V-belt drives: the three formulas that earn easy marks on the Red Seal millwright exam
By RedSealPractice
Why drive-train questions show up on nearly every millwright exam
Industrial Mechanic (Millwright) is a Red Seal trade, and the interprovincial exam keeps returning to the same piece of equipment: a motor, two sheaves, a belt and a driven shaft. Most of the calculation questions in that area are answered by three formulas, each one line long. Candidates rarely lose marks on the algebra. They lose them on units and on the difference between outside diameter and pitch (datum) diameter.
1. Speed ratio: derive it before anything else
Use pitch or datum diameter, never the outside diameter of the sheave:
Ratio = Ddriven / Ddriver and ndriven = ndriver × (Ddriver / Ddriven)
Worked example: a 100 mm driver sheave turning at 1750 rpm drives a 250 mm driven sheave. The ratio is 250 / 100 = 2.5:1, so the driven shaft turns 1750 × 100 / 250 = 700 rpm. With no slip, a belt drive always trades speed for torque: the driven shaft turns 2.5 times slower and carries roughly 2.5 times the torque.
That last point is the standard trap. When a question asks for torque at the driven shaft, the ratio goes the other way: Tdriven = Tdriver × (Ddriven / Ddriver). Same ratio, inverted use.
2. Belt length for an open drive
L = 2C + π(D + d)/2 + (D − d)² / (4C)
where C is the centre distance, D the large datum diameter and d the small one, all in the same unit.
Same sheaves, centre distance 400 mm:
- 2C = 800 mm
- π(250 + 100)/2 = 549.8 mm
- (250 − 100)² / (4 × 400) = 22 500 / 1600 = 14.1 mm
- L = 800 + 549.8 + 14.1 = 1363.8 mm
Belts are only sold in standard datum lengths, so a real installation does not get a 1363.8 mm belt. You move the motor instead: shorten or lengthen the centre distance using the same formula backwards, and keep the adjustment inside the motor slide base travel and inside the belt manufacturer's take-up range. If the required length falls between two stock sizes, choose the belt that puts the centre distance within the slide range, then verify belt speed and arc of contact on the smaller sheave.
3. Belt speed, and the ceiling that decides the answer
v = π D n / 60 000 with D in mm and n in rpm, giving metres per second.
The 250 mm sheave at 700 rpm runs at π × 250 × 700 / 60 000 = 9.2 m/s. Run the same sheave directly on the 1750 rpm motor and it hits 22.9 m/s. Classic V-belts are generally kept at or below roughly 30 m/s (about 6000 ft/min); past that they lose grip, generate heat and wear the sheave grooves. A question about a very fast drive is usually testing whether you recognised the belt speed limit, not the ratio.
Power, torque and speed are tied together by P(kW) = T(N·m) × n(rpm) / 9550. A 15 kW motor at 1750 rpm delivers 15 × 9550 / 1750 = 81.9 N·m. Multiply by the 2.5 ratio and the driven shaft sees about 205 N·m, which is what you use to size the coupling or check the reducer.
The three installation numbers that come up as multiple choice
- Deflection: at mid-span, a correctly tensioned V-belt deflects about 1/64 in per inch of span, roughly 1.6% of the span, with a firm thumb push.
- Alignment: sheave faces within about 1° (a straight edge across both faces, no visible gap). Misalignment is the number one cause of premature belt failure.
- Arc of contact: short centre distances and high ratios reduce the wrap on the small sheave. Below about 120° you are into slip and heat territory, and that is the point where a question expects you to recommend a longer centre distance or an idler.
How to answer these under exam pressure
Write the formula, substitute with units shown, and sanity-check the answer against reality: a driven shaft spinning faster than the motor means you mixed the diameters, and a belt speed above 30 m/s on a standard V-belt means you picked the wrong sheave. Two checks take ten seconds and catch most of the avoidable errors in the drive-train section.