BIZOMAT MAKEOS · Gears
Involute Gear Cutter Number
Which involute gear milling cutter number should cut this spur, helical or bevel gear?
The standard involute gear milling cutter number (1 to 8, and the half-number series) for a spur gear, or for a helical or bevel gear from its formative (equivalent) number of teeth.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Gear type | choice | Kind of gear being milled. |
| Number of teeth | teeth | Actual number of teeth. |
| Helix angle (helical) | ° | Helix angle of a helical gear. |
| Pitch cone angle (bevel) | ° | Pitch cone angle of a bevel gear (see the bevel gear tool). |
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: Gear type
- What it is
- The kind of gear being cut with a form milling cutter: spur, helical or bevel. Helical and bevel gears are cut with the cutter for their formative (equivalent) number of teeth.
- Units and format
- Choose one of 3 options from the list: Spur gear; Helical gear; Bevel gear.
- Example
- The form opens with “Helical gear” selected as a worked example. Choose the option that matches your case.
- Get it right
- For a helical gear only the helix angle is used, and for a bevel gear only the pitch cone angle.
What this means: Number of teeth
- What it is
- The actual number of teeth on the gear being cut, from the gear drawing.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 12 teeth to 10000 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.
- Effect on the result
- More teeth give more formative teeth and a lower cutter number.
- Get it right
- Enter the real tooth count; the tool works out the formative teeth for helical and bevel gears.
What this means: Helix angle (helical)
- What it is
- The angle between the helical teeth and the gear axis, measured at the pitch diameter. Only a helical gear uses it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 60°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The formative tooth count rises with 1 ÷ cos³ of the helix angle.
- Get it right
- Measured from the axis, not from the face of the gear.
What this means: Pitch cone angle (bevel)
- What it is
- The angle between the bevel gear’s axis and its pitch cone surface, from the gear drawing or the bevel gear tool. Only a bevel gear uses it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The formative tooth count rises with 1 ÷ cos of the pitch cone angle.
- Get it right
- This is the pitch cone angle of the gear being cut, not the shaft angle between the two gears.
Method and formulas
- Helical: formative teeth = N ÷ cos³ψ. Bevel: formative teeth = N ÷ cos δ (back-cone method).
- Regular cutters: No. 1 135–rack; 2 55–134; 3 35–54; 4 26–34; 5 21–25; 6 17–20; 7 14–16; 8 12–13.
- Half numbers: 1½ 80–134; 2½ 42–54; 3½ 30–34; 4½ 23–25; 5½ 19–20; 6½ 15–16; 7½ 13.
- Example: a 30-tooth helical gear at 30° has 46.188 formative teeth: use a No. 3 cutter.
Limitations
- Form cutters give approximately correct profiles; generated teeth (hobbing, shaping) are more accurate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Pick the right form cutter for milling gear teeth
- Find the equivalent teeth for helical and bevel gears
- Decide when a half-number cutter is worth using
Who it is for
- Machinists
- Toolmakers
What you get
- Formative (equivalent) number of teeth
- Regular cutter number
- Half-number cutter
Interpreting the result
- Use the half-number cutter when the tooth count is near the lower end of a regular cutter’s range and accuracy matters.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2148–2150, 820–829. Topic reference; no source tables or recommended settings are reproduced.
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