Lewis's equation in spur gears are used to find the

Concept:

In the Lewis analysis, the gear tooth is treated as a cantilever beam. The tangential component (WT) causes the bending moment about the base of the tooth.

The Lewis equation is based on the following assumptions:

1. The effect of the radial component (Wr), which induces compressive stresses, is neglected.
2. It is assumed that the tangential component (WT) is uniformly distributed over the face width of the gear. This is possible when the gears are rigid and accurately machined.
3. The effect of stress concentration is neglected.
4. It is assumed that any time, only one pair of teeth is in contact and takes the total load.

Lewis form factor is given by

\(y = \frac{{{t^2}}}{{6hm}}\)

• It is a dimensionless quantity
• It is independent of tooth size
• It is only a function of the shape

The analysis of the Bending stress in the gear tooth is done by Lewis equation