Whether it is the outer edge milling cutter for machining concave tooth surface or the inner edge milling cutter for machining convex tooth surface, in the process of milling the tooth surface of spiral bevel gear, the blade rotates at high speed around the rotation center line of the tool, and the spatial motion trajectory of the blade is a part of the hemispherical surface. Replace the cutting edge part of the gear milling tool with a more vivid hemispherical surface, and calculate and analyze the cutting edge radius, as shown in Figure 1. The plane of triangle OAB is the same as the bottom circular plane of the hemispherical surface where the blade is located, while triangle o0ab is on the (q) plane. The included angle between the bottom circular plane of the hemispherical surface where the blade is located and the (q) plane is θ’， And the intersection line between the hemispherical surface and the (q) plane is an arc segment ab. The center of arc segment AB is o0 point, the chord length is l, the arc radius is r, and the corresponding center angle is α。 In the actual gear cutting process, the arc segment AB is the tooth surface generating line, which is used as the cutting edge to cut the tooth surface of spherical involute spiral bevel gear.
According to the cutting principle of spiral bevel gear tooth surface, in order to simplify the cutting motion, the tool position q is equal to the radius r of the generating line of the tooth surface. In addition, in the process of cutting and generating the tooth surface of spiral bevel gear, the endpoint a of arc-shaped blade arc segment AB is cut along the junction line of cutting area and adjustment area, as shown in Fig. 2. Point C in the figure is located on the arc blade AB and at the midpoint of the tooth width. According to the definition of spiral angle of spiral bevel gear: the spiral angle is the included angle between the tangent direction of the tooth surface at the midpoint of the tooth width and the generatrix direction. It can be seen that the spiral angle of spiral bevel gear at the base cone is the included angle between the tangent direction of the tooth surface and the generatrix, and the tangent direction of the tooth surface here is the tangent direction of the tooth surface generating line – arc ab. The straight line segment CD in the figure is tangent to the tooth surface occurrence line AB at the midpoint C of the tooth width, then the size of ∠ OCD is the size of the helix angle. Next, calculate the expression of the helix angle.
Based on the tooth surface cutting principle of spherical involute spiral bevel gear based on the tooth surface generating line, it can be seen that in the process of cutting the tooth surface of spiral bevel gear by using the new method of three-axis linkage cutting, the movement of each point on the arc blade on the (q) plane is actually moving along the radial direction, so as to cover the whole angle μ The cutting area is shown in Figure 3. Point a on the arc blade moves along the radial direction of the straight line OA, and point B moves along the radial direction of the straight line ob, that is, any point on the blade moves along the radial direction with o as the center. Then the center angle corresponding to the arc blade AB is equal at any time in the tooth surface cutting process. In order to cut out the complete tooth surface of spiral bevel gear, the cutting edge must cover the whole cutting area in the process of tooth cutting movement. Then the arc cutting edge AB line segment in Figure 3 is the smallest line segment of the cutting edge, and the corresponding center angle is the smallest center angle of the arc cutting edge.
