Chip thinning calculator
Under half the cutter's diameter, the chip is thinner than the feed per tooth: hex = fz·√(1 − (1 − 2ae/D)²). A Ø20 mm end mill at ae 2 mm and 0.1 mm a tooth takes a chip only 0.06 mm thick; to cut the 0.1 mm chip the tool is rated for, program 0.167 mm a tooth. An entering angle under 90° thins the chip again, by sin κr.
Enter the cutter, the radial engagement, the entering angle and the feed, and the calculator gives the chip it really cuts, the feed that restores the target chip, and the feed rate if you give the spindle speed and the teeth.
Cut
Feed
Feed rate
- Compensated feed per tooth fz
- Max chip thickness hex at fz
- Engagement angle φ
- Feed factor (fz ÷ hex)
How it’s calculated
hex = fz·sin κr·√(1 − (1 − 2ae/D)²) while ae < D/2, and fz·sin κr from ae = D/2. The feed that restores a chip: fz = hex ÷ (sin κr·√(…)). The engagement angle φ = arccos(1 − 2ae/D); vf = n·z·fz.
Radial engagement
| ae/D | ae (mm) | φ | hex/fz | fz factor |
|---|---|---|---|---|
| 50 % | 10.000 | 90.0° | 1.000 | ×1.000 |
| 30 % | 6.000 | 66.4° | 0.917 | ×1.091 |
| 25 % | 5.000 | 60.0° | 0.866 | ×1.155 |
| 20 % | 4.000 | 53.1° | 0.800 | ×1.250 |
| 15 % | 3.000 | 45.6° | 0.714 | ×1.400 |
| 10 % | 2.000 | 36.9° | 0.600 | ×1.667 |
| 5 % | 1.000 | 25.8° | 0.436 | ×2.294 |
| 2 % | 0.400 | 16.3° | 0.280 | ×3.571 |
Entering angle
| κr | Lead angle | hex/fz (sin κr) | fz factor |
|---|---|---|---|
| 90° | 0° | 1.000 | ×1.000 |
| 75° | 15° | 0.966 | ×1.035 |
| 60° | 30° | 0.866 | ×1.155 |
| 45° | 45° | 0.707 | ×1.414 |
| 30° | 60° | 0.500 | ×2.000 |
| 20° | 70° | 0.342 | ×2.924 |
| 10° | 80° | 0.174 | ×5.759 |
What is chip thinning?
A milling tooth takes a chip whose thickness is the feed per tooth times the sine of the angle between the feed and the tooth's path. With half the cutter's diameter or more in the cut, the tooth crosses square to the feed somewhere in its arc and the chip reaches the full feed per tooth. With less, it never does: the chip is thickest where the tooth meets the stock, at fz·sin φ, where φ = arccos(1 − 2ae/D) is the engagement angle.
A thin chip rubs instead of cutting, which wears the edge and heats the work. Tool makers rate an edge by its maximum chip thickness, so at a light radial cut the feed per tooth is raised until the chip is back to their figure: fz = hex ÷ √(1 − (1 − 2ae/D)²).
What does the entering angle do?
A cutting edge set at an entering angle κr spreads the same feed over a longer edge, so the chip measured square to the edge is fz·sin κr. A square-shoulder cutter (90°) takes the full feed; a 45° face mill takes 0.707 of it, so its feed per tooth can be 1.41 times the rated chip; a high-feed cutter at about 10° can feed several times higher still. Some catalogues give the lead angle instead, measured from square: lead = 90° − κr, and the chip is fz·cos(lead).