The key geometric dimensions of the milling edge of the new spiral bevel gear include: the top edge thickness L, the edge radius R and the total height h, as shown in Figure 1. Because the expressions of the above key parameters of the outer edge milling cutter and the inner edge milling cutter designed in this paper are the same, this section takes the blade of the outer edge milling cutter for machining the concave tooth surface of spiral bevel gear as an example to calculate the above key parameters.

In fact, the process of spiral bevel gear tooth surface milling can be understood as the milling of spiral bevel gear groove, so as to realize the machining of spiral bevel gear tooth surface. The narrowest part of the tooth groove of the tapered spiral bevel gear is located at the tooth root of the small end of the bevel gear. In order to make the blade enter the root of the tooth groove of the small end of the bevel gear for tooth surface milling during the machining process, the edge thickness l of the end of the cutter tooth must be less than the tooth groove width of the root of the small end of the bevel gear. Next, the tooth slot width at the root of the small end of the bevel gear is calculated, so as to determine the edge thickness at the end of the blade.

Establish o-xyz coordinate system at the small end of the base cone of spiral bevel gear, as shown in Figure 2. It is assumed that the radius of the large end bottom circle of the base cone is Rb, the outer cone distance is re, and the tooth width b = re / 3. According to the proportional relationship, it is obvious that the radius of the small end of the base cone is 2rb / 3, and the cone distance from the small end to the top of the cone is 2re / 3. The starting points of the tooth profile of the left and right tooth surfaces of the small end of the bevel gear are E0 and F0 respectively. With the generation of tooth surface, E0 and F0 carry out pure rolling movement in the opposite direction on the base cone, so as to form the tooth profile of the convex and concave tooth surfaces on the small end of spiral bevel gear. Points E and F in the figure are the position points where E0 and F0 purely roll to the pitch cone on the base cone, that is, the intersection of the pitch cone of spiral bevel gear and the tooth profile on both sides of its small end convex and concave. A coordinate system o-xyz is established in the base cone, in which the vertex of the base cone is taken as the origin of the coordinate system and the rotation center line of the base cone is taken as the Z axis. Since the tooth profiles on both sides of the small end are symmetrically arranged, the symmetry plane of the small end tooth profile is taken as the XZ plane.

For the solution of the tooth groove width at the small end root cone of spiral bevel gear, the method is used to solve two key angles at the small end root cone—— θ And φ Sum the calculated value and α By substituting the numerical value into the formula, the tooth groove width at the root cone of the small end of the bevel gear can be solved. Since the thickness of the end edge of the cutter tooth must be less than the tooth groove width at the small end root cone, the thickness of the end edge of the cutter tooth is determined on this basis.