Mesh phasing for epicyclic gear vibration reduction

The effectiveness of planet phasing to suppress planetary gear vibration in certain harmonics of the mesh frequency is examined analytically in terms of the natural symmetries of planetary (or general epicyclic) gears. The conclusions are derived from examination of the physical forces acting at the sun-planet and ring-planet meshes. The analysis does not rely on assumptions of the nature of the dynamic excitation (e.g., static transmission error or time-varying mesh stiffness) or on an underlying dynamic model. The analysis leads to simple rules for when a particular harmonic of mesh frequency is suppressed in the dynamic response. An important implication is that certain expected resonances when a mesh frequency harmonic and a natural frequency coincide are suppressed. In fact, a substantial number of mesh frequency harmonics are suppressed even without optimization of the phasing. The phenomena are demonstrated with a dynamic finite element/contact mechanics simulation.