KEVOS® MAKEOS · Power Transmission
Crossed Flat Belt Drive Check (Length, Wrap, Tensions, Speed)
For this crossed (reversing) flat belt drive, how long is the belt, how much wrap does it get, and what tight-side tension does it need to carry the power without slipping?
Check of a crossed flat or round belt drive, which reverses the driven pulley: belt length and wrap on each pulley compared with an open drive (as the crossed belt length tool), belt speed, the effective pull for the power, the tension ratio at the point of slip from the friction and wrap (as the belt friction tool), the tight and slack side tensions with centrifugal tension added, checked against the belt’s allowable tension and speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Driving pulley diameter | mm | Diameter of the driving pulley. |
| Driven pulley diameter | mm | Diameter of the driven pulley. |
| Centre distance | mm | Distance between the pulley centres. |
| Power | kW | Power to transmit (include a service factor). |
| Driving pulley speed | rpm | Speed of the driving pulley. |
| Belt friction coefficient | Friction coefficient of the belt on the pulleys. | |
| Belt mass per metre | kg/m | Mass of the belt per metre of length. |
| Limits | ||
| Allowable belt tension | N | Allowable working tension of the belt (from its width and material). |
| Largest belt speed | m/s | Highest belt speed for the belt and joint. |
Method and formulas
- Crossed belt length = 2√(C² − s²) + s (π + 2 sin⁻¹(s ÷ C)) with s = (D₁ + D₂) ÷ 2; wrap = 180° + 2 sin⁻¹(s ÷ C) on both pulleys (as the crossed belt length tool).
- Tension ratio = e^(μθ) at the point of slip (as the belt friction tool); effective pull = P ÷ v.
- Slack side = pull ÷ (ratio − 1); tight side = slack × ratio; centrifugal tension m v² added to both.
- Example: a 1,708.9 mm belt wraps 208.96°; at 15.184 m/s it needs 267.19 N on the tight side.
Limitations
- Flat or round belt that can be twisted; check the belt maker allows crossing.
- Tensions at the point of slip; set the installed tension higher to keep a margin.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a reversing flat belt drive
- Check an old line-shaft belt for a new load
- Compare crossed and open belt wrap
Who it is for
- Maintenance engineers
- Restoration engineers
- Design engineers
What you get
- Belt length and wrap
- Belt speed, effective pull and tension ratio
- Tight and slack side tensions
Interpreting the result
- Crossing the belt increases the wrap on the small pulley, so a crossed drive grips better than an open one.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2473–2490, 165–168. Topic reference; no source tables or recommended settings are reproduced.
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Open the Crossed Flat Belt Drive Check (Length, Wrap, Tensions, Speed) calculator
