Analytical determination of mesh phase relations in general compound planetary gears

This paper systematically studies the mesh phase relations of general compound planetary gears. The mesh phase relations are described by the relative phases between mesh tooth variation functions of all gear meshes. The analysis allows for compound planetary gears having multiple mesh periods. A numbering method is proposed for accurate definition of the relative phases in a general compound planetary gear. By introducing the concepts of system-level, stage-level, and train-level relative phases, the relative phases between any two gear meshes in a compound planetary gear are calculated systematically. Important relations among these relative phases are derived. The results from this study are necessary for analytical or computational multibody studies on the static or dynamic response of general compound planetary gears.