KEVOS® MAKEOS · Mechanics
Belt, Rope and Band Friction (Capstan)
What is the most tension the tight side can hold for this wrap and friction?
Maximum tight-side tension of a belt, rope or band wrapped around a drum (capstan or Euler–Eytelwein relation), for flat and V-groove contact.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Slack-side (holding) tension | N | Tension on the low-tension side: belt slack-side tension, brake anchor force or holding force on a rope. |
| Coefficient of friction | Friction coefficient between belt, rope or lining and the drum, from the supplier or tests. | |
| Wrap angle | ° | Angle of contact around the drum (180° for equal pulleys; more for several turns). |
| Groove included angle (0 = flat) | ° | Included angle of a V-groove (e.g. 34–40° for V-belts); 0 for flat contact. |
Method and formulas
- Effective friction μₑ = μ for flat contact, or μ ÷ sin(β ÷ 2) in a groove of included angle β.
- T₁ ÷ T₂ = e^(μₑ θ), with θ in radians.
- Transmissible force = T₁ − T₂.
- Example: 200 N slack tension, μ 0.3 and 180° of wrap allow 513.27 N on the tight side.
Limitations
- Centrifugal tension of fast belts is not included and reduces the usable tension.
- Assumes slip is impending; the friction coefficient strongly affects the result.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check slip of a flat or V belt
- Size a band brake or rope brake
- Estimate holding force of a rope around a bollard
Who it is for
- Design engineers
- Maintenance engineers
- Technicians
What you get
- Maximum tight-side tension
- Tension ratio
- Net force (tight minus slack)
- Effective friction coefficient
Interpreting the result
- Keep the working tension ratio well below the slip limit to allow for wear, dirt and lubricant.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 165–168, 2473–2490. Topic reference; no source tables or recommended settings are reproduced.
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