A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs

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.