Natural frequency veering in planetary gears

To achieve noise and vibration reduction in planetary gear applications, key design parameters are often varied to avoid resonances, optimize load distribution, and reduce weight. In the plots of natural frequencies versus planetary gear parameters, veering phenomena occur when two eigenvalue loci approach each other, but then abruptly veer away. The importance of veering is manifested in the dramatic changes in the vibration modes of the veering natural frequencies and the consequent impact on response. This work analytically characterizes the rules of eigenvalue veering in planetary gears. The coupling factors between two close eigenvalue loci are approximated by perturbation analysis. Special veering patterns were obtained using the unique properties of planetary gear vibration modes. The results are illustrated by an example. Key design parameters were investigated, and generalized guidance is provided for tuning planetary gear natural frequencies.