BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Normal module
- What it is
- The normal module of the gear, equal to the module of the cutting tool.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The base tangent length scales in proportion.
- Get it right
- For a helical gear do not use the transverse module.
What this means: Number of teeth
- What it is
- The number of teeth on the gear being measured.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count the whole gear, not just the teeth spanned.
What this means: Normal pressure angle
- What it is
- The pressure angle of the tooth profile in the normal plane, set by the cutting tool.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the angle on the gear drawing.
What this means: Helix angle (0 = spur)
- What it is
- The angle of the teeth to the gear axis at the pitch circle. It changes the transverse pressure angle and the face width needed for the anvils.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- 0 means a spur gear; the face width check is then skipped.
What this means: Profile shift coefficient
- What it is
- The profile shift coefficient: how far the cutter was moved out (positive) or in (negative) from standard, as a multiple of the module.
- Units and format
- Enter a plain number with no unit. The form accepts -1 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For the same number of teeth spanned, a positive shift increases the base tangent length.
- Get it right
- Take it from the gear drawing; 0 means an unshifted gear. Enter the coefficient, not the shift in millimetres.
What this means: Teeth spanned (0 = recommended)
- What it is
- How many teeth the disc micrometer anvils span. 0 lets the tool choose the usual number, so the anvils touch near the pitch circle.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 500 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each extra tooth spanned adds one base pitch to the length.
- Get it right
- If you enter your own number, check that the anvils touch the flanks, not the tips or roots.
What this means: Face width (helical check)
- What it is
- The axial width of the gear teeth, used only on helical gears to check that the anvils fit across the face.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored for spur gears.
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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