KEVOS® MAKEOS · Gears
Gear Pair for a Given Centre Distance (Profile Shift, Tips, Contact Ratio)
What profile shifts make this spur gear pair fit my centre distance, what tip diameters does that give, and is the contact ratio and undercut acceptable?
Design of an external spur gear pair to an off-standard centre distance: working pressure angle from the centre distance, the sum of profile shift coefficients from the involute function, its split between pinion and gear, tip diameters with or without tip shortening to keep the standard clearance, the contact ratio with those tips (as the contact ratio tool), the undercut limit for each gear, and the working pressure angle check against the profile shift tool.
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 of the tooling. |
| Centre distance required | mm | Centre distance the housing fixes. |
| Share of the total shift on the pinion | % | How much of the total profile shift goes on the pinion (more on the pinion helps strength and avoids undercut). |
| Tip shortening | choice | Whether the tip diameters are reduced so the clearance stays at the standard value. |
| Smallest contact ratio wanted | Least transverse contact ratio you accept. |
Method and formulas
- Standard centre distance a = m (z₁ + z₂) ÷ 2; working pressure angle cos α_w = a cos α ÷ a_w.
- Σx = (inv α_w − inv α)(z₁ + z₂) ÷ (2 tan α); split by the share (as the profile shift tool in reverse).
- Centre distance factor y = (a_w − a) ÷ m; tip shortening k = Σx − y; tip radius r_a = m (z ÷ 2 + 1 + x − k).
- Contact ratio ε = [√(r_a1² − r_b1²) + √(r_a2² − r_b2²) − a_w sin α_w] ÷ (π m cos α) (as the contact ratio tool); no undercut if x ≥ 1 − z sin²α ÷ 2.
- Example: 55 mm needs Σx = 0.53289 (pinion 0.37302, gear 0.15987) at 22.69° working angle; contact ratio 1.4127.
Limitations
- External spur gears of standard full-depth proportions.
- Tooth tip thickness (pointing) at large shifts is not checked: verify it on the drawing.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Fit a gear pair into an existing housing
- Avoid undercut on a small pinion
- Check the contact ratio after shifting
Who it is for
- Gear engineers
- Design engineers
- Machinists
What you get
- Working pressure angle and total profile shift
- Shift, tip diameter and undercut check for each gear
- Contact ratio
Interpreting the result
- Putting most of the positive shift on the pinion strengthens it and keeps it clear of undercut.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2141–2160. 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 Gear Pair for a Given Centre Distance (Profile Shift, Tips, Contact Ratio) calculator
