A model for determining mesh stiffness of cylindrical gears is proposed

in this paper. The model takes into account the effects of tooth profile, tooth surface roughness, and tooth contact pattern on the mesh stiffness of cylindrical gears. The tooth profile is modeled using a modified form of the involute curve, which takes into account the effects of tooth undercut and tooth tip relief. The tooth surface roughness is modeled using the Greenwood-Williamson model, which considers the effects of asperity contact and elastic deformation.

The tooth contact pattern is modeled using the Hertzian contact theory, which considers the effects of elastic deformation and contact pressure on the mesh stiffness. The model is validated using experimental data from a set of cylindrical gears with different tooth profiles and surface roughnesses. The results show that the model accurately predicts the mesh stiffness of the gears under different operating conditions.

The proposed model can be used to optimize the design of cylindrical gears for specific applications, by selecting the appropriate tooth profile and surface roughness to achieve the desired mesh stiffness. The model can also be used to predict the effects of changes in operating conditions, such as changes in load, speed, or lubrication, on the mesh stiffness of the gears.