Page 70 - Gear Technology Solutions

4.10 Summary

Conjugacy between the members of straight bevel, spiral bevel and hypoid
gears was only the first step and goes back more than 100 years. Quickly, the
early scientists and engineers found out that conjugacy only gives us an im-
portant basis, but not a solution for power transmissions. Angular gearsets un-
der load experience deflections that move them away from their theoretical po-
sition by half a millimeter and more. Well designed and manufactured bevel
and hypoid gearsets today can live up to those requirements and still maintain
a power density that is four times higher than it was 50 years ago. Transmis-
sion errors of 50 to 150 micro-radiant that were normal in the 1970’s are in to-
day’s high-power density gearsets only between 5 and 15 micro-radiant. All
this was achieved by converting a global length and profile crowning (Figure
18, left) first back to conjugacy (Figure 18, center) and then into a UMC™-
optimized selective crowning which is limited to particular regions of the teeth
as shown in the right graphic in Figure 18 (also refer to chapter 18). It is nota-
ble that the flank center of the UMC-optimized Ease-Off is conjugate and the
transmission error is next to zero. In lapping, similar effects as in grinding are
achieved by utilizing low inertia spindles with rotational compliance and high-
speed torque control (SmartLap™).

Figure 18: From conventional crowning via conjugate to UMC-optimized

The dream of conjugate angular gearsets turned out to be a false objective.
Gear scientists, gear engineers and gear manufacturers worked very success-
fully for many decades on finding the optimal flank forms and the optimal non-
conjugate flank surface interaction. The conjugate tooth design today is con-
sidered simple compared to sophisticated higher order surface modulation.
There is still room for improvement, but this cannot be achieved by going back
to antiquated conjugate designs.

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