# Tooth surface of spiral bevel gear with spherical involute tooth profile

Taking the tooth surface generating line as the cutting edge, the complete tooth surface of spiral bevel gear with spherical involute tooth profile can be cut by simple three-axis linkage. Among them, the linkage three axes are: gear blank rotation ω 1. Blade revolution ω And blade rotation ω 0 On the premise that the tool position q is equal to the blade radius r, it can be seen from the above analysis that the rotation speed of the three must meet the following expression:

If the above relationship is satisfied, the arc-shaped blade AB will process the concave tooth surface of the right-hand spiral bevel gear as shown in Figure 1. Divide the rectangular coordinate system where the (q) plane in Fig. 1 into four quadrants, and the machining of the concave tooth surface of the right-hand spiral bevel gear is located in the third quadrant ω 1、 ω And ω The speed of 0 satisfies equation (2.39), and ω 1 and ω Steering and ω And ω When the turning directions of 0 are opposite, point a at the tail end of the blade will simply roll on the base cone along the radial direction of the (q) plane – the intersection direction of the cutting area and the adjustment area, so as to completely cut the concave tooth surface of the right-hand spiral bevel gear.

Based on the above analysis of the machining of the concave tooth surface of the right-hand spiral bevel gear, for the machining of the concave tooth surface of the left-hand spiral bevel gear, the principles of the two are basically the same, taking the generation line of the tooth surface as the cutting edge and the inverse motion of the generated motion of the tooth surface as the cutting motion. Since the generation of the concave tooth surface of the left-hand spiral bevel gear is generated by expanding the arc generation line from the big end to the small end and the base cone to the face cone, the cutting process of the concave tooth surface of the left-hand spiral bevel gear is the same as that of the right-hand spiral bevel gear, and it is also generated by cutting the small end to the big end and the face cone to the base cone, as shown in Fig. 2. Moreover, on the premise that the tool position q is equal to the blade radius r, the speed of gear blank ω 1. Revolution speed of blade ω And the rotation speed of the blade ω The speed of 0 must also meet the formula. The difference is that the concave tooth surface of the left-hand spiral bevel gear is processed in the fourth quadrant, and the rotation direction of the three linkage shafts is just opposite to that of the right-hand spiral bevel gear. As long as the above conditions are met, the arc-shaped blade AB can also cut the concave tooth surface of the complete spherical involute tooth profile left-hand spiral bevel gear without principle error.

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