Gear Strength Calculator: Lewis Form Factor

Material properties are based on data from the Society of Automotive Engineers, Technical Report on Fatigue Properties, SAE J1099

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The Lewis Form Factor approach to gear strength follows the same logic as a standard cantilevered beam. A force is applied near the tip of the gear tooth which causes the tooth to deflect. The maximum allowable force is determined by the geometry of the gear and either the yield stress of the material, or its endurance limit. The yield stress is the point at which a material plastically deforms and no longer "bounces back" to its original shape. The endurance limit is typically lower, but represents the greatest stress the material can repeatedly (typically over ten million times) experience before it fails via cyclic fatigue failure.

Gears are complex shapes, which in return require complex calculations. However, in the world of involute spur gears, most gears look similar. Since the fundamental shape is derived from the involute profile, the profile is the same regardless of whether a gear has a diametral pitch of 24 or 48, or a module or 0.5 or 3. That is, as long as the pressure angle and tooth count remain the same.

With that knowledge, Wilfred Lewis set out to find simplifying constants to make gear strength calculations easier. Back in 1893 Lewis determined the appropriate constants for 14.5º and 20º pressure angle gears from 10 to over 300 teeth. As one might expect the constants vary much more for low tooth count gears.  

This calculator conforms to the bending equations found in Wilfred Lewis's "Investigation of the Strength of Gear Teeth." Proceedings of the Engineers Club, Philadelphia, 1893. Material properties are based on data from the Society of Automotive Engineers', Technical Report on Fatigue Properties, SAE J1099, 2018.

Below is a table of the Lewis Form Factor constants for 14.5º and 20º pressure angle gears, from 10-300 teeth.