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Gears are manufactured with thin rims for several reasons. Steel gears are manufactured with thin rims and webs where low weight is important. Nonmetallic gears, manufactured by injection molding, are designed with thin rims as part of the general design rule to maintain uniform thickness to ensure even post-mold cooling. When a thin-rimmed gear fails, the fracture is thought the root of the gear, as shown in Fig. 1a, rather than the usual fillet failure shown in Fig. 1b.
This article discusses the relationships among the fillet stress on a thin rim planet gear, the radial clearance between the gear rim and the gear shaft, the tooth load, the rim thickness, the radius of curvature of the center line of the rim, the face width and the module.
A common design goal for gears in helicopter or turboprop power transmission is reduced weight. To help meet this goal, some gear designs use thin rims. Rims that are too thin, however, may lead to bending fatigue problems and cracks. The most common methods of gear design and analysis are based on standards published by the American Gear Manufacturers Association. Included in the standards are rating formulas for gear tooth bending to prevent crack initiation (Ref. 1). These standards can include the effect of rim thickness on tooth bending fatigue (Ref 2.). The standards, however, do not indicate the crack propagation path or the remaining life once a crack has started. Fracture mechanics has developed into a useful discipline for predicting strength and life of cracked structures.
The geometry factor, which is a fundamental part of the AGMA strength rating of gears, is currently computed using the Lewis parabola which allows computation of the Lewis form factor.(1) The geometry factor is obtained from this Lewis factor and load sharing ratio. This method, which originally required graphical construction methods and more recently has been computerized, works reasonably well for external gears with thick rims.(2-6) However, when thin rims are encountered or when evaluating the strength of internal gears, the AGMA method cannot be used.
For over 50 years, the Do Nothing Machine has entertained the public eye with its complex machinery, a mountain of over 700 gears put together for the express purpose of doing nothing.