Lewis Bending Stress: Why Does Lewis Factor Depend on x?

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SUMMARY

The Lewis bending equation for spur gear teeth incorporates the Lewis form factor, which is dependent on the vertical distance x from the triangle formed by the base t and fillet a. This relationship is established through the equation x = t²/4h, where h represents the height and t the width of the gear tooth. The parameter x is crucial as it simplifies the tooth into a cantilever beam for analysis. Comprehensive explanations and derivations can be found in "Shigley's Mechanical Engineering Design."

PREREQUISITES
  • Understanding of Lewis bending equation for spur gears
  • Familiarity with cantilever beam theory
  • Knowledge of gear tooth geometry
  • Access to "Shigley's Mechanical Engineering Design" for reference
NEXT STEPS
  • Study the derivation of the Lewis bending equation in detail
  • Explore cantilever beam analysis techniques
  • Research gear tooth geometry and its impact on performance
  • Examine alternative methods for gear tooth stress analysis
USEFUL FOR

Mechanical engineers, gear designers, and students studying gear mechanics will benefit from this discussion, particularly those focused on the analysis and design of spur gears.

dsaun777
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How come in the lewis bending equation for spur gear tooth does the lewis form factor depend on x? x being the vertical distance measured from the triangle that is formed from the base t and fillet a. I know that you can express the height h and width t in terms of x such that x= t^2/4h, but why?

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The distance ##x## is the length of the cantilever to which the tooth is simplified in this method. Good explanation and derivation is provided in "Shigley's Mechanical Engineering Design".
 
FEAnalyst said:
The distance ##x## is the length of the cantilever to which the tooth is simplified in this method. Good explanation and derivation is provided in "Shigley's Mechanical Engineering Design".
No, h is the length, t is the width and F is the face. X is a separate parameter that deals with the tooth.
 
dsaun777 said:
No, h is the length, t is the width and F is the face. X is a separate parameter that deals with the tooth.
Right, I didn’t look closely at the image. What is the source of this figure ? I haven’t seen this parameter being used in literature. Standard derivations with just the cantilever length seem more reasonable.
 
FEAnalyst said:
Right, I didn’t look closely at the image. What is the source of this figure ? I haven’t seen this parameter being used in literature. Standard derivations with just the cantilever length seem more reasonable.
Agreed.
 

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