The cutter head coordinate system SG for machining hypoid gear wheel is shown in Figure 1. The vector diameter RC and normal vector NC of a point m on the cutter head in the cutter head coordinate system can be expressed as:
Where, R0 – radius of cutter head; UG – surface parameters of cutter head; θ G – is the surface parameter of the cutter head, α— For the tooth profile angle of the cutter head, take a positive value for the inner cutter (corresponding to the convex surface of the hypoid gear wheel), take a negative value for the outer cutter (corresponding to the concave surface of the hypoid gear wheel), and W2 is the tool tip distance. Therefore, the value of the tip radius of the cutter head is:
Where, the positive sign corresponds to the outer knife (cutting out the concave surface of the hypoid gear wheel), and the negative sign represents the inner knife (cutting out the convex surface of the hypoid gear wheel).