Take the moving direction of the milling blade at the midpoint of the tooth surface cutting process of spiral bevel gear as the x-axis, and the cone vertex is the zero point, as shown in Figure 1. Combined with the cutting motion of spiral bevel gear and the two axis linkage milling motion analysis in this section, the two axis linkage motion required for cutting – the linear moving speed V in the X direction and the rotation speed of gear blank ω 1. The following requirements must be met: ω Parameter relation of:
If the above relationship is satisfied, the point milling of the tooth surface can be carried out in the tooth line direction of the bevel gear blank, and the envelope generation processing of the whole spiral bevel gear tooth surface can be realized by gradually feeding in the tooth height direction.
For the machining of the convex tooth surface of spiral bevel gear, the same method is used to calculate the two-axis linkage cutting motion of the convex tooth surface based on the research of the three-axis linkage cutting method. Unlike the concave tooth surface of spiral bevel gear, the machining of the convex tooth surface is from the big end to the small end, and the schematic diagram of the cutting motion is shown in Figure 2.
The displacement expression of the cutting edge point on the x-axis during the machining of convex tooth surface can be solved by using the same analysis method as the cutting motion of concave tooth surface:
Where: R – radius of generating line of spiral bevel gear tooth surface;
L0 — initial feed position of the blade point on the x-axis;
ω—— The revolution speed of the blade during three-axis linkage machining, in which it is equivalent to the parameter variable.
By deriving the time t from the displacement expression formula of the blade point, the velocity expression of the blade point along the x-axis can be obtained:
Then for the machining of the convex tooth surface of spiral bevel gear, the linkage movement – the linear movement V of the blade and the rotation movement of the gear blank ω 1 must meet the following requirements for parameter variables ω Relationship between:
Based on the above analysis, using the proposed new method of two-axis linkage milling of spiral bevel gear to process the convex and concave tooth surfaces of spiral bevel gear has the following similarities and differences. The differences are as follows: ① the concave tooth surface is machined, and the point milling blade is machined from the small end to the large end, while the machining of convex tooth surface is just the opposite; ② For the machining of concave tooth surface and convex tooth surface, the quadrant position of the blade relative to the tooth blank is different; ③ For the processing of different tooth surfaces, the rotation direction of the tooth blank around its own rotation axis is different. The same points are as follows: ① for the machining of convex and concave tooth surfaces, the blade is generated layer by layer from the top of the tooth to the root of the tooth; ② In the process of gear cutting, the rotation speed of gear blank is equal.