Distinctive behaviors of mesh force and transmission error in mesh stiffness model of spur planetary gear system considering elastic ring gear

In a planetary gear set with an elastic ring gear, there are several pairs of flexible internal meshing simultaneously. The interactions between them are often ignored when considering their mesh stiffness. This study is devoted to investigating the effect of the number of equally spaced planets and the number of fixed supports of ring gear on mesh force and loaded-static transmission error (LSTE) as well as related mesh stiffness through a 2D system-level finite element model. This model is first validated by the comparison with the traditional potential energy method (PEM) when the ring gear is fully fixed. Then taking the number of planets and fixed supports as variables, 16 sets of analyses are conducted. Mesh force and LSTE extracted from the model, together with the mesh stiffness derived by them, are analyzed and concluded in the time domain and/or frequency domain. It is demonstrated that the number of planets has a certain impact on the ring-planet mesh stiffness. In terms of the number of planets and fixed supports, planetary gear systems can be classified into three categories according to the distinctive behaviors of mesh force and LSTE in the time domain and frequency domain.