Lewis method module for spur gears

Form factors

$$y_1 = 0.154 - \frac{0.912}{22} = 0.1125, \qquad y_2 = 0.154 - \frac{0.912}{66} = 0.1402$$

Compare $\sigma_o y$:

$$\text{Pinion: } 210 \times 0.1125 = 23.6, \qquad \text{Gear: } 100 \times 0.1402 = 14.0$$

The product is smaller for the gear (cast iron), so the gear is the weaker element and is used for design.

Design by trial of module

Load required: $F_t = \dfrac{P \times C_s}{v}$, with $v = \dfrac{\pi\, m\, z_1\, n_1}{60\,000}$ (m in mm). Gear capacity: $F_s = \sigma_{o2}\,C_v\, b\,\pi m\, y_2$ with $b = 10m$.

For example for $m = 5$:

$$F_s = 100 \times 0.3027 \times 50 \times \pi \times 5 \times 0.1402 = 3332\ \text{N} > 3255\ \text{N}$$

So the smallest standard module that works is m = 5 mm.

Dimensions

$$b = 10m = 50\ \text{mm}, \qquad d_1 = mz_1 = 5 \times 22 = 110\ \text{mm}, \qquad d_2 = 5 \times 66 = 330\ \text{mm}$$

Check of the pinion

$$F_{s1} = 210 \times 0.3027 \times 50 \times \pi \times 5 \times 0.1125 = 5619\ \text{N} > 3255\ \text{N}$$

so the pinion is also safe.

Answer: Module = 5 mm; face width = 50 mm; pinion pitch diameter = 110 mm; gear pitch diameter = 330 mm. The design is controlled by the cast iron gear.