Optimal tooth profile design of a gear shaper cutter when meshing with internal straight splines

In this paper the possibilities for practical realization of a non-traditional method for internal straight splines cutting by gear shapers, using internal gearing have been analyzed. Based on the theoretical research conducted, the equations of the gearing line have been determined, and later used for defining the parametric equations of shaper teeth profile. Gear shapers with a different number of teeth have been profiled. The effect of the number of shaper teeth over their contour is explored. It is theoretically proved that if the gear-shaper number of teeth is twice as small as that of the splines, the profile of the tool teeth is considerably simplified. In that case, the profile transforms to a part of a circle. It has also been found that when the shaper has only a few teeth, their profile contour is a broken curve. In this regard, a limiting condition for avoiding this curvature and a formula for determining the minimum number of gear shaper teeth has been defined.