A Slipping Flat-Belt Drive That Is Also Running the Machine Too Fast
A small workshop line shaft runs at 1440 rpm from a 3 kW motor through a flat belt. The driven machine needs 360 rpm and the available driven pulley is 300 mm; the centre distance is 1.2 m. The motor pulley is 100 mm. The belt is 40 mm wide, 4 mm thick, and has a coefficient of friction of 0.25; the angle of contact on the small pulley is about 165°. The machine runs but the belt slips when the load is applied, the belt has a shiny glazed surface, and the small pulley shows polishing. The operator tightens the belt by moving the motor until the shaft bearings feel hot, and proposes to reduce the driven pulley to 250 mm to increase speed.
1. Calculate the driven pulley diameter needed for 360 rpm and the speed actually obtained with the 300 mm pulley. Comment on the operator's proposal to fit a 250 mm pulley.
Read the worked answer
For a belt drive, N₁d₁ = N₂D₂. Required D₂ = N₁d₁/N₂ = (1440 × 100)/360 = 400 mm.
With the available 300 mm pulley, N₂ = (1440 × 100)/300 = 480 rpm, which is 33% faster than the machine needs. Fitting a 250 mm pulley gives N₂ = (1440 × 100)/250 = 576 rpm, making the speed error much worse.
The proposal is based on the mistaken belief that a smaller driven pulley reduces speed. It increases speed. The correct change is a 400 mm driven pulley, followed by a check that the larger pulley still gives enough arc of contact and does not overload the shaft.
2. Using the belt equation, estimate the tension ratio and the tight-side tension for 3 kW at the given speed. Is the 40 mm × 4 mm belt adequate?
Read the worked answer
Belt speed v = π × 0.1 × 1440/60 = 7.54 m/s. For 3 kW, T₁ − T₂ = 3000/7.54 = 398 N.
Belt equation: 2.3 log(T₁/T₂) = μθ = 0.25 × 165° in radians = 0.25 × 2.88 = 0.72. Thus log(T₁/T₂) = 0.313 and T₁/T₂ = 2.06. Then T₂ = 398/(2.06 − 1) = 375 N and T₁ = 773 N.
The belt area is 40 × 4 = 160 mm², so the tight-side stress is 773/160 = 4.8 N/mm². That is too high for a normal fabric or leather flat belt, which is why it slips and glazes. The belt is undersized, not merely loose.
3. Recommend remedies for the slip, including tensioning and alternatives, and explain why over-tightening is not acceptable.
Read the worked answer
First replace the glazed belt and clean the pulley; glaze lowers the effective μ. Align the pulleys and set tension by deflection - roughly 16 mm per metre of span - not by bearing heat. Over-tightening raises shaft bearing loads, which is why the bearings became hot; it also stretches the belt and shortens its life.
Fit the correct 400 mm driven pulley. To improve grip, increase the arc of contact with an idler on the slack side, or change to a wider flat belt or a V-belt drive. A V-belt gives a much higher effective friction for the same tension and is the practical solution for a 3 kW machine at this speed.