Constraint conditions of working tooth surface of spiral bevel gear

When the gear pair is driven, the meshing point of the tooth surface expands into an approximate elliptical contact area under the load, and the load is distributed in this area. As the contact center moves closer to the boundary of the tooth surface, the shape of the contact area changes, but it is impossible to exceed the boundary of the working tooth surface under any circumstances, as shown in the figure, that is:

In the formula:

R (T) – meshing point vector;

S (T) – instantaneous contact ellipse;

D – working tooth surface.