A global iterative model for mesh stiffness and mesh force estimation of flexible internal meshing in spur planetary gear sets

This paper develops a mesh stiffness model for flexible internal meshing with favorable accuracy and computational efficiency, where the interactions between multiple ring-planet branches are introduced. Based on the curved beam element submodel and the minimum potential energy principle (MPEP), the estimation of mesh stiffness is transformed into an optimization problem. Mesh forces are iteratively generated to better satisfy the MPEP until the predetermined thresholds are reached. The mesh stiffness is then calculated from the final group of mesh forces. Simulations of the finite element method validate the merits of this model. By changing the ring thickness, the number of fixed supports, and especially the number of planets, the variation rules of mesh stiffness as well as mesh force are summarized. It is demonstrated that the fluctuations of mesh stiffness and mesh force caused by the alternation of single and double tooth engagement become more distinct and tend to present within certain ranges around their mean value due to the increment of the thickness of ring gear or the number of fixed supports. In addition, the low-stiffness area of the mesh stiffness curve for flexible internal meshing is influenced by the number of planets, especially when this number is greater than the number of fixed supports.