A non-linear dynamic model for planetary gear sets

Abstract: A discrete non-linear torsional vibration model of a single-stage planetary set is pro-posed in the current study. The model includes all possible power flow configurations, any number of planets in any spacing arrangement and any planet mesh phasing configurations. It also includes time variation of gear mesh stiffnesses as well as clearance (backlash) non-linearities. The non-linear equations of motion are solved semi-analytically using multi-term harmonic balance method (HBM) in conjunction with inverse discrete Fourier transform and Newton–Rapson method. The HBM solutions are compared with numerical simulation results to demonstrate the accuracy of the HBM formulation. Another comparison with predictions of a deformable-body dynamic model is also provided to assess the accuracy of the discrete model. Limited parametric studies are presented at the end, to show the influence of key gear design parameters on dynamic response