KEVOS® MAKEOS · Gears
Bevel Gear Milling Offset and Caliper Settings (Cutter Setover, Cutting Angle, Chordal Thickness at Both Ends)
When milling a bevel gear with a formed cutter in two cuts, how far must I offset the blank from the central position, what cutting angle do I set on the dividing head, and what chordal thickness and chordal addendum do I set the gear tooth caliper to at the large and small ends of the tooth?
Set-up for milling a bevel gear with a rotary formed cutter by the handbook method: pitch diameter and pitch cone radius C = D ÷ 2 sin γ, the ratio C ÷ F for reading the offset factor, the number of teeth N ÷ cos γ for selecting the cutter, the depth 1.157 ÷ P at which to measure the cutter thickness, the offset T ÷ 2 − factor ÷ P from the cutter’s measured thickness and the factor you read from the handbook table, the dividing head cutting angle (pitch cone angle less addendum angle), and the circular and chordal thickness and chordal addendum at the large end (T = 1.5708 ÷ P, Tc = T − T³ ÷ 6D², Sc = S + T² cos γ ÷ 4D) and at the small end in the ratio (C − F) ÷ C.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module m (25.4 ÷ P) | mm | Module of the gear; for a diametral pitch P it is 25.4 ÷ P. |
| Teeth in gear being cut N | teeth | Number of teeth in the bevel gear being milled. |
| Pitch cone angle γ | ° | Pitch cone angle of the gear being milled. |
| Face width F | mm | Width of face (tooth length). |
| Cutter and offset factor | ||
| Cutter thickness at pitch line, measured at depth 1.157 ÷ P | mm | Thickness of the formed cutter at its pitch line, measured with a gear tooth caliper at the depth shown. |
| Offset factor from the handbook table (for the cutter number and C ÷ F) | Factor read from the handbook’s offset factor table for the cutter number and the ratio C ÷ F shown here. | |
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: Module m (25.4 ÷ P)
- What it is
- Module of the bevel gear being milled, the pitch diameter per tooth in millimetres.
- 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 4.233333 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, depth and tooth thickness.
- Get it right
- For an inch diametral pitch P, enter 25.4 ÷ P.
What this means: Teeth in gear being cut N
- What it is
- Number of teeth in the bevel gear being milled.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 24 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the pitch diameter and the cutter selection.
- Get it right
- Count the teeth on the drawing or the part.
What this means: Pitch cone angle γ
- What it is
- Pitch cone angle of the gear being milled.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.000001° to 89.9°. 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
- Sets the pitch cone radius and the cutting angle.
- Get it right
- Take it from the gear drawing or the milled bevel gear tool.
What this means: Face width F
- What it is
- Width of face, the length of the teeth along the pitch cone.
- 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 31.75 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider face makes the small-end teeth smaller.
- Get it right
- Keep it to a third of the pitch cone radius or less.
Cutter and offset factor
What this means: Cutter thickness at pitch line, measured at dep…
- What it is
- Thickness of the formed cutter at its pitch line.
- 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 4.4323 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The offset rises by half of any increase.
- Get it right
- Measure it with a gear tooth caliper set to the depth shown, after each sharpening.
What this means: Offset factor from the handbook table (for the…
- What it is
- Offset factor from the handbook table for milling bevel gears.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.28 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger factor reduces the offset.
- Get it right
- Read it for the cutter number and the ratio C ÷ F the tool shows.
Method and formulas
- D = N m; C = D ÷ (2 sin γ); ratio C ÷ F; N′ = N ÷ cos γ.
- Measure the cutter thickness T at depth S + A = 1.157 m.
- Offset = T ÷ 2 − factor × m (factor ÷ P in inches).
- Cutting angle = γ − α, where tan α = S ÷ C.
- Large end: T = 1.5708 m; Tc = T − T³ ÷ 6D²; Sc = S + T² cos γ ÷ 4D.
- Small end: t = T (C − F) ÷ C; s = S (C − F) ÷ C; tc = t − t³ ÷ 6(D − 2F sin γ)²; sc = s + t² cos γ ÷ 4(D − 2F sin γ).
- Example: offset the blank 1.0308 mm each side of centre and set the dividing head to 27.614°.
Limitations
- The offset factor comes from the handbook table for the cutter number and C ÷ F; enter it, do not guess it.
- The offset is a starting setting: trial cuts and caliper checks at both ends correct it, as the handbook describes.
- Bevel gear cutters are relieved on the sides, so measure the cutter thickness each time it is sharpened.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the blank over by the right amount for the two cuts on each tooth space
- Set the dividing head to the cutting angle
- Check the teeth at both ends with a gear tooth caliper
Who it is for
- Machinists and gear cutters
- Gear designers
- Students
What you get
- Pitch cone radius and the ratio C ÷ F for the factor table
- Number of teeth for selecting the cutter
- Depth at which to measure the cutter
- Offset of the blank from the central position
- Dividing head cutting angle
- Chordal thickness and chordal addendum at the large and small ends
Interpreting the result
- If the large end is right and the small end too thick, the blank was offset too much; if the small end is right and the large end too thick, it was not offset enough.
- File the small-end tooth sides afterwards as the handbook shows to correct the milled form.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2188–2189. Topic reference; no source tables or recommended settings are reproduced.
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