The tooth surface of spiral bevel gear is machined by end milling. In order to express the cutting scheme of bevel gear tooth surface more vividly, the schematic diagram of spiral bevel gear cutting scheme is established by CATIA software, as shown in the figure. Taking machining the concave tooth surface of right-hand spiral bevel gear as an example, the tooth cutting scheme is analyzed. The (q) plane, tooth blank base cone and fixed rotary shaft in the figure are auxiliary elements required for analysis, which do not actually exist. The (q) plane in the figure is tangent to the tooth blank base cone in the straight line OC, while the intersection lines of the adjustment area and the cutting area are the straight line of and the straight line og respectively, which are located on the (q) plane. The intersection line between the rotary surface of the blade of the external edge milling cutter and the (q) plane is the tooth surface generation line of the spiral bevel gear to be machined. In the actual machining, the (q) plane should be a horizontal plane, but in order to facilitate the view and analysis, the CATIA assembly drawing of the whole gear cutting motion scheme is rotated by an angle. In the actual cutting process, the tooth blank of spiral bevel gear should be inclined by a base cone angle relative to the horizontal plane—— δ b。
From the analysis of cutting motion, it can be seen that taking the tooth surface generation line as the cutting edge for cutting the tooth surface of spiral bevel gear needs a linear motion and two rotational motions to realize the milling of the tooth surface, which are: the linear movement of the blade, the rotational movement of the blade around its end point and the rotation movement of the gear blank. For vertical milling machines, generally, the linkage shaft is mainly concentrated on the horizontal workbench, and the motion of the tool is less used as the linkage control. Therefore, the linear motion of the blade and the rotary motion around its end point are attached to the gear blank, which is realized by the motion of the gear blank relative to the tool. As shown in the figure, for the machining of concave tooth surface of right-hand spiral bevel gear, the tool should move from right to left along the direction of straight line of. In this paper, it is realized by controlling the gear blank to move from left to right relative to the tool; The blade should have rotated clockwise around the fixed axis Oh (observed from top to bottom). In the actual scheme, the gear blank rotates counterclockwise around the fixed axis while moving along the of straight line (observed from top to bottom). That is, the three gear cutting linkage movements in the figure: a linear motion with speed V; There are also two rotational motions with speeds of ω 1 and ω 2. It is realized by controlling the movement of gear blank.
Based on the above analysis, in order to enable the arc-shaped blade to carry out pure rolling on the base cone, and cut the tooth surface of spherical involute spiral bevel gear on the gear blank without over cutting, the linear moving speed V of the gear blank and its two rotation speeds（ ω 1 and ω 2) The speed relation of must satisfy the formula.