Subtopic: Power transmission systems – gear trains, differential, final drives and power take-off
Question Statement:
An engine at 1200 rpm drives a 1.2 m diameter rigid wheel on a non-deformable surface at 5 km/h forward speed, through a gearbox (3:1), differential (4:1), and final drive (n:1). Neglecting wheel deformation/slip, find n. (Rounded to 2 decimal places)
Official Answer Key:
4.20 to 4.70
Step-by-Step Solution & Explanation
Wheel speed = forward speed/(π×D) = (5000 m/h)/(π×1.2) = 1326.3 rev/h = 22.10 rpm. Total reduction ratio = engine rpm/wheel rpm = 1200/22.10 = 54.29. This equals (gearbox)×(differential)×(final drive) = 3×4×n = 12n. So n = 54.29/12 = 4.52.
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