BIZOMAT MAKEOS · Power Transmission
Roller Chain Drive Design
Will this roller chain and sprocket pair carry the power, how long is the chain, and how smooth will it run?
Design check of a roller chain drive: sprocket pitch diameters, chain speed, design power with service factor against the per-strand rating and multi-strand factor, working pull and its safety factor on breaking load, chain length rounded to an even number of links, the exact centre distance for it, wrap on the small sprocket and chordal speed variation.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power transmitted. |
| Small sprocket speed | rpm | Speed of the small sprocket. |
| Small sprocket teeth | Teeth on the small sprocket. | |
| Large sprocket teeth | Teeth on the large sprocket. | |
| Chain pitch | mm | Chain pitch. |
| Target centre distance (pitches) | Preferred centre distance in pitches (30–50 is common). | |
| Service factor | Service factor for the driver and load. | |
| Power rating of one strand at this speed | kW | Power rating of one strand at the small sprocket speed and tooth count (from the chain maker or standard). |
| Multi-strand factor (1 for single) | Factor for multiple strands (from the chain maker). | |
| Chain breaking load | kN | Minimum breaking load of the chain. |
| Chain mass per metre | kg/m | Mass per metre of the chain. |
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 chain carries from the driving sprocket to the driven machine. It sets the chain pull and, with the service factor, the design power.
- 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 5.5 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Design power rises in proportion and the chain pull rises with it.
- Get it right
- Use shaft power at the sprocket; the service factor is applied separately.
What this means: Small sprocket speed
- What it is
- Rotational speed of the smaller sprocket. With its teeth and the chain pitch it sets chain speed, and chain ratings are quoted at this speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 10000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 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 chain speed, which lowers pull for the same power.
- Get it right
- Use the small sprocket’s speed even when it is the driven one.
What this means: Small sprocket teeth
- What it is
- Number of teeth on the smaller sprocket. It sets the pitch diameter, chain speed and how uneven the chain motion is (chordal action).
- Units and format
- Enter a plain number with no unit. The form accepts 7 to 150. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 19 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth reduce chordal speed variation and raise chain speed.
- Get it right
- Count teeth, not tooth spaces between missing teeth; the tool warns below 17 teeth.
What this means: Large sprocket teeth
- What it is
- Number of teeth on the larger sprocket. With the small sprocket teeth it sets the speed ratio, pitch diameter and chain length.
- Units and format
- Enter a plain number with no unit. The form accepts 7 to 300. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 57 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The output speed is n₁ × z₁ ÷ z₂; check this gives the speed you need.
What this means: Chain pitch
- What it is
- Distance between the centres of adjacent chain rollers. It identifies the chain size and sets the sprocket diameters and chain length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15.875 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pitch diameters, chain speed and length all scale with pitch.
- Get it right
- Chain sizes are often named in inches or eighths of an inch; convert to millimetres (1 inch = 25.4 mm).
What this means: Target centre distance (pitches)
- What it is
- The centre distance you would like between the sprocket shafts, counted in chain pitches. The tool rounds the chain to an even number of links and reports the exact centre distance.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 200. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Divide the millimetre distance by the chain pitch; this field is in pitches, not millimetres.
What this means: Service factor
- What it is
- Multiplier on the transmitted power for the smoothness of the driver and the shock of the driven load, giving the design power.
- 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 1.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Design power rises in proportion, needing a higher-rated chain.
- Get it right
- Take it from the chain maker’s or standard’s service factor table.
What this means: Power rating of one strand at this speed
- What it is
- Power one strand of the chosen chain can carry at the small sprocket’s speed and tooth count, from the chain maker’s rating chart or standard.
- 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 8 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Capacity = rating × multi-strand factor, compared with the design power.
- Get it right
- Read the rating at your actual small-sprocket speed and teeth, for the lubrication method you will use.
What this means: Multi-strand factor (1 for single)
- What it is
- Multiplier on the single-strand rating for duplex, triplex or wider chains. Multi-strand chains carry less than a whole multiple of one strand.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use 1 for single-strand chain; take the multi-strand value from the chain maker, not the number of strands.
What this means: Chain breaking load
- What it is
- Minimum tensile breaking load of the chain from the chain maker or standard. It is divided by the working pull to give the safety factor on breaking.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 10000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The breaking safety factor rises in proportion.
- Get it right
- Use the minimum breaking load, not the average ultimate strength some catalogues also print.
What this means: Chain mass per metre
- What it is
- Mass of one metre of the chain. It sets the centrifugal pull that adds to the working pull at speed.
- 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 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
- Adds mass × speed² to the chain pull.
- Get it right
- For multi-strand chain use the mass of the whole chain, from the catalogue.
Method and formulas
- PD = p ÷ sin(180° ÷ z); chain speed v = z₁ p n₁ ÷ 60,000.
- Design power = P × SF against rating × multi-strand factor; pull = P ÷ v + m v²; safety factor = breaking load ÷ pull.
- Links L = 2C + (z₁ + z₂) ÷ 2 + [(z₂ − z₁) ÷ 2π]² ÷ C, rounded up to even; exact C = p ÷ 4 {L − (z₁ + z₂) ÷ 2 + √[(L − (z₁ + z₂) ÷ 2)² − 8 ((z₂ − z₁) ÷ 2π)²]}.
- Chordal speed variation = 1 − cos(180° ÷ z₁).
- Example: 5.5 kW at 300 rpm on 19/57 teeth needs 120 links at 643.72 mm centres.
Limitations
- Ratings depend on lubrication; the per-strand rating must match your lubrication method.
- Two-sprocket drive without idlers.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Select a roller chain for a conveyor or machine drive
- Lay out sprockets and centre distance
- Check an existing chain against a power increase
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Pitch diameters, speeds and chain pull
- Rating and breaking-load checks
- Chain length, centre distance, wrap and chordal action
Interpreting the result
- Small sprockets under 17 teeth run rough and wear fast; more teeth smooth the drive.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2537–2556. Topic reference; no source tables or recommended settings are reproduced.
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