Hobbing conditions of high order elliptic gears

The gear hobbing condition of non-circular gear is that the pitch curve is not concave, that is, the radius of curvature of each point on the pitch curve is greater than 0. The curvature radius of high-order elliptical gear pitch curve described by the formula is:

Therefore, the conditions for no concave part on the pitch curve are as follows:

According to the formula:

Hobbing conditions obtained from the formula:

The value of gear hobbing discriminant function f of four kinds of high-order elliptic gear pitch curves shown in Fig. 1 is shown in Fig. 2, in which: F < 0 at some polar angles in Fig. 2D, which cannot be rolled; The pitch curves of other gears are f > 0 at all polar angles, which can be hobbed.

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