BIZOMAT MAKEOS · Power Transmission
V-Belt or Flat Belt Drive Design
How many belts does this drive need, how long are they, and what load do they put on the shafts?
Design of an open belt drive: driven pulley size and speed, belt speed, exact pitch length, wrap angle, tension ratio from the friction coefficient and groove angle (Euler), design power with service factor, centrifugal tension, tight and slack side tensions, the number of belts for an allowable tension per belt, and the resultant shaft load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power to transmit. |
| Driver speed | rpm | Speed of the driving pulley. |
| Driver pitch diameter | mm | Pitch diameter of the driving pulley. |
| Speed ratio (driver ÷ driven speed) | Driver speed ÷ driven speed (above 1 reduces speed). | |
| Centre distance | mm | Distance between shaft centres. |
| Service factor | Service factor for the driver and driven machine. | |
| Belt | choice | V-belt (wedging in a 38° groove) or flat belt. |
| Friction coefficient | Friction coefficient between belt and pulley. | |
| Belt mass per metre | kg/m | Mass per metre of one belt. |
| Allowable tight-side tension per belt | N | Allowable tight-side tension of one belt (from the belt maker’s rating). |
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
- Power the belt drive must carry from the driving pulley to the driven machine, normally the rated output of the motor or the absorbed power of the load.
- 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
- Effective pull rises in proportion, so more belts may be needed.
- Get it right
- Use shaft power, not electrical input; the service factor is applied separately.
What this means: Driver speed
- What it is
- Rotational speed of the driving (motor) pulley. With its diameter it sets 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
- Higher speed raises belt speed, which lowers effective pull but raises centrifugal tension.
- Get it right
- Use the motor’s full-load speed from its nameplate, not the synchronous speed.
What this means: Driver pitch diameter
- What it is
- Pitch diameter of the driving pulley: the diameter at the belt’s pitch line, where the belt neither stretches nor compresses. The driven pulley is this times the ratio.
- 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 125 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, which lowers the effective pull for the same power.
- Get it right
- Use the pitch (datum) diameter from the pulley catalogue, not the outside diameter of the rim.
What this means: Speed ratio (driver ÷ driven speed)
- What it is
- Driver speed divided by driven speed. Above 1 the drive slows the machine down and the driven pulley is larger; below 1 it speeds it up.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Divide driver speed by driven speed, not the reverse; entering the inverse swaps which pulley is larger.
What this means: Centre distance
- What it is
- Distance between the centres of the two pulley shafts. With the pulley diameters it sets belt length and the wrap angle on 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 500 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 increases the wrap angle and belt length.
- Get it right
- Allow for the take-up adjustment range; the tool rejects a centre distance too small for the pulleys.
What this means: Service factor
- What it is
- Multiplier on the transmitted power that allows for the type of driver, the driven machine’s shock and the daily running hours.
- 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
- Design pull rises in proportion, so more belts may be needed.
- Get it right
- Take it from the belt maker’s service factor table for your driver and driven machine.
What this means: Belt
- What it is
- Whether the drive uses V-belts that wedge into a grooved pulley or a flat belt on a plain crowned pulley. V-belts grip harder for the same friction.
- Units and format
- Choose one of 2 options from the list: V-belt (38° groove); Flat belt.
- Example
- The form opens with “V-belt (38° groove)” selected as a worked example. Choose the option that matches your case.
- Get it right
- The V-belt option assumes a 38° groove, so the friction coefficient is raised by the wedge effect automatically.
What this means: Friction coefficient
- What it is
- Friction coefficient between the belt and the pulley surface. For V-belts enter the plain coefficient; the tool adds the wedge effect itself.
- 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 raises the tension ratio, so each belt carries more and fewer are needed.
- Get it right
- Do not enter an already wedge-adjusted (effective) coefficient for V-belts, or the wedge is counted twice.
What this means: Belt mass per metre
- What it is
- Mass of one metre of a single belt. It sets the centrifugal tension, which uses up part of the belt’s allowable tension at speed.
- Units and format
- Enter a number in kg/m: kilograms per metre of length. The form accepts 0 kg/m to 20 kg/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 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 is mass × speed², so heavy belts lose capacity quickly at high speed.
- Get it right
- Use the mass per metre of one belt from the catalogue, not of the whole set.
What this means: Allowable tight-side tension per belt
- What it is
- Highest tension one belt may carry on its tight side, from the belt maker’s rating for the belt section. Centrifugal tension is subtracted to leave what can drive.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 1000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 N 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 tension reduces the number of belts.
- Get it right
- Use the allowable working tension per belt, not the breaking strength.
Method and formulas
- d₂ = d₁ × ratio; v = π d₁ n₁ ÷ 60,000; φ = asin[(d₂ − d₁) ÷ 2C]; length = 2C cos φ + π (d₁ + d₂) ÷ 2 + φ (d₂ − d₁); wrap = 180° − 2φ.
- Tension ratio e^(μ′θ), with μ′ = μ ÷ sin 19° for V-belts.
- Effective pull F_e = P × SF ÷ v; centrifugal tension T_c = m v²; belts n = ⌈F_e e^(μθ) ÷ (e^(μθ) − 1) ÷ (T_max − T_c)⌉.
- Shaft load = n √(t₁² + t₂² + 2 t₁ t₂ cos 2φ) with t = belt tension less centrifugal tension.
- Example: 7.5 kW at 1450 rpm on a 125 mm pulley needs 3 belts of 1,704.9 mm.
Limitations
- Uses an allowable tension per belt rather than the maker’s power rating tables; check with the belt catalogue.
- Open drive with two pulleys.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a V-belt drive for a motor and driven machine
- Check the shaft and bearing load from belt tension
- Decide whether to add a belt or enlarge the pulleys
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Driven pulley, belt speed, length and wrap
- Tensions and number of belts
- Shaft load
Interpreting the result
- Larger pulleys raise belt speed and cut tension, often saving a belt.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2487–2536. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Set belt tension by its frequency
In Vibrating Machine Elements by the Numbers
What it covers: Turn a belt span's natural frequency into its tension, set RF-3's belts to a target frequency, and catch the mass and span-length errors that fool a meter.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.