Chip Thinning Corrected Feed per Tooth (Milling)
Computes the feed per tooth corrected for radial chip thinning in milling, f_z,corr = f_z / sin(φ_max), where sin(φ_max) = √(1 − (1 − 2·a_e/D)²) as long as the radial depth of cut a_e is less than half the cutter diameter D, and equals 1 above that. When the cutter engages little material sideways, each tooth enters and leaves the cut before reaching the point of maximum thickness, and the chip actually formed is THINNER than the programmed feed — the edge starts rubbing instead of cutting, generates heat, work-hardens the surface and wears fast, which is why light finishing passes often destroy tools quicker than heavy roughing. Correcting the feed restores the catalogue chip thickness: with a 12 mm cutter engaging only 1.2 mm, or 10 % of the diameter, the feed must rise 67 % for the tooth to cut at the intended thickness. Above half the diameter there is no thinning and the correction is neutral. Enter the target feed per tooth, the cutter diameter and the radial depth of cut.
Result
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Radial Chip Thinning: Corrected Feed per Tooth in Milling
Trocoidal strategies, dynamic roughing, wall finishing: in any cut with small radial engagement, the catalogue feed per tooth produces a chip thinner than intended. The tooth leaves the cut before reaching maximum thickness, the edge rubs instead of cutting, temperature climbs and the tool dies early — and the programmer blames the cutter when the real culprit is a feed set too low. This page returns the corrected feed that restores the catalogue chip thickness, from the target feed, the cutter diameter and the radial depth of cut.
The correction is f_z,corr = f_z / sin(φ_max), with cos(φ_max) = 1 − 2·a_e/D, hence sin(φ_max) = √(1 − (1 − 2·a_e/D)²). The angle φ_max marks where the tooth exits the cut, and instantaneous chip thickness equals f_z·sin(φ). With the page defaults — f_z = 0.1 mm/tooth, a 12 mm cutter and a_e = 1.2 mm, or 10 % of the diameter — the sine is 0.6 and the output reads 0.1667 mm/tooth, 67 % above the programmed value. Two points close in exact form and serve as a check: at a_e = D/4 the factor is 2/√3 and the output is 0.1155; at a_e = D/2 the tooth reaches full thickness, the factor is 1 and the output returns to 0.1000.
The correction covers radial thinning only. A ball nose, a round insert or a tool with a lead angle calls for the axial correction, which works from the effective diameter and is a separate calculation this page leaves out. The model also relies on the classical circular tooth path, ignoring the real trochoidal trajectory and cutter runout. And the factor blows up as engagement drops: 2.29 at 5 % of the diameter, 3.57 at 2 %, and past that point the limit stops being geometric — it becomes the maximum feed of the insert, the room available for chip evacuation and the table feed the machine can reach. Above half the diameter thinning vanishes and the page hands back the feed unchanged.
Frequently asked questions
Why does the result stay put once a_e exceeds half the diameter?
Does it apply to a ball nose or a round insert?
Is there a limit to raising the feed per tooth?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.