Enter the net tangential belt force (tight-side minus slack-side tension), the radius of the drive pulley, and the efficiency of the drive into the calculator to determine the pulley torque.
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Pulley Torque Formula
The following formula can be used to calculate the useful torque available at a pulley when a net tangential belt force acts at radius r and an efficiency factor is applied.
T = F*r*\eta
- Where T is the torque (N·m)
- F is the net tangential belt force (N), often F = T1 − T2 (tight-side tension minus slack-side tension)
- r is the radius of the drive pulley (m)
- η is the efficiency of the system (decimal). If you enter efficiency as a percent, use η = (percent)/100.
To calculate pulley torque, multiply the net tangential belt force by the radius of the drive pulley, then multiply by the efficiency factor. (If you need the required input torque to achieve a target output torque, you would divide by η instead.)
Pulley Torque Definition
Pulley torque is the torque transmitted to or from a pulley by a belt (or rope). For a belt drive, the torque on the pulley is set by the net tangential belt force at the rim times the pulley radius.
Example Problem
How to calculate pulley torque?
To calculate a pulley torque, first determine the net tangential force acting on the pulley (often the difference between the tight-side and slack-side belt tensions). For this problem, the net tangential belt force is 200 N.
Next, determine the radius of the drive pulley. In this problem, the drive pulley radius is measured to be 0.35 m.
Next, determine the efficiency of the system. This is the approximate efficiency rating of the belt-drive system after taking into account friction and losses in the transfer of power from the motor to the pulley (or vice versa). We will use a conservative 0.75 (75%) for this problem.
Finally, calculate the pulley torque using the formula:
T = F*r*η
= 200 * 0.35 * 0.75
= 52.5 N·m.
FAQ
Do pulleys multiply torque?
Yes—belt-and-pulley systems can increase torque at the driven pulley when the driven pulley has a larger radius (or diameter) than the driver. Ideally (ignoring losses), torque increases in proportion to the pulley radius ratio while speed decreases in inverse proportion, so power is approximately conserved.
In belt drives, transmitted torque comes from unequal belt tensions (tight side vs slack side), so the “effective force” that creates torque is the difference between those tensions acting at the pulley radius.
What is the torque on a pulley?
The torque on a pulley is the net tangential belt force times the pulley radius: T = (T1 − T2)r. If you apply an efficiency factor to estimate useful output torque, you can use T = (T1 − T2)rη.
