Page 348 - Gear Technology Solutions

25 Recommended Maximal Blade Curvature Radii

25.1 The Counter Intuitive Inverse

It is common to define the cutting-edge radius of a curved blade not with the
curvature value but with the radius. Measurements also show the radius be-
cause that is the dimension the gear engineer is familiar with. However, the
Ease-Off is designed and optimized with the curvature value instead of the ra-
dius. For example, if the profile crowning should be doubled, then the existing
curvature value can be multiplied by 2 in order to obtain the new curvature val-
ue. The curvature is the inverse of the radius and in case of doubling the pro-
file crowning, the new radius is calculated:

1/Rnew = 2•1/Rold → Rnew = Rold/2

The calculation of the new curvature to double the profile crowning is:

Cnew = 2•Cold

If a profile radius of Rcorr should be added to an existing radius Rold then the
following calculation is used:

-1
Rnew = (1/Rold + 1/Rcorr)

In the case of using curvatures for the operation the calculation becomes:

Cnew = Cold + Ccorr

It appears more intuitive to use the curvature instead of the radius and add,
subtract or multiply the curvature values to achieve a certain change. Due to
the inverse influence of the radius to the crowning properties it becomes diffi-
cult to understand that a variation on a 1000mm radius of, for example 100mm
on a 12mm long cutting edge only changes the cutting-edge geometry by
0.0016mm. The radius variation is quite large, where the physical surface vari-
ation is negligible.

25.2 Profile Crowning and Crowning Variation

The cutting-edge form variation (equal profile crowning) can be calculated ac-
cording to the graphics and the formula in Figure 1. Radius R delivers a profile

333