A nonlinear dynamic model for compound planetary gear sets

A discrete nonlinear torsional vibration model of a compound planetary set comprises d number of decks is proposed in this 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 nonlinear model equations of motion were obtained by assembling equations of motions of single separate decks according to central elements connections. Equations of motions were solved using HBM in conjunction with inverse Fourier Transform. Dynamic gear mesh forces for first, second and fourth gear ratios were obtained.