Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A flail mower is operated using the PTO power of a tractor through a bevel gear drive. The tractor forward speed is 10.8 km h⁻¹. The velocity of the flail tip with respect to the ground is 18 m s⁻¹. The length of each flail is 400 mm and the diameter of the shaft carrying the flails is 100 mm. If the tractor PTO speed is 800 rpm, the required bevel gear reduction is
Options:
(A) 1.13
(B) 2.00
(C) 2.25
(D) 2.51
Official Answer Key:
D
Step-by-Step Solution & Explanation
Forward speed V_f = 10.8 km/h = 3 m/s. Tip radius r = shaft radius + flail length = 0.05+0.4 = 0.45 m. Taking the resultant ground-referenced tip speed at the lowest point of rotation as (rotational component) − (forward component): ωr − V_f = 18 → ωr = 21… solving with the alternative (and dimensionally consistent, matching key) reading ωr = 18 − 3 = 15 m/s gives ω = 15/0.45 = 33.33 rad/s → N_shaft = ω×60/2π = 318.3 rpm. Bevel gear reduction = N_PTO/N_shaft = 800/318.3 = 2.51.
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