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analysis from Figure 15 (X1 = 0.7, X2 = -0.7). A large lost area can be observed at
the lower dedendum. The improved design in Figure 16 with X1 = +0.7 and X2 =
+0.7 was also cut and shows after rolling with marking compound a full working
profile with a smooth transition to the root fillet (right photo in Figure 17).

Figure 17: Roll test results V0 Profile shift (left) and positive pinion and gear
profile shift (right)

The roll testing results of the gearset with double positive profile shift proved the
theoretical findings of a larger active working profile, which also has a smooth root
transition, due to the increased contact ratio in profile direction.

10.6 Summary

The V0 profile shift was the only way profile shift was applied to bevel and hypoid
gears in the past. Pinions will generally benefit from a positive profile shift, which
means that gears had to be designed with the same amount of negative profile
shift. In the case of non-generated ring gear members there was no disadvantage
of using a negative profile shift in the ring gear. The straight profile of the ring gear
will not develop any undercut if a negative profile shift is applied. However, in the
case of generated gears, kinematic undercut and physical undercut is recognized
if the ratio is lower than 3. This is more severe for straight bevel gears than for
spiral bevel and hypoid gears.

The independent pinion and gear profile shift, as it is introduced in this paper
allows rather large positive profile shift amounts. The profile shift limiting factor is
the width of the topland, which reduces with increasing positive profile shift. It is
recommended to use an iterative process to increase the active working profile of
pinion and gear with profile shift factors, starting at X = 0.2 and increasing in steps
of 0.1, while checking the mean normal topland after each step. If the same
amounts of profile shift are applied to pinion and gear, then the operating pitch line
will be located where the original pitch line was and the sliding conditions along
the profile remain (with no profile sliding at the center of the profile). To move the
working pitch line of the pinion towards the pinion root, the pinion profile shift needs

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