KEVOS® MAKEOS · Gears
Helical Gear Milling Cutter Selection (Preferred Formula with Cutter Diameter, Lead, Tooth Depth)
Which involute formed cutter do I use to mill a helical gear, by the handbook’s preferred formula that allows for the cutter diameter, and what lead, tooth depth and tooth thickness go with it?
Selecting the formed milling cutter for a helical gear by the handbook’s preferred formula N′ = N sec³ α + Pn Dc tan² α (written N′ = N K + Q K′ with K = sec³ α, K′ = tan² α and Q = Pn Dc), which gives correct results for all combinations of helix angle and tooth number, compared with the approximate N′ = N ÷ cos³ α; the cutter number from the involute cutter series (regular and half-number); with the pitch diameter N ÷ (Pn cos α), lead π D cot α, whole depth 2.157 ÷ Pn and tooth thickness 1.571 ÷ Pn at the pitch line.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Teeth in the helical gear N | teeth | Actual number of teeth in the helical gear. |
| Helix angle α | ° | Helix angle of the gear teeth, measured from the axis. |
| Normal module mn (25.4 ÷ Pn) | mm | Normal module of the gear and cutter; for a normal diametral pitch Pn it is 25.4 ÷ Pn. |
| Pitch diameter of the cutter Dc | mm | Pitch diameter of the formed cutter, from the cutter maker or the handbook’s cutter table. |
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: Teeth in the helical gear N
- What it is
- Actual number of teeth in the helical gear to be milled.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The cutter tooth number rises in proportion.
- Get it right
- Count the teeth on the drawing, not the equivalent number.
What this means: Helix angle α
- What it is
- Helix angle of the gear teeth, measured from the gear axis.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 75°. 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
- A larger angle raises the cutter tooth number sharply.
- Get it right
- Set the milling machine table to this angle.
What this means: Normal module mn (25.4 ÷ Pn)
- What it is
- Normal module of the gear teeth, the size of tooth in the normal plane.
- 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 1.27 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales every diameter, lead and tooth dimension.
- Get it right
- For an inch normal diametral pitch Pn, enter 25.4 ÷ Pn.
What this means: Pitch diameter of the cutter Dc
- What it is
- Pitch diameter of the formed involute cutter you will use.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 48.006 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger cutter raises the cutter tooth number.
- Get it right
- Measure the cutter as it is now, after sharpening.
Method and formulas
- K = sec³ α; K′ = tan² α; Q = Pn Dc = Dc ÷ mn.
- N′ = N K + Q K′ (preferred); N′ = N K (approximate); round and look up the involute cutter series.
- D = N mn ÷ cos α; lead L = π D cot α; set the table to α.
- Whole depth 2.157 mn (2.157 ÷ Pn); tooth thickness at the pitch line 1.571 mn (1.571 ÷ Pn).
- Example: 15 teeth at 30° give N′ = 35.694 (cutter No. 3) against 23.094 by the approximate formula.
Limitations
- The cutter series covers 12 teeth to a rack; below 12 cutter teeth the gear is outside the series.
- The cutter pitch diameter changes as the cutter is sharpened; use its current size.
- Formed cutters give an approximate involute; hob or grind gears that need accuracy.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose the involute cutter for milling a helical gear on a dividing head
- Check whether the approximate formula picks the wrong cutter
- Find the lead, tooth depth and tooth thickness for milling
Who it is for
- Machinists and gear cutters
- Toolmakers
- Gear designers
What you get
- Factors K = sec³ α, K′ = tan² α and Q = Pn Dc
- Cutter teeth N′ by the preferred and approximate formulas
- Cutter number in the regular and half-number series
- Pitch diameter and lead of the gear
- Whole depth and tooth thickness at the pitch line
Interpreting the result
- At high helix angles with few teeth the approximate formula picks too high a cutter number (too few teeth).
- A larger cutter diameter raises N′, so the same gear may need a different cutter with another cutter size.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2204–2206, 2150. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Helical gears and axial thrust
What it covers: Convert between normal and transverse module, size a helical pair to a centre distance, and calculate the axial thrust and face overlap the helix creates.
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