BIZOMAT MAKEOS · Power Transmission
Pulley Speed Ratio
What speed will the driven pulley run at, ignoring belt slip?
Calculate the ideal speed of a driven pulley, the speed ratio and the belt speed from the two pitch diameters and the driver speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Driver pulley pitch diameter | mm | Pitch diameter of the driving pulley (not the outside diameter for V-belts). |
| Driven pulley pitch diameter | mm | Pitch diameter of the driven pulley. |
| Driver speed | rpm | Speed of the driving pulley, for example the motor speed. |
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: Driver pulley pitch diameter
- What it is
- The diameter of the driving pulley measured at the belt’s pitch line, where the belt neither stretches nor compresses as it bends. The driving pulley is usually on the motor.
- Units and format
- Enter a number in mm: millimetres. The form accepts 1 mm to 5000 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 driver raises the driven speed and the belt speed in direct proportion.
- Get it right
- For V-belt and timing pulleys the pitch diameter differs from the outside diameter; take it from the pulley catalogue.
What this means: Driven pulley pitch diameter
- What it is
- The diameter at the belt’s pitch line of the pulley on the machine being driven.
- Units and format
- Enter a number in mm: millimetres. The form accepts 1 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The driven speed is inversely proportional to this diameter; belt speed does not change.
- Get it right
- Use the pitch diameter, not the outside diameter over the rim or teeth.
What this means: Driver speed
- What it is
- The rotational speed of the driving pulley, usually the motor shaft speed under load.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.01 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Driven speed and belt speed are both directly proportional to driver speed.
- Get it right
- An induction motor runs slightly below its synchronous speed; use the nameplate full-load speed.
Method and formulas
- Speed ratio = driven pitch diameter / driver pitch diameter.
- Driven speed = driver speed / speed ratio; belt speed (m/s) = π × driver diameter (mm) × driver speed / 60,000.
- Example: 100 mm and 250 mm pulleys at 1,500 rpm give a ratio of 2.5, a driven speed of 600 rpm and a belt speed of 7.853982 m/s.
Limitations
- Slip and creep, which make the driven speed slightly lower in practice, are ignored.
- Belt length, centre distance, wrap angle and power rating are not checked; the Open Belt Drive Geometry tool covers length and wrap.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose pulley sizes for a target speed
- Check belt speed against the belt maker’s limit
- Estimate a driven machine speed
Who it is for
- Design engineers
- Maintenance engineers
What you get
- Ideal driven speed (rpm)
- Speed ratio
- Belt speed (m/s)
Interpreting the result
- Use the result as the nominal speed; measure the actual speed where it matters.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2484–2487. Topic reference; no source tables or recommended settings are reproduced.
- Budynas R. G. and Nisbett J. K., Shigley’s Mechanical Engineering Design, 10th edition (McGraw-Hill, 2015), chapter 17, Flexible Mechanical Elements. Topic reference; no source tables or recommended settings are reproduced.
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