KEVOS® MAKEOS · Gears
Gear Span (Base Tangent) Measurement
What should the span measurement over k teeth read for this spur or helical gear?
Base tangent length (span measurement, Wildhaber) over k teeth for external spur and helical gears, including profile shift, with the number of teeth to span.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal module | mm | Normal module. |
| Number of teeth | teeth | Number of teeth. |
| Normal pressure angle | ° | Normal pressure angle. |
| Helix angle (0 = spur) | ° | Helix angle at the pitch circle; 0 for spur. |
| Profile shift coefficient | Profile shift coefficient from the gear drawing (0 if not shifted). | |
| Teeth spanned (0 = recommended) | teeth | Number of teeth to span; 0 chooses the usual value so the anvils touch near the pitch circle. |
| Face width (helical check) | mm | Face width, to check the anvils fit across a helical gear. |
Method and formulas
- inv α = tan α − α; αt = atan(tan αn ÷ cos β).
- W = mn cos αn [π(k − 0.5) + z inv αt] + 2 x mn sin αn.
- Recommended k = (z/π)[√((1 + 2x/z)² − cos²αt) ÷ cos αt − inv αt − 2x tan αn ÷ z] + 0.5, rounded (z αt ÷ 180° + 0.5 when x = 0).
- Helical: the face width must exceed W sin βb, with sin βb = sin β cos αn.
- Example: module 3, 30 teeth: span 4 teeth and expect W = 32.258 mm.
Limitations
- External gears; internal gears need measurement over pins.
- Thinned tooth thickness for backlash must be subtracted from W (by the normal thickness reduction × cos αn).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect tooth thickness with a disc micrometer
- Set hobbing depth
- Check profile-shifted gears
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Teeth spanned
- Base tangent length W
- Face width needed for helical gears
Interpreting the result
- Subtract the design thinning for backlash to get the inspection value.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2236–2248. Topic reference; no source tables or recommended settings are reproduced.
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