How To Calculate The Speed Of Two Different Pulleys

Pulleys provide a simple way to transfer power from one shaft to another. By using pulleys with various diameters, you can specify the mechanical advantage and the relative speeds of the shafts. As with other simple machines, pulleys may exhibit a mechanical advantage by trading distance for force. A small fast-moving pulley, for instance, can transfer a greater force to a large slow-moving pulley as a trade-off for its rotational distance. In other words, if the output pulley were smaller, the input pulley wouldn't need to rotate as much to get the same output shaft speed.

1. Determine the Drive Speed

Determine the drive speed of the drive shaft. How you do this will vary greatly depending on the equipment you're working with. Some engines, motors or devices may have a tachometer. Alternatively, you may find information on the manufacturer's website or in the documentation.

2. Measure the Pulley's Pitch Diameter

Measure the drive pulley's pitch diameter. The pitch diameter is the point where little or no slippage occurs between the belt and the pulley. Although it's very difficult to determine accurately, in most cases it will be somewhere in between the base and the top of the pulley's groove. Inspect the belt while it's off of the pulley by bending it. The outer surface will stretch, and the inner will compress. The pitch diameter coincides with the point where neither compression nor stretching occurs.

3. Calculate the Pulley Ratio

Calculate the pulley ratio by dividing the pulley's pitch diameter by the pitch diameter of the drive pulley. For example, suppose the drive-shaft has a diameter of 2.2 inches, and two pulleys driven by the belt have diameters of 4.4 inches and 2.8 inches. The first ratio is:

\(\frac{4.4}{2.2}=2\)

and the second ratio is:

\(frac{2.8}{2.2}=1.27\)

4. Calculate the Speeds

Calculate the speed of each pulley by dividing the drive speed by the pulley ratio. For example, given a drive speed of 750 RPM, the speed of the first pulley is:

\(\frac{750}{2}=275\text{ RPM}\)

and the speed of the second pulley is:

\(\frac{750}{1.27}=591\text{ RPM}\)