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

In summary: It's better to stick with the standard derivations using just the cantilever length. The figure seems to be from a textbook or research paper, but it's not a widely accepted or commonly used parameter in the field. In summary, the distance ##x## in the Lewis bending equation for spur gear tooth is the length of the cantilever to which the tooth is simplified. It is not a widely used parameter and standard derivations typically only use the cantilever length. Good explanation and derivation of this equation can be found in "Shigley's Mechanical Engineering Design".
  • #1
dsaun777
296
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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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  • #2
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".
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 

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

1. What is Lewis bending stress?

Lewis bending stress is a type of stress that occurs in a material when it is subjected to a bending force. This stress is caused by the tensile and compressive forces that act on the material as it bends.

2. How is Lewis bending stress calculated?

Lewis bending stress is calculated using the Lewis factor, which is a dimensionless number that takes into account the geometry and material properties of the bending object. The formula for Lewis bending stress is σ = Wc / (2bh), where Wc is the bending force, b is the width of the material, and h is the height of the material.

3. Why does the Lewis factor depend on x?

The Lewis factor, represented by x, depends on the geometry of the material and the type of loading it is subjected to. It takes into account the shape, size, and orientation of the material, as well as the location of the bending force.

4. How does Lewis bending stress affect the strength of a material?

Lewis bending stress can cause a material to bend or deform, which can lead to failure if the stress exceeds the material's yield strength. It is important to consider Lewis bending stress when designing structures or machines to ensure that the material can withstand the applied forces.

5. What factors can affect the Lewis factor?

The Lewis factor can be affected by various factors such as the type of material, the shape and size of the material, the location and magnitude of the bending force, and the type of loading (e.g. static or dynamic). It is important to carefully consider these factors when calculating the Lewis bending stress to ensure accurate results.

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