A mixed FEM and lumped-parameter dynamic model for evaluating the modal properties of planetary gearboxes

Planetary gearboxes are extensively used in mechatronic applications due to their compactness and high reduction ratios. The complex kinematic of such systems and the requirement of low-vibration-gears suggest studying these gearboxes with appropriate dynamic models. To this purpose, a planar lumped parameter model with 18 degrees of freedom was implemented. Model parameters such as the stiffness of the bearings and the gear meshes were calculated using dedicated FEM simulations. Two different gearbox configurations were simulated and experimentally tested. The compared results showed a good agreement. The main goal of the research was to assess the validity of such methodology for the prediction of the system eigenfrequencies. Additionally, from a kinematic analysis of the gearbox it was possible to individuate the self-excitation frequencies. The overlapping of these self-excited frequencies with the eigenfrequencies of the system was individuated as the major cause of the gearbox noise.