In the contact area diagram of the hypoid gear TCA in the example, the theoretical contact area is smaller than this contact area. In the motion graph, the point where two motion curves intersect is the turning point from one pair of tooth surfaces to the other pair of tooth surfaces (as shown in Figure 1). The theoretical contact area of the tooth surface can be determined by solving the position of this point on the tooth surface.

In the example shown, the theoretical contact area can be determined according to the above method. According to the motion curve, the theoretical rotation angle of the big wheel at the exchange point of the gear pair contact is obtained. The tooth top direction is 0.0869, the tooth root direction is -0.0785, and the corresponding rocker angles are 60.64 ° and 50.93 °. Green contact area as shown in Figure 2.

At the conversion point, the distance from the intersection of the motion curve on the motion curve graph to the horizontal axis is the maximum theoretical motion error. Its size is directly related to the stability, noise and other performance of the hypoid gear in the transmission process. This error should be minimized in the design and production of spiral bevel gear.

The theoretical rotation angle of the large gear on the whole tooth surface of the hypoid gear is 0.1082 in the addendum direction and -0.1297 in the root direction. The theoretical overlap of the hypoid gear is: