AGMA 908-B89

The procedures in this Information Sheet describe the methods fordetermining Geometry Factors forPitting Resistance, I, and Bending Strength, J. These values are thenused in conjunction with therating procedures described in AGMA 2001-B88, Fundamental RatingFactors and Calculation Methodsfor Involute Spur and Helical Gear Teeth, for evaluating various spurand helical gear designsproduced using a generating process.

Pitting Resistance Geometry Factor, I. A mathematical procedure isdescribed to determine theGeometry Factor, I, for internal and external gear sets of spur,conventional helical and low axialcontact ratio, LACR, helical designs.

Bending Strength Geometry Factor, J. A mathematical procedure isdescribed to determine theGeometry Factor, J, for external gear sets of spur, conventionalhelical and low axial contactratio, LACR, helical design. The procedure is valid for generated rootfillets, which are producedby both rack and pinion type tools.

Tables. Several tables of precalculated Geometry Factors, I and J, areprovided for variouscombinations of gearsets and tooth forms.

Exceptions. The formulas of this Information Sheet are not valid whenany of the followingconditions 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 orgreater than two, mp ≥ 2.0.Additional information on high transverse contact ratio gears isprovided 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 activeprofile. The effect of thisundercut is to move the highest point of single tooth contact,negating the assumption of thiscalculation method. However, the reduction in tooth root thickness dueto protuberance below theactive profile is handled correctly by this method.

(7) The root profiles are stepped or irregular. The J factorcalculation uses the stress correctionfactors developed by Dolan and Broghamer. These factors may not bevalid for root formswhich are not smooth curves. For root profiles which are stepped orirregular, other stresscorrection factors may be more appropriate.

(8) Where root fillets of the gear teeth are produced by a processother 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 ofscallops).

Bending Stress in Internal Gears. The Lewis method is an acceptedmethod for calculating thebending stress in external gears, but there has been much researchwhich shows that Lewis’ methodis not appropriate for internal gears. The Lewis method models thegear tooth as a cantilever beamand is most accurate when applied to slender beams (external gearteeth with low pressure angles),and inaccurate for short, stubby beams (internal gear teeth which arewide at their base). Mostindustrial internal gears have thin rims, where if bending failureoccurs, the fatigue crack runsradially 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 themagnitude and the location ofthe maximum bending stress. Since the boundary conditions stronglyinfluence the ring-bendingstresses, the method by which the internal gear is constrained must beconsidered. Also, the timehistory of the bending stress at a particular point on the internalgear is important because thestresses alternate from tension to compression. Because the bendingstresses in internal gears areinfluenced by so many variables, no simplified model for calculatingthe bending stress in internalgears can be offered at this time.

Footnote * – Refer to AGMA 112.05 for further discussion of standard(reference) diameters.

Edition:

B89

Published:

04/01/1989

Number of Pages:

79