A modified method for determining mesh stiffness of gears based on finite element method and elastic contact theory

A method for determining mesh stiffness of gears was presented using a combination of the finite element method and elastic contact theory. The contact point bending deformations were separated from the original compliances matrix which was obtained using sub-structure method, while contact deformations were derived using an analytical formula of elastic line contact deformation. The time-varying mesh stiffness and load distributions of tooth could be obtained by solving the nonlinear deformation compatibility equations. Taking a gear pair as an example, the mesh stiffness using the presented method is within 6% difference with the aerospace standard. As finite element method has an obvious advantage in predicting global deflection and the elastic contact theory can compute local contact deformation accurately, the method pressented combines these advantages to increase the computation efficiency compared to conventional finite element method. Given the nonlinearity of contact deformations problem, the mesh stiffness is increasing nonlinearly with the increase of total mesh force.