Evaluating the Time-Varying Mesh Stiffness of a Planetary Gear Set Using the Potential Energy Method

Time-varying mesh stiffness is a periodic function caused by the change of the number of the contact tooth pairs and the contact positions of the gear teeth. In this study, we have derived the analytical equations of the time-varying mesh stiffness of a planetary gear set using the potential energy method. Three simulations are conducted with a common planetary gear set under fixed carrier, fixed ring gear, and fixed sun gear. The results indicate that the obtained time-varying mesh stiffness can reflect the stiffness variation, and the proposed approaches can be extended in the future to model the stiffness of a planetary gear set when faults are introduced.