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GATE 2019 ME (ME1) – Question 17

Theory of Machines · Gears and gear trains · 1 mark · Multiple choice

A 20° full-depth spur gear transmits 20 kW at 200 rad/s. Pitch-circle diameter is 100 mm. Find the radial tooth force magnitude.

  1. 0.36 kN
  2. 0.73 kN
  3. 1.39 kN
  4. 2.78 kN

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Correct answer: (B) 0.73 kN

Explanation

Torque is $T=P/\omega=20000/200=100$ N·m. The tangential force is $F_t=T/r=100/0.05=2000$ N. Hence $F_r=F_t\tan20^\circ=727.94$ N, or **0.73 kN, B**.