KEVOS® MAKEOS · Gears
Profile Shift and Working Centre Distance
What working centre distance and pressure angle result from these profile shifts, and are the teeth undercut?
Working pressure angle, working centre distance and centre distance modification for a spur gear pair with profile shift, the undercut check and the backlash change at an actual centre distance.
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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 | ° | Standard pressure angle. |
| Pinion profile shift coefficient | Profile shift coefficient of the pinion (positive = cutter withdrawn). | |
| Gear profile shift coefficient | Profile shift coefficient of the gear. | |
| Actual centre distance (0 = not set) | mm | Housing centre distance, to find the backlash change from the zero-backlash position. |
Method and formulas
- inv αw = 2(x₁ + x₂) tan α ÷ (z₁ + z₂) + inv α (solved by Newton’s method).
- Standard a₀ = m(z₁ + z₂) ÷ 2; working aw = a₀ cos α ÷ cos αw.
- No undercut when x ≥ 1 − z sin²α ÷ 2.
- Circumferential backlash change ≈ 2(a_actual − aw) tan αw.
- Example: x₁ = 0.2 on 14/40 teeth gives αw = 21.099° and aw = 54.39 mm.
Limitations
- Zero-backlash working distance; tooth thinning for backlash is separate.
- Large positive shifts can give pointed teeth; check tip thickness.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Fit a gear pair to a non-standard centre distance
- Avoid undercut on small pinions
- Estimate backlash change from centre distance
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Working pressure angle
- Working centre distance and modification
- Undercut check for each gear
- Backlash change at the actual centre distance
Interpreting the result
- Distribute the total shift between pinion and gear to balance strength and avoid undercut on the pinion.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2141–2160. Topic reference; no source tables or recommended settings are reproduced.
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