1. The working tooth surfaces of the two meshing gears are the convex tooth profile and the concave tooth gallery, that is, the concave teeth cover the convex teeth during meshing, so as to improve their contact strength.

2. In theory, it is better to make the arc radius of the convex and concave tooth profiles equal, so that the instantaneous line contact along the entire tooth height can be obtained. However, due to various errors during manufacture and installation of the gear shaft, if the radius of the tooth profile arc of the convex and concave teeth is equal, the tooth top edge will be contacted due to the influence of the error. Therefore, when designing the tooth profile, there needs to be a small difference between the arc radii of the convex and concave working tooth profiles (the arc radius of the concave tooth profile is slightly larger than that of the convex tooth profile). In this way, when the gear is running, there is only one point contact at the beginning (avoiding the contact between the top edge and the edge), after a period of operation, the tooth surface gradually runs in, and the curvature radius of the contact arc of the convex tooth surface and the concave tooth surface tends to be equal, reaching the Ideal for instantaneous line contact along the tooth height.

Transmission gear shaft

3. In the case of correct meshing of the two tooth surfaces, due to the difference in the radius of the tooth profile arc between the two tooth surfaces, if the gear teeth are absolutely rigid, the tooth surfaces are not worn, and have absolute smoothness, at this time, the tooth surfaces are in point contact. In fact, under the action of load, the gear material is elastically intersected, and the tooth surface after processing is not absolutely smooth. After the gear runs, the tooth surface gradually wears and runs in. Therefore, under the action of load, the actual contact part of the two meshing tooth surfaces firstly appears in an approximate elliptical contact area. If the load is further increased, a "correction-shaped" contact area will appear. Some literatures believe that when there are two points of contact on the same tooth of a circular arc gear under load, the contact area of the tooth surface is approximately trapezoidal due to the longitudinal deformation of the gear teeth and the difference in the radius of curvature of each point on the tooth surface.

In a word, the contact area of the meshing tooth surface of the arc gear increases a lot after a good running-in. If the geometric dimensions of the arc gear and the involute gear are the same, since the equivalent radius of curvature of the arc gear is dozens of times larger than the equivalent radius of curvature of the involute gear, the contact stress will be greatly reduced, and the contact strength will be greatly improved.