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AGMA 908-B89 Document Information:
Title
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth
American Gear Manufacturers Association
Publication Date:
Apr 1, 1989
Scope:
The procedures in this Information Sheet describe the methods for
determining Geometry Factors for
Pitting Resistance, I, and Bending Strength, J. These values are then
used in conjunction with the
rating procedures described in AGMA 2001-B88, Fundamental Rating
Factors and Calculation Methods
for Involute Spur and Helical Gear Teeth, for evaluating various spur
and helical gear designs
produced using a generating process.
Pitting Resistance Geometry Factor, I. A mathematical procedure is
described to determine the
Geometry Factor, I, for internal and external gear sets of spur,
conventional helical and low axial
contact ratio, LACR, helical designs.
Bending Strength Geometry Factor, J. A mathematical procedure is
described to determine the
Geometry Factor, J, for external gear sets of spur, conventional
helical and low axial contact
ratio, LACR, helical design. The procedure is valid for generated root
fillets, which are produced
by both rack and pinion type tools.
Tables. Several tables of precalculated Geometry Factors, I and J, are
provided for various
combinations of gearsets and tooth forms.
Exceptions. The formulas of this Information Sheet are not valid when
any of the following
conditions exist:
(1) Spur gears with transverse contact ratio less than one, mp <
1.0.
(2) Spur or helical gears with transverse contact ratio equal to or
greater than two, mp ≥ 2.0.
Additional information on high transverse contact ratio gears is
provided in Appendix F.
(3) Interference exists between the tips of teeth and root fillets.
(4) The teeth are pointed.
(5) Backlash is zero.
(6) Undercut exists in an area above the theoretical start of active
profile. The effect of this
undercut is to move the highest point of single tooth contact,
negating the assumption of this
calculation method. However, the reduction in tooth root thickness due
to protuberance below the
active profile is handled correctly by this method.
(7) The root profiles are stepped or irregular. The J factor
calculation uses the stress correction
factors developed by Dolan and Broghamer. These factors may not be
valid for root forms
which are not smooth curves. For root profiles which are stepped or
irregular, other stress
correction factors may be more appropriate.
(8) Where root fillets of the gear teeth are produced by a process
other than generating.
(9) The helix angle at the standard (reference) diameter(Footnote *)
is greater than 50 degrees.
In addition to these exceptions, the following conditions are assumed:
(a) The friction effect on the direction of force is neglected.
(b) The fillet radius is assumed smooth (it is actually a series of
scallops).
Bending Stress in Internal Gears. The Lewis method is an accepted
method for calculating the
bending stress in external gears, but there has been much research
which shows that Lewis' method
is not appropriate for internal gears. The Lewis method models the
gear tooth as a cantilever beam
and is most accurate when applied to slender beams (external gear
teeth with low pressure angles),
and inaccurate for short, stubby beams (internal gear teeth which are
wide at their base). Most
industrial internal gears have thin rims, where if bending failure
occurs, the fatigue crack runs
radially through the rim rather than across the root of the tooth.
Because of their thin rims,
internal gears have ring-bending stresses which influence both the
magnitude and the location of
the maximum bending stress. Since the boundary conditions strongly
influence the ring-bending
stresses, the method by which the internal gear is constrained must be
considered. Also, the time
history of the bending stress at a particular point on the internal
gear is important because the
stresses alternate from tension to compression. Because the bending
stresses in internal gears are
influenced by so many variables, no simplified model for calculating
the bending stress in internal
gears can be offered at this time.
Footnote * - Refer to AGMA 112.05 for further discussion of standard
(reference) diameters.
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