Pulleys and Belts

Pitch Diameter and Drive Ratio

Pulleys and belts have two uses; to increase or reduce speed or torque, or to transfer power from one shaft to another. If the transfer of power is all you need, then two pulleys of the same diameter will do the trick. But most of the time you'll also want to take the opportunity to trade speed for torque, or vice versa. This is done by using pulleys of different pitch diameters.

The pitch diameter of a pulley is not the outside diameter. Or the inside diameter. In fact, the pitch diameter is very difficult to measure directly. If you cut a belt and look at the end, you'll see a row of fibers near the outside surface. This is the tension carrying part of the belt; the rest of the belt exists only to carry the forces from the pulley to and from these fibers. The pitch diameter of any pulley is measured at these fibers. If you think about this for a moment, you'll see that the pitch diameter of a pulley depends not just on the pulley itself, but on the width of the belt. If you put a B series belt on an A series pulley, it will ride higher than usual, increasing the effective pitch diameter.

The ratio of the pitch diameters is called the drive ratio, the ratio by which torque is increased and speed is decreased, or vice versa. Power is the product of speed and force, or in the case of things that spin, speed and torque. Pulleys do not effect power; when they increase torque, it is at the expense of speed, and vice versa.

Maximum Load and Initial Tension

How much load can be put on a belt before it slips depends on a lot of stuff, but most importantly the initial tension, the force squeezing the pulleys toward each other at rest. Everyone has seen the results of too little initial tension - a slipping alternator belt that eventually results in a dead battery. Too much initial tension isn't good either, as it unnecessarily stresses the belt and wears the bearings. Initial tension is the force on a single strand; the force on the bearings will be twice this, as there are two strands.

This calculator generates an approximation of a minimum, so you'll want to add some to provide a safety margin.

Pulley and Belt Calculator

Power hp
R.P.M. Pulley 1 rpm
Pitch Diameter 1 inches
Pitch Diameter 2 inches
Center Distance inches
Initial Tension lbs
Bearing Force lbs
Maximum Tension lbs
Minimum Tension lbs
Cyclic Variation lbs
Belt Speed fpm
Belt Length inches
Wrap Angle 1 degrees
Wrap Angle 2 degrees
R.P.M. Pulley 2 rpm
Torque Shaft 1 ft-lbs
Torque Shaft 2 ft-lbs
Drive Ratio

Example: a 1/3 horsepower motor turning a 5" pitch diameter pulley at 1750 rpm, driving a 2.5" pulley 12" away.

The required initial tension will be 7.6 pounds on each strand, 18.3 total on the bearings. Interestingly, the bearing load decreases when running: under load, the belt will be under a maximum tension of 9.1 pounds on the tight side, and a minimum tension of only 4.3 pounds on the slack side, 13.4 pounds total. This may seem weird, but that's only because it is. What happens is that the belt stretches under load, becoming looser.

The cyclic variation is the difference between the maximum and minimum tensions, 4.8 pounds. It is the cyclic variation in tension, not the tension itself, that fatigues and eventually kills the belt.




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