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Cutting Movement of Bevel Gears

Based on the above expression, profile of gears surface is formed accurately in accord with surface generating principle by the milling cutters which processes gears along tracing of generating line ML that is also generation line, if the generation line is as chord of face circular milling cutters. The plane Q spread on the base cone is equal to that plane Q turn around a center with angular velocity ω(b) and rotate around axis of the base cone at the angle rate of -ω(t) simultaneity, namely, the plane Q relative to of the base cone move with angular velocity ω(b)-ω(t). When the base cone rotate ω(t) around axis of itself, spreading movement of tooth surface established can be decomposed that: base cone rotates with angular velocity vector ωt , at the same time generation line ML on the plane Q rotate around itself axis at the angle rate vector of ωb relative to space coordinate. So there is a relationship between them:






Figure 1. Analysis of Cutting Movement









Figure 2. Cutting Movement of Circular Milling Cutters 





As shown in figure 1, according to above motion rela1tionship, chord of face circular milling cutters rotate with angular velocity ω(b) following plane Q. When generation line is in line segment WV, the chord cut in small end of bevel gear. When the chord moves to W1, it shows that the cutter will cut into root cone, and the overcut will happen. Tool edge rotates following Q. Meanwhile, it moves along chord direction. So the motion direction of the tool edge is along line segment OW’ in order to avoid overcut. Because circular milling cutters rotate with angular velocity ω(b) the velocity of perpendicular to line OW direction is:





According to right triangle OGW, the velocity of OW direction is shown:


As shown in figure 2, circular milling cutters which is selected feature simple structure. Main cutting edge of milling cutters is in the same plane and the plane is vertical to tool shaft. The main cutting edge in high speed rotation form rotary plane Σ, chord WV in which can be as generation line to realize motion of tooth surface generation.


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