The cutter for machining helical offset non orthogonal face gear is involute helical gear shaper cutter, and the involute tooth profile and coordinate system of its end face are shown in the figure. In the coordinate system SS, the position vector rs of the tooth surface of the helical gear shaper cutter can be expressed as the formula:
Where: RPS = Mtns / 2 is the radius of the dividing circle on the end face; Ｒbs =Ｒpscos α T is the radius of the base circle on the end face; θ cs = 2π/Ns － ( tan α t － α T) represents the center angle corresponding to 1 / 2 of the tooth slot width on the base circle; θ S represents the angle parameter of the end face involute profile; λ S is the angle of the involute of the end face of the helical gear shaper cutter around the axis ZS; Ls = Ｒps /tan β Is the spiral lead on the indexing circle; β Is the helix angle; α t. MT is the end face pressure angle and end face modulus of helical gear shaper cutter respectively. Then the unit normal vector ns of the tooth surface of the helical gear shaper is expressed as the formula:
