GATE 2020 ME (ME2) – Question 51
A steel spur pinion has module m = 1.25 mm, 20 teeth, pressure angle 20°, speed 1200 rpm, face width F = 50 mm, Lewis factor Y = 0.322 and dynamic factor $K_v=1.26$. It drives a 60-tooth gear. Lewis formula is $\sigma=K_vW^t/(FmY)$, with tangential tooth load $W^t$. If maximum bending stress is 400 MPa, find transmitted power (kW), to one decimal.
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Correct answer: 9.8 to 10.8
Explanation
Lewis formula gives tangential load $W_t=\sigma FmY/K_v=400(50)(1.25)(0.322)/1.26=6388.889$ N. Pitch diameter is25 mm and speedπ(0.025)(1200)/60=1.570796 m/s. Power=WtV/1000=**10.0 kW**. Use the pinion pitch diameter, not the60-tooth gear diameter.