Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth
|Publication Date:||1 April 1989|
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.
Several tables of precalculated Geometry Factors, I and J, are provided for various combinations of gearsets and tooth forms.
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 1. 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) diameter2 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.
1 Numbers in brackets [ ] refer to the bibliography.
2 Refer to AGMA 112.05 for further discussion of standard (reference) diameters.