Evaluating the time-varying mesh stiffness of a planetary gear set using the potential energy method

TLDR

Time‑varying mesh stiffness, a periodic function caused by changing contact tooth pairs and positions, is a primary source of vibration in gear transmissions and is traditionally evaluated either by time‑consuming finite‑element modeling or by more general analytical methods. The study aims to provide an efficient, effective evaluation of time‑varying mesh stiffness for planetary gear sets. Using the potential‑energy method, the authors derive analytical equations—without modifying the gear tooth involute curve—that apply to any planetary gear transmission structure. The derived equations are applied to three common transmission configurations—fixed carrier, fixed ring gear, and fixed sun gear—yielding detailed discussions of their mesh stiffness behavior.

Abstract

Time-varying mesh stiffness is a periodic function caused by the change in the number of contact tooth pairs and the contact positions of the gear teeth. It is one of the main sources of vibration of a gear transmission system. An efficient and effective way to evaluate the time-varying mesh stiffness is essential to comprehensively understand the dynamic properties of a planetary gear set. According to the literature, there are two ways to evaluate the gear mesh stiffness, the finite element method and the analytical method. The finite element method is time-consuming because one needs to model every meshing gear pair in order to know the mesh stiffness of a range of gear pairs. On the other hand, analytical method can offer a general approach to evaluate the mesh stiffness. In this study, the potential energy method is applied to evaluate the time-varying mesh stiffness of a planetary gear set. Analytical equations are derived without any modification of the gear tooth involute curve. The developed equations are applicable to any transmission structure of a planetary gear set. Detailed discussions are given to three commonly used transmission structures: fixed carrier, fixed ring gear and fixed sun gear.