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Planetary gears are recognized as one of the most effective forms of power transmission. A dynamic model of an N-stage power-split planetary gear set is proposed in this article. Three-dimensional translations and axial rotation of all members, mesh stiffness, bearing stiffness, and the interstage coupling stiffness are considered. Subsequently, equations of motion of the whole system are derived. Natural frequencies and vibration modes are obtained by solving the eigenvalue problem governed by corresponding equations. According to the modal properties, all vibration modes of the N-stage system can be categorized as N + 2 groups: the overall axial translational–rotational mode, the overall radical translational mode, and the ith-stage planet mode ( N i  &gt; 3). Furthermore, the typical vibration modes of a two-stage system are graphed. It is also found that the radical interstage coupling stiffness has an impact on natural frequencies of the overall radical translational modes, while the axial and twist coupling stiffness only affect the natural frequencies of the overall axial translational–rotational modes.

Modal properties of a multi-stage power-split planetary gear set