KEVOS® 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. |
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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