BIZOMAT MAKEOS · Gears
Spur Gear Contact Ratio
What transverse contact ratio does this spur gear pair have?
Transverse contact ratio of an external spur gear pair from module, tooth counts, pressure angle and profile shifts, with base pitch and length of contact.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module. |
| Pinion teeth | teeth | Pinion tooth count. |
| Gear teeth | teeth | Gear tooth count. |
| Pressure angle | ° | Pressure angle. |
| Pinion profile shift | Pinion profile shift coefficient (0 if standard). | |
| Gear profile shift | Gear profile shift coefficient. |
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: Module
- What it is
- The module of the gear pair: pitch diameter divided by number of teeth, which sets the tooth size and base pitch.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a diametral pitch gear, the module is 25.4 divided by the diametral pitch.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller gear of the external pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 1000 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.
What this means: Gear teeth
- What it is
- The number of teeth on the larger gear of the external pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Pressure angle
- What it is
- The standard pressure angle of the gear teeth, which sets the base circle and the line of action.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. 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.
What this means: Pinion profile shift
- What it is
- The profile shift coefficient of the pinion, a multiple of the module; zero for a standard unshifted gear.
- Units and format
- Enter a plain number with no unit. The form accepts -1 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is a coefficient, not a distance in millimetres.
What this means: Gear profile shift
- What it is
- The profile shift coefficient of the larger gear, a multiple of the module; zero for a standard unshifted gear.
- Units and format
- Enter a plain number with no unit. The form accepts -1 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Tip radius rₐ = m(z/2 + 1 + x); base radius r_b = m z cos α ÷ 2.
- Working distance aw from the profile shifts (involute relation).
- ε = [√(rₐ₁² − r_b1²) + √(rₐ₂² − r_b2²) − aw sin αw] ÷ (π m cos α).
- Example: 20/50 teeth at 20° give a contact ratio of 1.6558.
Limitations
- Standard addendum (tip diameter not shortened); tip relief and chamfers reduce the effective ratio.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check smoothness and load sharing of a gear pair
- Compare tooth counts and pressure angles
- Verify a gear design
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Tip and base radii
- Working centre distance
- Length of contact and base pitch
- Contact ratio
Interpreting the result
- Keep the contact ratio above about 1.2; values near 2 give very smooth running.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
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