An analyzing method of coupled modes in multi-stage planetary gear system

This paper analyzed the natural frequency and coupled mode characteristics in multi-stage planetary gear system. A dynamic model of multi-stage planetary gears with general description is established based on the lumped mass method. Solving the associated eigenvalue problem, the vibration modes of the system with identical, equally spaced planets are classified into rotational, translational and planet modes with unique properties. A criterion to distinguish the dominant vibration stage for the two coupled mode types, rotational mode and translational mode, are provided by comparing the eigensensitivity to the component parameters of different planetary stages. Taken the dominant vibration stage as an independent single-stage planetary gear system, the natural frequencies and vibration modes are observed to be similar to the multi-stage. It is shown that the coupling in the multi-stage planetary gear system grows as the frequency reduces. In rotational modes and translational modes, the highest eigensensitivity to mesh stiffness and planet bearing stiffness of each stage are associated with different frequencies in the higher-frequency range, while the highest eigensensitivity to bearing stiffness of carriers, rings, and suns occurred in the lower-frequency range.