Mesh Phasing Relationships in Planetary and Epicyclic Gears

The multiple tooth meshes in planetary and epicyclic gears have varying numbers of teeth in contact under operating speed, and these numbers of teeth all fluctuate at the same mesh frequency. All sun-planet meshes have the same shape and periodicity of variation of numbers of teeth in contact at the multiple meshes, but these variations are, in general, not in phase with each other. The same is true for the ring-planet meshes. Additionally, there is a phase difference between the sun-planet and ring-planet meshes. This work sets out a complete analytical description of each of these mesh phase relationships. Mesh phasing has a dramatic impact on the static and dynamic behavior of planetary and epicyclic gears. This work provides the necessary relationships to properly incorporate mesh phasing in analytical models.