The feed per tooth to program when the cutter takes a light radial cut, works with a small lead angle or cuts with the side of a ball nose, so the real chip matches the chip load your cutter maker recommends. With the ball-nose effective diameter, spindle speed, feed rate and scallop height.
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A tooth cuts its thickest chip where its path is furthest from the direction of feed. With a light radial cut the tooth leaves the material before it reaches that point, a lead angle tilts the edge, and a ball nose cuts on a smaller diameter than its nominal size. In each case the real chip is thinner than the feed per tooth, so the feed must go up by the chip thinning factor to keep the chip the cutter was designed for. On a ball nose a stepover smaller than half the effective diameter thins the chip a second time, so the two factors are multiplied. The scallop height is the cusp left on a flat floor; tool tilt and a curved surface change it.
The formulas are the ones Sandvik Coromant publishes in its milling formulas and the Machinery's Handbook section on milling feeds. They are geometry only: runout, deflection and the tool's own edge preparation change the real chip. Never exceed the maximum feed per tooth the cutter maker states, whatever this calculator gives.
This calculator gives the feed per tooth to program when a milling cutter does not cut its full chip: a light radial cut along a wall, a small lead angle on a face or high-feed mill, a round insert at shallow depth, or a ball nose cutting near its tip. In each case the real chip is thinner than the feed per tooth, so the tool rubs and wears unless the feed goes up. CNC programmers and machinists use it to set the feed for high-efficiency (dynamic) milling, finishing passes and 3D ball-nose work, and to find the spindle speed for the ball's effective diameter.
Program 0.083 mm per tooth, 1768 mm/min at 5305 rpm. The chip is then the 0.05 mm the cutter was designed for, and the job runs 67 % faster than with the catalogue feed.
When the radial depth of cut is less than half the cutter diameter, each tooth leaves the material before it reaches the point where its path is furthest from the feed direction. The thickest chip is then smaller than the feed per tooth. The same happens with lead angles below 90° and with ball-nose cutters at shallow depth. A chip that is too thin rubs, heats the edge and shortens tool life, so the feed per tooth is raised to bring the chip back to the recommended value.
For radial engagement ae below half the cutter diameter Dc, the maximum chip thickness is hex = fz × √(1 − (1 − 2·ae/Dc)²). The factor is fz / hex. At 10 % stepover it is 1.67, at 5 % 2.29 and at 2 % 3.57. At 50 % or more the factor is 1 and no compensation is needed. These are the formulas Sandvik Coromant publishes.
A ball nose cuts on the diameter where the surface meets the ball, not on its nominal size. Without tilt, De = 2 × √(ap × (Dc − ap)). A Ø10 mm ball at 0.2 mm depth cuts on only 2.8 mm, so the spindle speed must be about 3.6 times higher to reach the planned cutting speed. Tilting the tool by β increases it: De = Dc × sin(β + arccos((Dc − 2·ap)/Dc)). If the stepover is smaller than De/2 it thins the chip again on that diameter, so the calculator also multiplies by the radial factor √(1 − (1 − 2·ae/De)²). With Ø10 mm, ap 0.2 mm and ae 0.3 mm a 0.06 mm chip load becomes a feed of 0.346 mm per tooth.
The centre of the ball has zero cutting speed. Without tilt it is always in the cut on flat or shallow surfaces, where it rubs and gives a poor finish. Tilting the tool by more than the contact angle arccos((Dc − 2·ap)/Dc) moves the centre out of the cut, raises the effective diameter and improves both finish and tool life. 10–15° is a common value.
Yes. With a lead angle κr the chip is spread along a longer edge and its thickness is hex = fz × sin κr. A 45° face mill needs 1.41 × the chip load, a 15° high-feed cutter 3.86 ×. Round inserts behave like a lead angle that changes with depth: κr = arccos((iC − 2·ap)/iC). Never exceed the maximum feed per tooth the cutter maker gives.
Yes. The formulas assume steady engagement. In corners and on full-width entries the engagement suddenly grows, and a feed that is 3 or 4 times the chip load can break the edge. Use toolpaths that hold the engagement constant (dynamic or trochoidal milling), keep runout low, and stay within the maker's maximum feed per tooth.
What you need to build, measure or check the result.
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Shrink fit or hydraulic tool holderLow runout for thin chipsView on Amazon →As an Amazon Associate I earn from qualifying purchases. Prices and availability are shown on Amazon.