Page 127 - Gear Technology Solutions

A starting point for the following example was the conjugate design from
Figure 9. Figure 14 shows the circular length crowning which was achieved
with a 3° dish angle of the cutter blades. The Ease-Off shown in Figure 14
represents the flank area of the gear. The relief along the topland of the gear
was generated with a second order Modified Roll, starting at a profile point
which is 10% of the whole depth away from the tip. The correction amount was
chosen to be .020mm with its maximal amplitude (at the tip). In order to avoid
a weakening of the root by selecting a root relief motion, a tip relief on the
pinion tooth was used instead. The root relief of .030mm labeled on the Ease-
Off in Figure 14 was achieved only with a pinion tip relief. The Tooth Contact
graphics in Figure 14 show the calculated contact pattern inside of the
boundaries of the gear tooth. The path of contact direction is perpendicular to
the pitch line (neutral bias) and therefore the roll motion of pinion and gear
moves along the conjugate profile. In this example, the mean point and the
contact pattern are in the middle of the profile and the face width. For a
differential transmission, the deflections under load have to be determined and
a contact position correction ensures a contact spread under load without a
hard contact at the heel boundary. A hard contact at top and root is prevented
with the kinematic tip and root relief.

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Figure 14: Coniflex Pro gearset with length crowning and kinematic
top and root relief

In the bottom graphic on the right of Figure 14, the motion transmission graph
is plotted. There are three identical transmission graphs representing the
meshing of three consecutive pairs of teeth. The transmission error graph in
the middle for example has nearly zero amplitudes in its midsection. As the
contact is transferred to the preceding pair of teeth, a motion error of 25 mrad is

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