Nonlinear dynamics of planetary gears with equal planet spacing

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. The resulting vibration causes tooth separation leading to nonlinear effects such as classical jump phenomena and sub- and superharmonic resonance. The nonlinear dynamics of the planetary gear is examined by both numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is validated by parallel finite element and numerical integration simulations.