An ideal open belt has a common pitch-line speed at both effective pitch radii. This calculator applies that relation and an entered scalar efficiency to a steady operating point.
Variable Transmission of Motion Interactive Calculator
Enter input speed, effective pitch radii, input torque and an assumed efficiency. Results describe one ideal steady operating point—not a variable-sheave actuator, belt selection or capacity rating.
Equation Used
- The belt has no slip and both entered radii are effective pitch radii.
- The drive is open and speeds are reported as magnitudes.
- Input speed, torque, radii and entered efficiency are steady during each calculation.
- The torque result follows ideal reciprocal ratio multiplied by the entered efficiency.
- Belt length, center distance, wrap, tension, traction, slip, variable-sheave coordination, ratings, stress, wear, guarding and safety are omitted.
Ideal Effective-Pitch-Radius Belt Model
The U.S. Department of Energy uses pitch diameter for belt-drive speed ratio. NASA variable-speed belt-drive tests show that real drives also depend on axial force, traction, centerline force and operating efficiency. This calculator evaluates only the stated steady operating-point calculation.
What This Calculator Represents
The tool equates ideal pitch-line speed at two entered effective radii, derives output rpm, applies an entered scalar efficiency to reciprocal torque and reports driver pitch-line speed.
Ideal Transmission Calculations
Nout=Nin q
Tout=Tin(Rdriven/Rdriver)eta
belt pitch-line speed=2 pi Rdriver Nin/60000
Radii are millimetres, speeds are rpm, torque is N m and belt speed is m/s.
Worked Idealized Example
For 1800 rpm, driver radius 50 mm, driven radius 30 mm, input torque 10 N m and entered efficiency 90%, the ideal ratio is 1.67:1, output speed is 3000 rpm, output torque is 5.4 N m and belt speed is about 9.42 m/s.
Model Boundary
- Calculated: ideal no-slip radius ratio, output speed, driver pitch-line speed and reciprocal torque multiplied by entered efficiency.
- Illustrated: an open belt over exact-ratio effective pitch circles.
- Not calculated: belt length, center distance, wrap, tension, traction, slip, efficiency prediction, sheave actuation, stress, wear, capacity, guarding or safety.
Frequently Asked Questions
Are the entered radii outside radii?
No; the equations require effective pitch radii.
Does the calculator predict efficiency?
No; efficiency is an input.
Does it include slip?
No.
Does it coordinate variable sheaves?
No.
Does it select a belt or check wrap and tension?
No.
Can it establish a safe drive rating?
No.
References
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