Describe belt-and-pulley drives, calculate the velocity ratio from pulley diameters, and explain their advantages over gears

What this dot point is asking

SEAB wants you to describe belt-and-pulley drives, calculate the velocity ratio from pulley diameters, and explain their advantages over gears. This is a calculation outcome closely related to gears: you find the velocity ratio and output speed, and you explain direction and the pros and cons of belts versus gears. Belt drives appear in many machines and appliances.

The answer

What a belt-and-pulley drive does

A belt-and-pulley drive transmits rotary motion from one shaft to another using a belt looped over two pulleys (wheels). The driver pulley is turned by the power source; the belt carries the motion to the driven pulley on the output shaft. Like gears, a belt drive can change the speed and torque between the shafts, but it does so at a distance and without the pulleys touching.

Direction of drive

With an open (uncrossed) belt, both pulleys turn the same way. Crossing the belt into a figure-of-eight makes the driven pulley turn in the opposite direction to the driver. So unlike a single pair of meshing gears (which always reverse), a belt drive can give either direction depending on whether the belt is crossed.

Velocity ratio

The velocity ratio of a belt drive compares the pulleys by diameter:

(This works because the belt speed is the same on both pulleys, so a larger pulley turns more slowly.) A velocity ratio of $3:1$ means the driven pulley turns once for every three turns of the driver. A larger driven pulley slows the output; a smaller driven pulley speeds it up.

Output speed

The output (driven) speed follows from the ratio:

A driver at $900\ \text{rev/min}$ through a $3:1$ ratio gives an output of $300\ \text{rev/min}$. As with gears, slowing the output increases torque, and speeding it up reduces torque: the speed-torque trade-off applies.

Advantages and disadvantages over gears

Belt drives have real advantages: they run quietly and smoothly, are cheaper than gears, need no lubrication, can transmit motion over a larger distance between shafts, and the belt can slip if the machine jams, protecting it from damage. Their disadvantages: the belt can slip, so the drive is not perfectly precise and can lose a little speed, and it transmits less power than gears before slipping. Gears are precise and carry high power but are noisier, costlier and need lubrication. The choice depends on whether precision or smooth, cheap, protective transmission matters more.

Examples in context

Example 1. A pillar drill with stepped pulleys. A pillar drill has cone-shaped stepped pulleys on the motor and the spindle, so moving the belt to different steps changes the velocity ratio and therefore the drill speed. The operator selects a high speed for small bits in wood and a low speed (high torque) for large bits in metal. The belt drive gives an easily changed, quiet drive, ideal for a workshop machine.

Example 2. A car engine's accessory belt. A single belt from the crankshaft pulley drives several accessories (alternator, water pump) at different speeds set by their pulley sizes. The belt runs quietly, needs no lubrication, and can slip slightly if an accessory seizes, protecting the engine. The belt-and-pulley system distributes rotary motion smoothly across the engine bay where gears would be noisy and complex.

Try this

• Cue. A driver pulley of $50\ \text{mm}$ drives a driven pulley of $150\ \text{mm}$. State the velocity ratio. Answer: driven over driver $= 150/50 = 3$, so $3:1$.

• Cue. With a $3:1$ belt drive and an input of $1200\ \text{rev/min}$, find the output speed. Answer: output $=$ input $\div$ ratio $= 1200/3 = 400\ \text{rev/min}$.

• Cue. Give one advantage and one disadvantage of a belt drive over gears. Answer: advantage: quiet, cheap, no lubrication, slips to protect a jammed machine; disadvantage: the belt can slip, so it is less precise and carries less power than gears.