# Cutting principle of convex tooth surface based on generation line of spiral bevel gear tooth surface

Based on the analysis of the generation principle of convex tooth surface, it can be seen that the convex tooth surface of right-hand spiral bevel gear is formed by expanding the generation line of arc tooth surface from the small end to the large end of gear blank and from the base cone to the face cone. At the same time, based on the research on the cutting principle of concave tooth surface of spiral bevel gear based on the tooth surface generation line, it can be seen that taking the tooth surface generation line as the cutting edge and the inverse motion of the tooth surface generation motion as the cutting motion, the complete spiral bevel gear tooth surface can be cut only by three-axis linkage. As shown in Figure 1, the machining of convex tooth surface of right-hand spiral bevel gear is located in the fourth quadrant. In order to maintain a pure rolling relationship between the arc blade AB and the base cone, the blade rotates ω Rotation with base cone ω The speed relationship of 1 must meet the following requirements: ω/ω 1= sin δ b ； At the same time, in order to prevent over cutting caused by the blade entering the adjustment area, the blade rotates on the premise that the blade position q is equal to the blade radius R ω And rotation ω The speed size relationship of 0 must meet: ω 0= 2 ω 。 That is, the rotation speed of the base cone ω 1. Revolution speed of blade ω And the rotation speed of the blade ω The speed of 0 must meet the formula. On the basis that the three-axis linkage gear cutting motion meets the above relationship, the convex tooth surface of right-hand spiral bevel gear can be cut from the large end of gear blank to the small end and the face cone to the base cone by rotating in the direction of Figure 1.

Based on the above analysis, the cutting motion of convex tooth surface of spherical involute left-hand spiral bevel gear is analyzed in the same way based on the generation principle of spherical involute tooth surface, as shown in Fig. 2.

For the machining of the convex tooth surface of the left-hand spiral bevel gear, in order to make the arc blade pure rolling on the base cone and cut out the tooth surface of the bevel gear without over cutting, the three linkage axes are the rotation of the base cone ω 1. Revolution of blade ω And the rotation of the blade ω The speed of 0 must also meet the formula. And the rotation direction of the three axes is shown in Figure 2: ω 1 and ω In the opposite direction, ω And ω 0 turns in the opposite direction. If the above relationship is satisfied, the blade can simply roll on the base cone along with the tangent plane of the base cone — (q) plane, and cut the convex tooth surface of the left-hand spiral bevel gear from the big end of the gear blank to the small end and from the face cone to the base cone. The machining of convex tooth surface of left-hand spiral bevel gear is located in the third quadrant.

So far, the cutting generation motion of convex and concave tooth surfaces without rotation direction has been analyzed and studied. It is summarized as follows: ① for the spiral bevel gear tooth surface with spherical involute tooth shape, whether it is left-handed or right-handed, convex or concave, on the premise of the phase of tool position Q and blade radius r, the three rotation speeds of linkage must meet the formula, And the rotation direction of the gear blank is opposite to the rotation direction of the blade, and the rotation direction of the blade is opposite to the rotation direction of the blade; ② The processing of concave tooth surface is carried out from small end to large end; The machining of convex tooth surface is carried out from the big end to the small end; ③ The machining of left-hand convex tooth surface and right-hand concave tooth surface is located in the third quadrant, while the machining of left-hand concave tooth surface and right-hand convex tooth surface is located in the fourth quadrant.

Scroll to Top