Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
A chain drive is used to transmit power from a DC motor to the shaft of a solar energy operated thresher by reducing the speed from 240 rpm to 120 rpm. The number of teeth on the driving sprocket is 20 and the pitch circle diameter of the driven sprocket is 600 mm. The pitch of the chain used, in mm, is __________. (Rounded off to 2 decimal places)
Official Answer Key:
46.00 to 48.00
Step-by-Step Solution & Explanation
Step 1 — teeth on the driven sprocket. For a chain drive, N₁T₁ = N₂T₂:
240 × 20 = 120 × T₂ ⇒ T₂ = 40 teeth
Step 2 — pitch from the sprocket geometry. The pitch circle diameter of a sprocket with T teeth and chain pitch p is:
D = p / sin(180°/T)
Step 3 — substitute for the driven sprocket (D = 600 mm, T = 40):
600 = p/sin(180/40) = p/sin(4.5°)
p = 600 × sin(4.5°) = 600 × 0.078459
p = 47.08 mm
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