Analytical approach to mesh stiffness modeling of high-speed spur gears

The centrifugal effect is a natural phenomenon in rotor dynamics, significantly changing the deformation responses in high-speed conditions. However, this phenomenon is generally unexplored in high-speed gears. This paper developed an analytical mesh stiffness model to bridge the kinematics and the centrifugal fields of spur gears. Starting from the elasticity of fillet-foundation, this model refined and extended the bi-dimensional formulas to consider gears in simultaneous rotating and meshing. The proposed load-sharing model additionally considered the extended tooth contact and centrifugal expansions, non-iteratively determining the complicated tooth engagement regions. Analytical formulas are further implemented with a fast numerical method, which removed restrictions of classical fillet-foundation formulas and covered both thick-walled and thin-walled gears. Quasi-static and dynamic solutions are compared with existing models, FEM, and experiments, showing the acceptable accuracy of this model and demonstrating noticeable centrifugal stiffening in high-speed conditions. To this end, sensitivities of centrifugal stiffening to multi-parameters are further investigated and characterized.