Environmental Engineering Reference
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Figure 3: Highest point of single tooth contact.
UTS
σ
mean allowable
tensile stress
cycles
max allowable
stress - 70% of
allowable for
unidirectional
application
Figure 4 : Goodman fatigue stress diagram.
maximum with an alternating range from zero to the maximum. In the case of an
idler such as an epicyclic planet as shown later, tooth load reverses as it alternately
meshes with the sun and annulus. The mean root stress obtained by taking the alge-
braic sum of the tensile and compressive stresses divided by 2 is therefore, negative
and while this leads to a greater permissible alternating range about the mean, the
allowable tensile maximum stress is only some 70% of that of the limit for unidirec-
tional application. As a fi rst approximation, for a given gear volume, fi llet stresses
are inversely proportional to pitch, i.e. if pitch is doubled, stress is halved.
Again, historically, this has led to a simple criterion for tooth bending known
as the “ C ” factor. As for the “ K ” factor this can be arranged as a volumetric
expression viz.
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