A physical explanation for the effectiveness of planet phasing to suppress planetary gear vibration

The effectiveness of planet phasing to suppress planetary gear vibration in certain harmonics of the mesh frequency is examined based on 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. Instead, the inherent system symmetries imply distinct relationships between the forces at the multiple meshes. These relationships lead naturally 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. Systems with equal planet spacing and those with unequally spaced, diametrically opposed planets are considered. In both cases, a substantial number of mesh frequency harmonics are suppressed naturally without optimization of the phasing. The phenomena are demonstrated with a dynamic finite element/contact mechanics simulation. (C) 2000 Academic Press.