An ideal belt drive relates shaft speed through the effective pitch diameters of its driver and driven sheaves. This calculator evaluates that no-slip ratio, belt pitch-line speed and ideal output torque from an assumed transmitted horsepower.
Variable Speed Device Interactive Calculator
Enter input speed, effective pitch diameters and assumed transmitted power. Results are an ideal steady-state calculation—not a split-sheave actuator design, belt selection, efficiency prediction or safety rating.
Equation Used
- The belt has no slip and both entered diameters are effective pitch diameters.
- The drive is open, so the two shafts rotate in the same direction.
- Input speed and diameters are steady during each calculation.
- Entered horsepower is treated as ideal transmitted output power with no efficiency loss.
- Belt length, center distance, wrap, tension, sheave coordination, selection limits, dynamics, guarding, stress, wear and safety are omitted.
Ideal Effective-Pitch-Diameter Belt Model
The U.S. Department of Energy's Microhydropower Handbook identifies pitch diameter as the basis for belt-drive speed ratio. NASA variable-speed belt-drive work shows that real split sheaves additionally depend on coordinated flange position, axial force, centerline force, traction and efficiency. This calculator evaluates only the ideal steady-state diameter calculation.
What This Calculator Represents
The tool treats the two entered values as effective pitch diameters, equates their ideal pitch-line speeds, derives output rpm, and converts assumed transmitted horsepower to ideal output torque. It does not calculate how a variable sheave reaches or sustains those diameters.
Ideal Belt-drive Calculations
Nout = Nin q
belt pitch-line speed = pi Ddriver Nin/12
ideal output torque (lb-in) = 63025 HP/Nout
Diameters are inches, speeds are rpm and belt speed is ft/min. The torque result assumes lossless transmission of the entered horsepower.
Worked Idealized Example
For 1000 rpm, a 6-inch driver pitch diameter, a 1-inch driven pitch diameter and 5 hp, the ideal ratio is 6:1, output speed is 6000 rpm, driver pitch-line speed is about 1571 ft/min and ideal output torque is about 52.5 lb-in.
Model Boundary
- Calculated: ideal no-slip diameter ratio, output speed, driver pitch-line speed and lossless horsepower-to-torque conversion.
- Illustrated: an open belt over two effective pitch circles.
- Not calculated: belt length, center distance, wrap angle, tension, traction, slip, efficiency, sheave flange position, actuator force, belt rating, stress, wear, guarding, capacity or safety.
Frequently Asked Questions
Are the entered diameters outside diameters?
No; the equations require effective pitch diameters.
Does the calculator include belt slip?
No.
Is the output torque a rated value?
No; it is the ideal torque corresponding to the entered horsepower at the calculated speed.
Does it coordinate two split sheaves?
No.
Does it select a belt or check wrap and tension?
No.
Can it establish a safe operating speed?
No; use manufacturer ratings and applicable guarding requirements.
References
- U.S. Department of Energy, Microhydropower Handbook: belt-drive pitch diameter, speed ratio and preliminary selection.
- NASA TM-81652, Axial force and efficiency tests of fixed center variable speed belt drive: sheave forces, traction and efficiency dependencies absent from the ideal calculation.
- OSHA 29 CFR 1910.219: guarding and pulley-speed requirements for mechanical power-transmission apparatus.
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