose that system experiences a diverse transformation range of the periodic motion, non-periodic states systematically and quantitatively when the parameters are changed. Analysis results show that the variation of meshing frequency as the external excitation could transit the states of the system. Additionally, the motions and the routes of entering chaos at low excitation frequency and at high excitation frequency are different. Under the bifurcation parameter of dimensionless backlash and damping coefficient, the system motion is observed. The higher damping coefficient and suitable backlash could suppress the region of chaos. Correspondingly, parameters of the system should be designed properly and controlled timely for the better operation and enhancing life of the system.