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.

这项工作通过分析推导出行星啮合相位如何影响行星/行星齿轮振动的规则。定义了一个关键量，它取决于啮合频率谐波数、齿圈齿数和行星总数。对于网格频率的每个谐波，该数量指示存在或不存在哪些中心构件（太阳、载体和环）运动，哪些力和力矩分量可以从中心构件传递到其周围分量，哪些模式存在于给定谐波处的响应，以及哪些模式可以在给定谐波中发生共振。推导和啮合定相规则都不依赖于行星齿轮模型；只需要网格频率下响应的循环对称性和周期性。啮合定相规则适用于直齿轮/螺旋行星齿轮，其中每个组件具有六个三维刚体自由度。它们适用于具有高速陀螺效应和忽略旋转效应的系统。使用有限元/接触力学模型和分析模型的动态模拟确认了网格定相规则。使用这些啮合相位规则进行设计和故障排除可为减少行星齿轮的振动提供显着的好处。