KEVOS® MAKEOS · Gears
Spur Gear Contact Diameters, Contact Ratio and LPSTC
Where does contact start on each gear, what is the contact ratio, and where is the lowest point of single tooth contact?
For two spur gears at standard centre distance: the contact (start of active profile) diameter on each gear, the contact ratio by two independent formulas, the lowest point of single tooth contact (LPSTC) on each gear for contact stress checks, and the maximum hob tip radius for the tooth system.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module (25.4 ÷ diametral pitch). |
| Teeth on gear 1 (pinion) | Number of teeth on the first gear. | |
| Teeth on gear 2 | Number of teeth on the second gear. | |
| Pressure angle | ° | Pressure angle. |
| Outside diameter of gear 1 (0 = standard) | mm | Actual outside diameter of gear 1; 0 uses the standard m (z + 2). |
| Outside diameter of gear 2 (0 = standard) | mm | Actual outside diameter of gear 2; 0 uses the standard value. |
| Dedendum constant b (dedendum = b × module) | Dedendum as a multiple of module for the tooth system (1.25 for standard full depth). |
Method and formulas
- With P = 1 ÷ m: cos A = N cos φ ÷ (D₀ P); tan b = tan φ − (N ÷ n)(tan A − tan φ); contact diameter d_c = n cos φ ÷ (P cos b), and likewise for the other gear.
- Contact ratio m_f = N (tan A − tan B) ÷ 2π = n (tan a − tan b) ÷ 2π (both are reported as a check).
- LPSTC: tan c = tan a − 2π ÷ n; d_L = n cos φ ÷ (P cos c).
- Maximum hob tip radius = m (0.785398 cos φ − b sin φ) ÷ (1 − sin φ).
- Example: 20 and 40 teeth, module 1, contact begins at 18.878 mm on the pinion with a contact ratio of 1.6352.
Limitations
- Standard centre distance and standard tooth thickness; operating centre distance changes the result.
- A contact diameter at or below the base circle indicates interference.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Specify the form diameter a ground or hobbed profile must reach
- Find the critical diameter for Hertz stress
- Check contact ratio after changing outside diameters
Who it is for
- Gear designers
- Gear inspectors
- Machinists
What you get
- Contact diameter on each gear
- Contact ratio
- LPSTC diameters and maximum hob tip radius
Interpreting the result
- Keep the true involute form diameter below the contact diameter, and the contact ratio above about 1.4 for power gears.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2155–2157. Topic reference; no source tables or recommended settings are reproduced.
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Open the Spur Gear Contact Diameters, Contact Ratio and LPSTC calculator
