The intersection of the tooth surfaces on both sides of the helical gear tooth and the thickness of the tooth top is zero, which is an important geometric feature of the sharpening of the tooth top of the helical gear. Now suppose that the cusp of the helical gear is located on the two tooth surfaces of a tooth and on the X2 axis, and the distance from this point to the coordinate origin o is L2, as shown in the figure.
By substituting the assumptions of the above formula into the surface gear equation, the maximum outer radius of the helical gear with constant tip can be obtained:
The tooth root transition surface of helical gear is formed by cutting the tooth top line of the tool, that is, the tooth top line of the tool is transformed into the coordinate system of helical gear through the method of coordinate transformation, which is a part of the curve obtained. In the coordinate system S2 of helical gear, the basic equation of the transition surface of helical gear is obtained as follows:
By substituting the formula and meshing equation into the basic equation of the transition surface, the component expression of the transition surface can be obtained.