Gearbox Ratio Choice for a Winch
A winch drum of 200 mm diameter must raise a 500 kg load at 0.5 m/s. A 4-pole motor runs at 1440 rpm and delivers 3 kW. Two gearboxes are available: a 30:1 unit rated 2.5 kW and a 40:1 unit rated 3.5 kW. The drum is driven directly from the gearbox output. The installer calculates the required drum speed and finds both ratios give different line speeds. The client insists on the exact 0.5 m/s and asks which gearbox to buy, warning that the cheaper 30:1 unit is 'close enough'.
1. Calculate the drum speed needed for 0.5 m/s and the output speed each gearbox provides, then judge whether either meets the requirement.
Read the worked answer
Drum circumference = pi x 0.2 = 0.628 m. Required drum speed = 0.5 / 0.628 = 0.796 rev/s = 47.8 rpm.
30:1 gearbox output = 1440/30 = 48 rpm. Line speed = 48/60 x 0.628 = 0.502 m/s. 40:1 gearbox output = 1440/40 = 36 rpm. Line speed = 36/60 x 0.628 = 0.377 m/s.
The 30:1 unit gives 0.502 m/s, within 0.5 percent of target. The 40:1 gives 0.377 m/s, about 25 percent slow. So the 30:1 unit meets the speed requirement and the 40:1 does not, despite being the more powerful unit.
2. Check the power and torque demand and decide whether the 30:1 gearbox rating is acceptable.
Read the worked answer
Load power = F x v = (500 x 9.81) x 0.5 = 4905 x 0.5 = 2453 W = 2.45 kW.
Motor delivers 3 kW, so the load is within motor capacity. The 30:1 gearbox is rated 2.5 kW, which is just above the 2.45 kW load but leaves almost no margin. Output torque at the drum = P/omega = 2453/(2 x pi x 0.796) = 2453/5.0 = 490 N·m, matching F x r = 4905 x 0.1 = 490 N·m, as expected.
Judgement: the 30:1 unit meets speed and just meets power, but a 2 percent margin is too thin for a winch with starting shocks. The correct call is the 30:1 ratio with a higher-rated unit, or a variable-speed drive, rather than the 40:1 gearbox that misses the speed target.