19.4 Use of Strength Formulas
The load carrying ability of gears was defined in section 13.1 by means of the
Barth revision of the Lewis Formula.
The same formula can be applied to the metric module type gearing using the
following approach:
Express the module size gear in terms of diametral pitch. The diametral pitch
obtained in this manner will be a decimal value, All other parameters will be
inch-system units, In other words, the module-size gear is treated as an odd-diametral
pitch inch-size gear.
For the Lewis formula without the Barth modification, we illustrate the
metric formulation explicitly*. The classic Lewis equation, as
given in section 13.1, was as follows:
Wt = FSY
(67)
Pd
where: F = Gear-face width, inches
Yc = Y
(68)
p
Then the metric formulation is (expressed in SI units):
Wt =
p mFSYc (69)and for metric units:
Wt = Transmitted tooth force, in Newtons (N)
F = Face width in millimeters
Associated with inch gearing the same value of Lewis factor, Yc can be used. However, this is limited to metric gears that have addenda and
dedenda proportioned in the same values as the American gear standards for which
the Yc factor applies. Fortunately, the metric ISO gear standard and American
inch gears are compatible in this regard. Nevertheless, this may not be true of
all metric gears (non-ISO standard) and one must carefully watch for this possible difference, then use
the proper Lewis factor, Yc if a difference exists.
Other rating factors require great care in conversion to SI units—especially
if the formulas involved are not dimensionally uniform—and cannot be
transformed as readily as the Lewis formula. Further discussions of gear ratings
for metric gears can be found in ref. 4.
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