KEVOS® MAKEOS · Manufacturing
Milling Mean Chip Thickness and Equivalent Chip Thickness (Feed per Tooth for Light Radial Cuts)
In end, side or face milling with a given radial depth, cutter diameter, number of teeth and feed per tooth, what is the angle of engagement, the mean chip thickness and the equivalent chip thickness, and what feed per tooth keeps the chip as thick as I want when the radial cut is light?
Chip geometry in milling by the handbook: the angle of engagement AE from cos AE = 1 − 2(ar/D) for end and side milling, or cos AE = 1 − 2(ar/D)² for face milling with the cutter centred on the work; the mean chip thickness over the arc of engagement, hm = fz (1 − cos AE) ÷ AE (end milling) or fz × 2 sin(½AE) ÷ AE (centred face milling), which reproduces the handbook Table 2a; the equivalent chip thickness ECT = fz × z ÷ π × (ar ÷ D) × aa ÷ CEL; the feed per tooth needed for a target mean chip thickness, and its ratio to the feed at the reference engagement (full slot for end milling, ar/D = 0.74 for face milling); with a check against the minimum chip thickness you set.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Operation | choice | End or side milling with the cutter at the edge of the cut, or face milling with the cutter centred on the work (eccentricity near zero). |
| Cutter diameter D | mm | Diameter of the milling cutter. |
| Radial depth (width) of cut ar | mm | Radial depth (width) of cut; equal to the cutter diameter for a full slot. |
| Number of teeth z | teeth | Number of teeth (inserts) on the cutter. |
| Feed per tooth fz | mm | Feed per tooth now used or planned. |
| Axial depth ÷ cutting edge length aa/CEL | Ratio of axial depth of cut to cutting edge length; the handbook uses about 0.95 for a square shoulder (90°) cutter. | |
| Targets | ||
| Mean chip thickness wanted | mm | Mean chip thickness you want; the handbook’s reference is 0.108 mm (full slot end milling at 0.17 mm per tooth). |
| Least mean chip thickness you accept | mm | Smallest mean chip thickness you accept; the handbook gives about 0.02 to 0.04 mm as the practical minimum. |
| Spindle speed (for the feed rate) | rpm | Spindle speed, for the feed rate at the feed per tooth found. |
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: Operation
- What it is
- Whether the cutter cuts at the edge of the work (end or side milling) or is centred on it (face milling).
- Units and format
- Choose one of 2 options from the list: End or side milling (cutter at the edge of the cut); Face milling (cutter centred on the work).
- Example
- The form opens with “End or side milling (cutter at the edge of the cut)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the engagement angle formula and the reference feed.
- Get it right
- Face milling the side of a part with ar/D of 0.5 or less behaves as end milling.
What this means: Cutter diameter D
- What it is
- Diameter of the milling cutter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With the radial depth, sets the engagement.
- Get it right
- Use the effective cutting diameter for inserts with a lead angle.
What this means: Radial depth (width) of cut ar
- What it is
- Radial depth (width) of cut taken by the cutter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.125 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lighter radial cut thins the chip.
- Get it right
- Equal to the cutter diameter for a full slot.
What this means: Number of teeth z
- What it is
- Number of teeth or inserts on the milling cutter.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 200 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- ECT rises in proportion; mean chip thickness does not.
- Get it right
- Count effective teeth; some cutters have unequal or staggered teeth.
What this means: Feed per tooth fz
- What it is
- Feed per tooth now used or planned.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mean chip thickness and ECT rise in proportion.
- Get it right
- Feed rate ÷ (teeth × rpm).
What this means: Axial depth ÷ cutting edge length aa/CEL
- What it is
- Axial depth of cut divided by the cutting edge length in contact.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.95 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- ECT rises in proportion.
- Get it right
- About 0.95 for a square shoulder (90°) cutter; less for cutters with a lead angle.
Targets
What this means: Mean chip thickness wanted
- What it is
- Mean chip thickness you want the cutter to take.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.108 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the feed per tooth reported.
- Get it right
- The handbook reference is 0.108 mm (full slot at 0.17 mm per tooth).
What this means: Least mean chip thickness you accept
- What it is
- Smallest mean chip thickness you accept before the cutter starts to rub.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.03 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fails the cut when the chip is thinner.
- Get it right
- The handbook gives about 0.02 to 0.04 mm as the practical minimum.
What this means: Spindle speed (for the feed rate)
- What it is
- Spindle speed of the milling cutter.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 200000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only changes the feed rate reported.
- Get it right
- From the cutting speed and cutter diameter.
Method and formulas
- End or side milling: cos AE = 1 − 2 (ar/D); hm = fz (1 − cos AE) ÷ AE (AE in radians) = 2 fz (ar/D) ÷ AE.
- Face milling, centred: cos AE = 1 − 2 (ar/D)²; hm = fz × 2 sin(½AE) ÷ AE.
- ECT = fz × z ÷ π × (ar/D) × aa/CEL; equivalently ECT = hm (z/2)(AE/180°) for end milling.
- Feed for the target: fz = hm(target) ÷ (hm/fz); ratio to the reference feed fz/fz0 = (hm/fz at the reference) ÷ (hm/fz), reference ar/D = 1 for end milling and 0.7355 for face milling.
- Example: 3.125 mm wide on a 25 mm cutter gives AE 41.41° and hm 0.034591 mm at 0.1 mm/tooth; 0.31222 mm/tooth gives 0.108 mm.
Limitations
- The tabulated relations assume no run-out and evenly sharpened teeth; run-out thins the chip on some teeth.
- Raising the feed per tooth for a light cut raises the chip load at the cutter entry; check the cutter maker’s maximum feed.
- Face milling relations are for the cutter centred on the work; off-centre face milling behaves like end milling.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Raise the feed per tooth for light radial cuts so the cutter cuts instead of rubbing
- Compare end and face milling set-ups by chip thickness
- Find the ECT to use with tool-life data
Who it is for
- CNC programmers
- Machinists
- Process engineers
What you get
- Angle of engagement AE
- Mean chip thickness hm and hm ÷ fz
- Equivalent chip thickness ECT
- Feed per tooth for the chip thickness wanted, and its ratio to the reference feed
- Feed rate at that feed
Interpreting the result
- Below about ar/D = 0.5 in end milling the chip thins quickly: the feed per tooth must rise to keep the same chip thickness.
- ECT is proportional to the number of teeth, while hm is not.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1162–1166. 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 · Library collection
Milling cutters and milling strategies: speeds, feeds, chip thickness and parts that are easy to mill
What it covers: How milling works, the main cutter types, climb versus conventional milling, calculating speed and feed, chip thinning, adaptive toolpaths, chatter and design rules that make milled parts cheaper.
Useful alongside · KEVOS® original book
Milling: feed per tooth, chip thinning and feed rate
What it covers: Calculate milling feed rates from feed per tooth, correct for radial chip thinning and lead angle, and estimate removal rate and time for side milling and face milling.
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