KEVOS® MAKEOS · Gears
Spur Gear Mesh Interference Check (Contact Start Diameters and Contact Ratio)
Does contact on each gear of this spur pair start above its true involute form diameter, so there is no interference, and is the contact ratio enough?
Check of a standard spur gear pair for tip-to-root interference: the diameter on each gear where contact begins (the start of active profile) from the mating gear’s outside diameter (as the spur contact diameters tool), compared with the true involute form diameter each gear actually has after cutting, the margin above it and above the base circle, and the transverse contact ratio from the outside diameters (as the contact ratio tool for standard gears).
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module of both gears. |
| Pinion teeth | Teeth on the pinion. | |
| Gear teeth | Teeth on the gear. | |
| Pressure angle | ° | Pressure angle. |
| Pinion outside diameter (0 = standard) | mm | Actual outside diameter of the pinion (0 for standard m(z + 2)). |
| Gear outside diameter (0 = standard) | mm | Actual outside diameter of the gear (0 for standard). |
| Pinion true involute form diameter | mm | Diameter on the pinion below which the tooth is no longer a true involute (from the cutting tool or drawing). |
| Gear true involute form diameter | mm | True involute form diameter on the gear. |
| Least contact ratio | Least transverse contact ratio you accept. |
Method and formulas
- From the mating outside diameter, the roll angle at the start of contact gives the start-of-active-profile diameter on each gear (as the spur contact diameters tool).
- No interference if the start diameter is at or above the true involute form diameter (and above the base circle).
- Contact ratio ε = [√(r_a1² − r_b1²) + √(r_a2² − r_b2²) − a sin φ] ÷ (π m cos φ) with a = m (z₁ + z₂) ÷ 2.
- Example: contact starts at 18.878 mm on the pinion (form 18.5 mm) and 38.67 mm on the gear (form 38.3 mm); contact ratio 1.6352.
Limitations
- Standard centre distance and unshifted teeth; shifted gears need the working pressure angle.
- Tip rounding and chamfers reduce the effective outside diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a pinion for interference with a large gear
- Set the form diameter on a gear drawing
- Check the effect of a reduced outside diameter
Who it is for
- Gear engineers
- Design engineers
- Gear inspectors
What you get
- Contact start diameter on each gear
- Margin over the form diameter and base circle
- Contact ratio
Interpreting the result
- If contact starts below the form diameter, reduce the mating outside diameter or use a profile shift.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2155–2157, 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
WORKOS 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 Spur Gear Mesh Interference Check (Contact Start Diameters and Contact Ratio) calculator
