Using the meshing principle of hypoid gear and based on the meshing equation, the tooth surface equation is deduced. The large gear adopts the forming method. The equation of the large gear tooth surface of the hypoid gear is obtained through the coordinate transformation of the cutter cone equation, and the small gear is produced according to the large gear tooth surface. The large gear tooth surface and the small gear tooth surface of the hypoid gear are a pair of conjugate tooth surfaces, so as to test the shape of the small gear tooth surface.
According to the meshing and transmission relationship of hypoid gear, the machining coordinate system of large wheel and the corresponding coordinate system of cutting tool in forming method, as well as the movable coordinate system and fixed coordinate system of small wheel in the process of envelope shovel are established respectively. The tooth surface equation of forming method large wheel is deduced. According to the envelope principle of hypoid gear small wheel, the meshing equation when shoveling into small wheel is deduced through the established small wheel coordinate system. Finally, the tooth surface equation of hypoid gear small wheel is deduced through coordinate transformation.