BIZOMAT MAKEOS · Power Transmission
Silent Chain Drive Check (Sprocket Diameters, Chain Length, Speed, Wrap)
For this inverted-tooth (silent) chain drive, what are the sprocket diameters, how many links do I order, what centre distance results, and are the chain speed and wrap acceptable?
Layout check of a silent (inverted-tooth) chain drive: pitch, outside and guide-groove diameters and the over-pin gauge for both sprockets (as the silent chain sprocket tool), chain length in pitches rounded to an even number of links, the exact centre distance for that length, chain speed and wrap on the small sprocket (as the chain length tool), the ratio and driven speed, checked against your chain speed limit, least small-sprocket teeth and least wrap.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch | mm | Pitch of the silent chain. |
| Small sprocket teeth | Teeth on the small (driving) sprocket. | |
| Large sprocket teeth | Teeth on the large sprocket. | |
| Approximate centre distance | mm | Centre distance you plan. |
| Small sprocket speed | rpm | Speed of the small sprocket. |
| Limits | ||
| Largest chain speed | m/s | Highest chain speed for the chain type and lubrication (from the maker). |
| Least small-sprocket teeth | Fewest teeth you accept on the small sprocket for smooth running. | |
| Least wrap on the small sprocket | ° | Least wrap angle you accept on the small 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 pitch of the silent (inverted-tooth) chain: the distance between the centres of adjacent link pins, from the chain maker’s catalogue.
- Units and format
- Enter a number in mm: millimetres. The form accepts 9.5 mm to 200 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
- All sprocket diameters and the chain speed rise in direct proportion to the pitch.
- Get it right
- Use the chain pitch, not a sprocket dimension; for an inch chain convert to millimetres (1 in = 25.4 mm).
What this means: Small sprocket teeth
- What it is
- The number of teeth on the small sprocket, which is the driving sprocket in this tool and whose speed sets the chain speed.
- Units and format
- Enter a plain number with no unit. The form accepts 13 to 200. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth raise the chain speed and the small sprocket diameter and reduce the ratio.
- Get it right
- Enter the small sprocket even if it is the driven one in your machine, and use its speed below.
What this means: Large sprocket teeth
- What it is
- The number of teeth on the large sprocket; with the small sprocket it sets the ratio and the driven speed.
- Units and format
- Enter a plain number with no unit. The form accepts 13 to 400. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 42 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth increase the ratio and the chain length and reduce the wrap on the small sprocket.
- Get it right
- It must be at least the small sprocket tooth count.
What this means: Approximate centre distance
- What it is
- The centre distance between the sprocket shafts that you plan; the tool rounds the chain to an even number of links and reports the exact distance for it.
- 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 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Treat it as a starting value: the exact centre distance will differ slightly, so allow adjustment or a tensioner.
What this means: Small sprocket speed
- What it is
- The rotational speed of the small sprocket, from the motor or gearbox output that drives it.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Chain speed rises in direct proportion to this speed.
- Get it right
- Give the speed of the small sprocket, not the large one; the driven speed is calculated.
Limits
What this means: Largest chain speed
- What it is
- The highest chain speed the chain maker allows for this chain type and lubrication method.
- 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 15 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the chain maker’s catalogue for your lubrication method; the limit changes with the lubrication.
What this means: Least small-sprocket teeth
- What it is
- The fewest teeth you accept on the small sprocket, set to keep chordal action, noise and wear acceptable.
- Units and format
- Enter a plain number with no unit. The form accepts 13 to 100. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the chain maker’s guidance or your company standard for the duty.
What this means: Least wrap on the small sprocket
- What it is
- The smallest angle of chain contact you accept around the small sprocket, measured at the sprocket centre.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 60° to 180°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Wrap shrinks as the ratio rises and the centre distance falls; take the limit from the chain maker.
Method and formulas
- Pitch diameter = P ÷ sin(180° ÷ N); outside = P (cot(180° ÷ N) + 0.08); guide groove = P (cot(180° ÷ N) − 1.16); over-pin gauge from the handbook formulas (as the silent chain sprocket tool).
- Length in pitches = 2C ÷ P + (N₁ + N₂) ÷ 2 + [(N₂ − N₁) ÷ 2π]² ÷ (C ÷ P), rounded up to an even number; exact centre distance for that length (as the chain length tool).
- Chain speed = P N₁ n ÷ 60 000; wrap = 180° − 2 sin⁻¹[(D₂ − D₁) ÷ 2C].
- Example: sprockets 85.211 and 169.94 mm pitch diameter; order 96 links for 407.36 mm centres; chain speed 5.334 m/s.
Limitations
- Sprocket formulas for 3/8 in (9.525 mm) and larger pitches.
- Layout only: power rating comes from the chain maker’s tables.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a silent chain drive
- Check sprocket blanks and gauge sizes
- Order chain length for a fixed centre distance
Who it is for
- Design engineers
- Maintenance engineers
- Machinists
What you get
- Sprocket diameters and gauge sizes
- Chain links and exact centre distance
- Chain speed, wrap and ratio
Interpreting the result
- Silent chains run quietly at high speed, but only if the small sprocket has enough teeth.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3457–3460, 2537–2560. Topic reference; no source tables or recommended settings are reproduced.
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Open the Silent Chain Drive Check (Sprocket Diameters, Chain Length, Speed, Wrap) calculator