Page 56 - Gear Technology Solutions

Kinematic Coupling Requirements

1. The flank surfaces of the generating gears of the two mating bevel gears
are congruent (same shape but mirror images, as given in the example
of Figure 6)

2. The generating gears of the two mating bevel gears require identical ax-
es of rotation (Top and bottom side of the generating gear in Figure 6
form the same generating gear which rotates in both cases around the
same axis and therefore satisfies condition 2)

3. The surface of engagement of pinion and ring gear must be identical to
the surface of engagement between pinion and generating gear and also
to the one between ring gear and generating gear (without detailed
knowledge of the surfaces of engagement, the global condition in Figure
6 seems to satisfy this requirement)

The generating gear principle has to be understood as the ultimate vehicle to
form the teeth of two mating gears. The first fundamental law of gearing is fully
executed by choosing trapezoidal profiles and by applying the kinematic cou-
pling requirements. Gears are designed and manufactured in order to mesh
with each other. What better way to manufacture them by way of a generating
gear? The generating gear is represented by the manufacturing machine; it
forms the teeth of the gear (at the bottom in Figure 6) while meshing with this
gear perfectly. If the pinion is manufactured with the same generating gear but
on the opposite side (at the top in Figure 6) and if the generating gear is imag-
ined infinitely thin, then the result is a pinion that perfectly meshes with the
gear having zero motion error. It is also given in such a case, that line contact
between the pinion and gear flank surfaces exists along the entire face width.

®
Coniflex Pro designed straight bevel gears are manufactured with peripheral
cutters, where the tangent to the cutter tip circle is aligned with the root line of
the tapered tooth and the blade profile is aligned with the profile on one side of
a generating gear tooth (Figure 6). With this process it is required that first e.g.
all left flanks are machined. In a second step, the cutter changes its orientation
such that the blade profile aligns now with the second side of a generating
gear tooth and e.g. all right flanks are machined. This way the generating roll
which is a rotation around the generating gear axis is repeated for each slot
twice (see Chapter 9). This kinematic condition satisfies the requirement from
Figure 6 and fulfills the kinematic coupling conditions. Coniflex is the fastest
straight bevel gear manufacturing process although each slot is addressed
twice to generate both flanks.

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