Abstract: A modified torsional model of planetary gear trains with equally-spaced pinions is developed and used to identify unique properties of natural frequencies and vibration modes. Compared with the purely torsional model, tangential displacements and bearing stiffness of the pinions are included in the governing equation of motion. On the basis of natural characteristics analysis, vibration modes of the undamped system are classified into three types, which are named rotational mode of the central members, rotational mode of the pinions and translational mode of the pinions, respectively. For each type of vibration modes the associated reduced-order eigenvalue problems are derived and closed-form analytical expressions of natural frequencies are presented for the pinion modes. Natural frequency sensitivities to system parameters are rigorously investigated, which reveals that pinion bearing stiffness affects the first natural frequency of the system significantly. Through a comparison of natural frequencies experimentally collected and numerically computed, the modified torsional model is proved to be more accurate than the purely torsional model and may be applied to dynamic design of epicyclic gearing with equally-spaced pinions.

Key words: Dynamic design, Dynamic model Natural characteristics, Planetary gear transmissions, MR damper self-powered ball screw disk permanent generator