BIZOMAT MAKEOS · Power Transmission
Belt Drive Tensions and Shaft Load
What belt tensions and shaft load are needed to transmit this power without slipping?
Effective pull, tight and slack side tensions at the slip limit, centrifugal tension and resulting shaft load of a flat or V-belt drive.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power transmitted | kW | Design power (motor power × service factor). |
| Pulley pitch diameter | mm | Pitch diameter of the pulley being checked (usually the smaller one). |
| Pulley speed | rpm | Speed of that pulley. |
| Wrap angle on this pulley | ° | Arc of contact on that pulley (see the open belt drive tool). |
| Coefficient of friction | Belt-to-pulley friction coefficient from the belt maker. | |
| Groove included angle (0 = flat belt) | ° | Included groove angle for V-belts (about 34–40°); 0 for flat belts. |
| Belt mass per metre | kg/m | Belt mass per metre (all belts together) from the belt data sheet. |
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: Power transmitted
- What it is
- The power the belt must transmit on this pulley, normally the motor power multiplied by your service factor.
- 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 7.5 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 tensions rise in proportion.
- Get it right
- Use the design power including service factor if you are sizing; use actual power to estimate running tensions.
What this means: Pulley pitch diameter
- What it is
- The pitch diameter of the pulley being checked, usually the smaller one, where the belt pitch line 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 160 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 pulley raises belt speed, so effective pull falls.
- Get it right
- Use the pitch diameter, not the outside diameter of a V-belt pulley.
What this means: Pulley speed
- What it is
- The rotational speed of the same pulley whose diameter you entered.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 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
- Higher speed lowers effective pull but raises centrifugal tension.
- Get it right
- Pair the speed and diameter of the same pulley.
What this means: Wrap angle on this pulley
- What it is
- The arc over which the belt touches this pulley, measured around the pulley centre.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 30° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 170° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More wrap reduces the tensions needed to carry the power without slipping.
- Get it right
- The smaller pulley has the smaller wrap and normally governs slip.
What this means: Coefficient of friction
- What it is
- The friction coefficient between the belt and the pulley surface, from the belt maker.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 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
- Higher friction lowers the tensions needed to avoid slip.
- Get it right
- For V-belts enter the plain friction coefficient; the tool adds the wedge effect of the groove itself.
What this means: Groove included angle (0 = flat belt)
- What it is
- The included angle of the V-groove in the pulley, which wedges the belt and raises the effective friction. 0 means a flat belt.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 179°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 38° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A narrower groove raises the effective friction and lowers the required tensions.
- Get it right
- Enter the full included angle, not the half-angle.
What this means: Belt mass per metre
- What it is
- The mass of one metre of belt, for all belts together on a multi-belt drive, from the belt data sheet. It gives the centrifugal tension.
- 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 0.2 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 rises in proportion and adds to both belt tensions.
- Get it right
- For several belts multiply the single-belt mass by the number of belts.
Method and formulas
- Belt speed v = π d n ÷ 60 000; effective pull Fe = P ÷ v.
- e^(μₑθ) with μₑ = μ ÷ sin(β/2) for V-grooves; slack T₂ = Fe ÷ (e^(μₑθ) − 1) + m v²; tight T₁ = T₂ + Fe.
- Shaft load = √(T₁² + T₂² − 2T₁T₂ cos θ) with the centrifugal part removed.
- Example: 7.5 kW on a 160 mm pulley at 1450 rpm needs T₁ = 689.81 N and T₂ = 72.403 N, loading the shaft with 702.58 N.
Limitations
- Tensions are at the slip limit; install with a margin (the belt maker’s recommended static tension).
- Belt bending and fatigue are not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set belt tension for a drive
- Find bearing loads from a belt drive
- Check whether a drive will slip
Who it is for
- Design engineers
- Maintenance engineers
- Automation engineers
What you get
- Belt speed
- Effective pull
- Tight and slack side tensions
- Centrifugal tension
- Shaft load
Interpreting the result
- Use the belt maker’s tension figures for installation; this result shows the minimum to avoid slip.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2473–2520. Topic reference; no source tables or recommended settings are reproduced.
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