BIZOMAT MAKEOS · Power Transmission
Flat Belt Drive Design (Wrap, Tensions and Belt Width)
What belt length and wrap does this flat belt drive have, what are the belt tensions, and how wide must the belt be for its allowable stress?
Design of an open flat belt drive: wrap angle on the small pulley, belt length for the centre distance, belt speed, effective pull with a service factor, tight and slack side tensions with the centrifugal tension of the belt (as the belt drive tensions tool), the belt width needed so the tight-side stress stays within your allowable, and the shaft load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power transmitted. |
| Service factor | Service factor for the driven machine. | |
| Small pulley diameter | mm | Diameter of the small pulley. |
| Large pulley diameter | mm | Diameter of the large pulley. |
| Centre distance | mm | Distance between pulley centres. |
| Small pulley speed | rpm | Speed of the small pulley. |
| Friction coefficient | Friction coefficient between belt and pulley. | |
| Belt thickness | mm | Belt thickness. |
| Belt density | kg/m³ | Density of the belt material. |
| Allowable belt stress | MPa | Allowable tensile stress in the belt including joint efficiency (your value from the belt maker). |
| Belt width chosen | mm | Belt width considered. |
| Largest belt speed | m/s | Largest speed for the belt and pulleys. |
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
- What it is
- The power the belt carries from the small pulley to the large one, usually the motor output or the power the driven machine needs.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 10000 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
- The effective pull, both belt tensions and the width needed rise in proportion.
What this means: Service factor
- What it is
- A multiplier on the power that allows for the type of driven machine, shock and running hours, from the belt maker’s service factor table.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effective pull and the width needed rise in proportion.
What this means: Small pulley diameter
- What it is
- The diameter of the smaller pulley, measured where the belt runs on it. It sets the belt speed and the wrap.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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 small pulley raises the belt speed, which lowers the pull and the width needed.
- Get it right
- Enter the smaller pulley here; the tool stops if it is larger than the other.
What this means: Large pulley diameter
- What it is
- The diameter of the larger pulley, measured where the belt runs on it. With the small pulley it sets the speed ratio and the wrap.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Centre distance
- What it is
- The distance between the centres of the two pulley shafts. It sets the belt length and how much the belt wraps the small pulley.
- 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 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer centres increase the wrap on the small pulley, which lowers the width needed.
What this means: Small pulley speed
- What it is
- How fast the small pulley turns. With its diameter it sets the belt 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
- A higher speed lowers the pull for the same power, but raises the centrifugal tension.
What this means: Friction coefficient
- What it is
- The friction coefficient between the belt surface and the pulley face, from the belt maker for the belt and pulley materials.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 1. 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 slack-side tension and the width needed.
What this means: Belt thickness
- What it is
- The thickness of the belt from its running face to its back, from the belt specification.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The width needed is inversely proportional to thickness.
What this means: Belt density
- What it is
- The mass per unit volume of the belt material. It sets the centrifugal tension the belt carries at speed.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 3000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1100 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher density raises the centrifugal stress, leaving less of the allowable for the load.
What this means: Allowable belt stress
- What it is
- The tensile stress the belt may carry on its tight side, already reduced for the joint efficiency, from the belt maker.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 50 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher allowable lowers the width needed.
- Get it right
- Make sure the value allows for the joint; joints are usually weaker than the belt itself.
What this means: Belt width chosen
- What it is
- The belt width you plan to use, compared with the width needed and used to report the belt stress.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 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.
What this means: Largest belt speed
- What it is
- The highest belt speed the belt and pulleys are rated for, from the belt and pulley maker’s data.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 100 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.
Method and formulas
- Wrap θ = 180° − 2 sin⁻¹[(D − d) ÷ 2C]; open belt length L = 2C + π(D + d) ÷ 2 + (D − d)² ÷ 4C.
- Effective pull F_e = P × SF ÷ v; centrifugal tension T_c = m v² with m = ρ b t; T₂ = F_e ÷ (e^{μθ} − 1) + T_c; T₁ = T₂ + F_e (as the belt drive tensions tool).
- Width so that T₁ ÷ (b t) ≤ σ_a: b = F_e e^{μθ} ÷ [(e^{μθ} − 1) t (σ_a − ρ v²)].
- Example: 7.5 kW at 12.147 m/s needs a 89.849 mm wide, 5 mm belt; the shaft load is 1,797.9 N.
Limitations
- Belt tension is assumed set so the drive just transmits the load with the service factor; real installation tension is often higher.
- Crossed belts and idlers change the wrap.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a flat belt for a fan, pump or line shaft
- Check a belt for a higher speed
- Find the shaft load for bearing selection
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Wrap angle, belt length and speed
- Tensions and shaft load
- Belt width needed
Interpreting the result
- Above about 25–30 m/s centrifugal tension eats into the belt’s capacity.
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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Open the Flat Belt Drive Design (Wrap, Tensions and Belt Width) calculator