A custom 20-tooth full-depth spur pinion has pressure angle 20°, width b = 10m and transmitted torque 95 N·m. Safe bending stress is 180 MPa and form factor Y = 0.342. Using Lewis equation $F_t=\sigma bYm$, find module m (mm, one decimal).
Pitch diameter is zm = 20m mm, so tangential force is $F_t=2T/(zm)=190000/(20m)=9500/m$ N. Lewis capacity is $180(10m)(0.342)m=615.6m^2$ N. Thus $m^3=9500/615.6=15.4321$, giving m ≈ 2.490 mm and **2.5 mm** after rounding.
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