Meshing stiffness calculation of elastic additional deformation of gear tooth root

Since the early computer was not widely used, the method based on mechanics of materials to calculate the time-varying meshing stiffness of gears was a widely used method at that time. The biggest advantage of this method was that the calculation amount was small, so the method of material mechanics was of great significance when there was no advanced computer at that time. In the material mechanics method, the meshing gear tooth is simplified as a cantilever beam with variable cross-section.

The deformation of the gear tooth in meshing under the action of meshing force is divided into bending deformation, additional elastic deformation of tooth root, meshing contact deformation and so on. The figure shows the cantilever beam model of gear teeth. Under the action of FB of meshing force F, the calculation method of comprehensive elastic deformation of point B is as follows.

Considering that the tooth root is not rigid, but elastic, the additional deformation caused by tooth root elasticity is calculated as follows:

When B / HP < 5:

When B / HP > 5: