A robust model for determining the mesh stiffness of cylindrical gears

• A robust model for determining mesh stiffness of cylindrical gears is proposed.
• The combination of FEM and analytical formula improves the steadiness of results.
• Application of substructure method reduces a lot of computational effort.
• Mesh stiffness is nonlinear with the change of total mesh force.
• A thorough study on the influences of gear parameters on mesh stiffness

A model for determining mesh stiffness of cylindrical gears is proposed using a combination of finite element method (FEM) and local contact analysis of elastic bodies. The deformation at each contact point is separated into a linear global term and a nonlinear local contact term. The global compliances are obtained using an even mesh technique and substructure method of a three-dimensional finite element analysis to make the deformation of a global term insensitive to the twist of gear structure under different gear basic parameters, while the local contact deformations are derived through an analytical line-contact formula deduced from the Hertzian contact theory. The time-varying mesh stiffness and load distribution can be well predicted in this model. It is proved that the mesh stiffness calculated from the proposed method is in close agreement with that from published formulae, but with less time consumption and improved steadiness compared with conventional FE models using contact elements. The sensitivities of total mesh force, gear basic parameters and body parameters on mesh stiffness are investigated and discussed.