This work developed an efficient model for calculating the mesh stiffness of spur/helical internal gear pairs by combining the finite element method (FEM) and analytical formula. The tooth global deformation is obtained by separation of the deformation of a full finite element model and a partial model, and the local contact deformation is derived by an analytical line contact formula based on Hertz contact theory. The transmission error and mesh stiffness of the gear pair can be acquired after solving the nonlinear contact equilibrium equations. Compared with the conventional FEM, the proposed method has much smaller computational consumption. Furthermore, it also overcomes the disadvantage that the analytical method is difficult to consider different ring gear structures. Then the influences of ring thicknesses and the number of support pins of the ring gear on the mesh stiffness are discussed. The results show that the ring flexibility will change the amplitude-frequency components of the mesh stiffness a lot.

这项工作通过结合有限元方法（FEM）和解析公式，开发了一种用于计算正齿轮/斜齿轮内啮合副的啮合刚度的有效模型。通过将完整的有限元模型和部分模型的变形分开来获得牙齿的整体变形，并通过基于赫兹接触理论的解析线接触公式得出局部接触变形。求解非线性接触平衡方程后，即可获得齿轮副的传动误差和啮合刚度。与传统的有限元法相比，该方法计算量小得多。此外，它还克服了分析方法难以考虑不同齿圈结构的缺点。然后讨论了齿圈厚度和齿圈支撑销数量对啮合刚度的影响。结果表明，环的柔韧性会极大地改变网格刚度的幅频分量。