BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Driving pulley diameter
- What it is
- The diameter of the driving pulley, the one on the motor or input shaft, measured where the belt runs.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Belt speed rises in direct proportion to this diameter, which lowers the effective pull for the same power.
- Get it right
- Use the diameter at the belt’s running surface; for a round belt in a groove, use the effective diameter at the belt centre.
What this means: Driven pulley diameter
- What it is
- The diameter of the driven pulley, which turns in the opposite direction in a crossed drive.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger driven pulley lengthens the belt, increases the wrap slightly and lowers the driven speed.
- Get it right
- The driven speed is the driving speed times D₁ ÷ D₂; check that it is the speed you need.
What this means: Centre distance
- What it is
- The distance between the centres of the two pulley shafts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer centre distance lengthens the belt and slightly reduces the wrap angle.
- Get it right
- It must exceed the mean of the two pulley diameters for a crossed belt; generous centres reduce rubbing where the belt crosses.
What this means: Power
- What it is
- The power the belt must carry from the driving to the driven pulley, including any service factor for the duty.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Effective pull and both side tensions rise in direct proportion to power.
- Get it right
- Enter kilowatts, not watts, and multiply the nominal power by your service factor first.
What this means: Driving pulley speed
- What it is
- The rotational speed of the driving pulley, normally the motor speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Belt speed rises in proportion to speed, so a faster drive needs less pull for the same power but adds centrifugal tension.
What this means: Belt friction coefficient
- What it is
- The friction coefficient between the belt and the pulley faces, from the belt maker’s data or tests on your materials.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher coefficient raises the tension ratio at slip, which lowers the tight-side tension needed.
- Get it right
- Use a value for the actual belt and pulley materials and conditions; oil or dust lowers it.
What this means: Belt mass per metre
- What it is
- The mass of one metre of belt, from the belt maker’s data or by weighing a known length.
- Units and format
- Enter a number in kg/m: kilograms per metre of length. The form accepts 0 kg/m to 100 kg/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 kg/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Centrifugal tension equals this mass times the belt speed squared and is added to both sides.
- Get it right
- Enter kilograms per metre of belt length, not per square metre of belt material.
Limits
What this means: Allowable belt tension
- What it is
- The largest working tension the belt may carry, from its width, material and joint, as given by the belt maker.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is compared with the tight-side tension including centrifugal tension; take the joint’s rating if it is lower than the belt’s.
What this means: Largest belt speed
- What it is
- The highest belt speed the belt and its joint are rated for, from the belt maker.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 200 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Joined belts often have a lower speed limit than endless ones; use the lower value.
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