Page 38 - Gear Technology Solutions

The curvature of the root line depends on the cutter radius, which results in a
deeper tooth at the center of the face width. The calculation of the additional
amount of root depth DR is explained in Figure 4.

Figure 4: Relationship between cutter radius, face width and DR

Several industrial users of Coniflex straight bevel gears claim that they experi-
enced a dam effect which increases the moment of inertia in tooth bending di-
rection compared to a noncurved root line.

A second positive effect is caused by the hourglass shape of the root slot
width. Not only is the tooth depth larger at midface, but also the tooth thickness
below the flank working area increases by:

Dh = 2 * DR * sina (1)

In the root bending stress calculation, the increase of root tooth thickness re-
duces the bending stress quadratic while the moment arm from the force ap-
plication point to the root (due to the depth increase) only increases linearly.
This shows in the root bending stress calculation (e.g. in a deflection beam
calculation) as follows:

s = M/W (2)
M = F * l (3)

W = b * h²/6 (4)

s = F • l / (b * h²/6) (5)

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