BIZOMAT MAKEOS · Power Transmission
Timing Belt Drive Design (Length, Mesh and Belt Width)
What belt length and centre distance does this timing belt drive need, are enough teeth in mesh, and how wide must the belt be for the power?
Design of a synchronous (timing) belt drive: pulley pitch diameters from the pitch and tooth counts, exact pitch length for the centre distance, rounding to a whole number of belt teeth and the centre distance that belt gives, teeth in mesh on the small pulley (as the timing belt tool), belt speed, effective pull from the power with a service factor, and the belt width needed from your allowable working tension per millimetre of width.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power transmitted. |
| Small pulley speed | rpm | Speed of the small pulley. |
| Service factor | Service factor for the driven machine and running hours (from the belt maker). | |
| Belt pitch | mm | Pitch of the belt teeth. |
| Small pulley teeth | Teeth on the small pulley. | |
| Large pulley teeth | Teeth on the large pulley. | |
| Approximate centre distance | mm | Centre distance you would like; the tool finds the nearest belt. |
| Allowable working tension per mm of width | N/mm | Allowable working tension per mm of belt width at this speed and pulley size (your value from the belt maker). |
| Belt width chosen | mm | Belt width being considered. |
| Least teeth in mesh | Least teeth in mesh on the small pulley (the belt maker’s rule, often 6). | |
| Largest belt speed | m/s | Largest belt speed for the belt and pulleys. |
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
- The power the belt carries from the small pulley to the large one, normally the motor output or the power the driven machine needs.
- 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 0.5 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effective pull and the belt width needed rise in proportion.
What this means: Small pulley speed
- What it is
- How fast the small pulley turns. With its pitch diameter it sets the 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
- A higher speed raises the belt speed, which lowers the pull and the width needed.
- Get it right
- Enter the small pulley speed, whether it is the driver or the driven pulley.
What this means: Service factor
- What it is
- A multiplier on the power that allows for the type of driven machine, shock loads and daily running hours, from the belt maker’s service factor table.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effective pull and the belt width needed rise in proportion.
What this means: Belt pitch
- What it is
- The distance from one belt tooth to the next, measured along the belt’s pitch line. Belt and pulleys must share the same pitch and tooth profile.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Belts of the same pitch but different tooth profiles do not run on each other’s pulleys.
What this means: Small pulley teeth
- What it is
- The number of teeth on the smaller pulley. With the pitch it sets that pulley’s pitch diameter and how many teeth are in mesh.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 200. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the smaller pulley here; the tool stops if it has more teeth than the large one.
What this means: Large pulley teeth
- What it is
- The number of teeth on the larger pulley. With the small pulley it sets the speed ratio.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 500. Use a whole number. 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.
What this means: Approximate centre distance
- What it is
- The distance between the two pulley shafts you would like. The tool picks the nearest whole-tooth belt and reports the exact centre distance for it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Allow adjustment in the mounting for fitting the belt and setting tension.
What this means: Allowable working tension per mm of width
- What it is
- The working pull each millimetre of belt width may carry at this belt speed and pulley size, from the belt maker’s rating data.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0.000001 N/mm to 1000 N/mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The belt width needed is inversely proportional to this value.
What this means: Belt width chosen
- What it is
- The belt width you plan to use, compared with the width needed for the power.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Choose a standard width the maker supplies for this pitch.
What this means: Least teeth in mesh
- What it is
- The fewest belt teeth you accept in engagement with the small pulley, from the belt maker’s rule. Too few teeth in mesh lets the belt jump teeth.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest belt speed
- What it is
- The highest belt speed the belt and pulleys are rated for, from the belt and pulley maker’s data.
- 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 40 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Pitch diameter = z p ÷ π; pitch length L = 2√[C² − ((D − d) ÷ 2)²] + π(D + d) ÷ 2 + (D − d) sin⁻¹[(D − d) ÷ 2C]; belt teeth = round(L ÷ p); centre distance found for that belt (as the timing belt tool).
- Wrap on the small pulley = 180° − 2 sin⁻¹[(D − d) ÷ 2C]; teeth in mesh = z₁ × wrap ÷ 360.
- Belt speed v = π d n ÷ 60 000; effective pull F_e = P × SF ÷ v; width needed = F_e ÷ allowable tension per mm.
- Example: a 110-tooth belt sets the centres at 199.36 mm; 9.4912 teeth mesh and the belt needs 11.586 mm of width.
Limitations
- Width from a single allowable tension per mm; makers’ rating tables include speed and pulley-size effects.
- Shaft loads depend on installation tension: follow the maker’s tensioning method.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a timing belt drive for a machine axis or pump
- Choose a belt width for a power
- Check teeth in mesh for a small pulley
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Pitch diameters, belt length and actual centre distance
- Teeth in mesh and belt speed
- Effective pull and belt width needed
Interpreting the result
- If too few teeth mesh, use a larger small pulley or a wider belt rating with a mesh correction.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2473–2535. Topic reference; no source tables or recommended settings are reproduced.
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.
Open the Timing Belt Drive Design (Length, Mesh and Belt Width) calculator