Impact of planet mesh phasing on the vibration of three-dimensional planetary/epicyclic gears

• DOI: 10.1016/j.mechmachtheory.2021.104422
• Publication Date: 2021-06-23T07:45:29Z
• Authors: Chenxin Wang; Bin Dong; Robert G. Parker
• Keywords: Phaser; Harmonic

Abstract This work analytically derives rules for how planet mesh phasing impacts the vibration of planetary/epicyclic gears. A key quantity is defined that depends on the mesh frequency harmonic number, ring gear tooth number, and total number of planets. This quantity dictates, for each harmonic of mesh frequency, which central member (sun, carrier, and ring) motions are present or absent, which force and moment components can be transmitted from the central members to their surrounding components, which modes are present in the response at the given harmonic, and which modes can experience resonance in the given harmonic. Neither the derivation nor the mesh phasing rules depend on a planetary gear model; only cyclic symmetry and periodicity of the response at the mesh frequency are required. The mesh phasing rules apply to spur/helical planetary gears where each component has six, three-dimensional rigid-body degrees of freedom. They apply to systems with high-speed, gyroscopic effects and those where rotational effects are neglected. Dynamic simulations using a finite element/contact mechanics model and an analytical model confirm the mesh phasing rules. Use of these mesh phasing rules for design and troubleshooting offers significant benefits to reduce vibration of planetary gears.