Due to the multiple tooth contact problem involving internal gear pair with small tooth number difference (IGPSTND), the existing analytical methods applied for standard spur or helix gear pairs to calculate the time-varying meshing stiffness (TVMS) are not suitable. In this paper, two methods are proposed for calculating the time-varying meshing stiffness in internal gear pairs with small tooth difference. In the first method, an analytical model is established by using the potential energy method, considering the clearance of initial contact tooth and the external load. The second method proposes the application of a hybrid finite element-analytical method. The proposed two methods are validated by the application of the finite element method. By taking the results of finite element analysis as a comparative reference, the results show that the finite element — analytical method is closer to the reference results than the results obtained by the analytical method, and both methods are less computationally expensive than finite element analysis.

由于涉及小齿数差内齿轮副（IPPSTND）的多齿接触问题，现有的用于标准直齿轮或螺旋齿轮副计算时变啮合刚度（TVMS）的分析方法并不适用。本文提出了两种计算小齿差内齿轮副时变啮合刚度的方法。第一种方法是利用势能法建立分析模型，考虑初始接触齿的间隙和外载荷。第二种方法提出了混合有限元分析方法的应用。所提出的两种方法通过有限元方法的应用得到验证。以有限元分析结果作为对比参考，