BIZOMAT MAKEOS · Power Transmission
Chain Linear Speed
How fast does this roller chain run, and how much does its speed fluctuate?
Calculate the average linear speed of a roller chain and the speed fluctuation caused by chordal action as it wraps a sprocket.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch | mm | Chain pitch, for example 12.7 mm for a ½-inch pitch chain. |
| Sprocket teeth | teeth | Number of teeth on the sprocket whose speed is entered. |
| Sprocket speed | rpm | Speed of that sprocket. |
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: Chain pitch
- What it is
- The distance from the centre of one chain roller or pin to the centre of the next, the basic size of a roller chain.
- Units and format
- Enter a number in mm: millimetres. The form accepts 1 mm to 300 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Average chain speed is directly proportional to pitch.
- Get it right
- Chain sizes are often named in inches: a ½-inch pitch chain is 12.7 mm. Do not use the roller diameter.
What this means: Sprocket teeth
- What it is
- The number of teeth on the sprocket whose speed you enter, either the driving or the driven sprocket.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 3 teeth to 500 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Average speed is proportional to teeth; more teeth also make the chordal speed variation smaller.
- Get it right
- Use the teeth of the same sprocket as the speed; mixing driver teeth with driven speed gives the wrong answer.
What this means: Sprocket speed
- What it is
- The rotational speed of the sprocket whose teeth you entered.
- 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 600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Average chain speed is directly proportional to sprocket speed; the chordal variation in percent does not change.
- Get it right
- For a motor driving through a gearbox, use the output shaft speed at the sprocket, not the motor nameplate speed.
Method and formulas
- Average speed (m/s) = pitch (mm) × teeth × speed (rpm) / 60,000.
- Chordal speed variation ΔV / V = (π / N) × [1 / sin(180° / N) − 1 / tan(180° / N)] for N teeth.
- Example: 12.7 mm pitch, 20 teeth, 600 rpm gives 12.7 × 20 × 600 / 60,000 = 2.54 m/s, with a chordal speed variation of about 1.236%.
Limitations
- Chain power rating, tension, lubrication regime and wear elongation are not checked.
- The chordal variation is the geometric fluctuation only; dynamic effects and resonance are not modelled.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check chain speed against the manufacturer’s limit
- Compare sprocket sizes for smoother running
- Convert sprocket speed to conveyor speed
Who it is for
- Design engineers
- Maintenance engineers
What you get
- Average chain speed (m/s and m/min)
- Chordal speed variation (%)
Interpreting the result
- More teeth reduce chordal variation, giving smoother, quieter running and less chain fatigue.
References
- Budynas R. G. and Nisbett J. K., Shigley’s Mechanical Engineering Design, 10th edition (McGraw-Hill, 2015), chapter 17, Flexible Mechanical Elements (roller chain). Topic reference; no source tables or recommended settings are reproduced.
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