Material Removal Rate — Milling

A rectangle sweeping through a solid: the width the cutter engages, times the depth it is down, times how fast the work is fed through it. Everything else about a milling operation is detail on top of this volume.

The two depths are named alike and behave nothing alike, and keeping them straight is most of the skill. $a_p$, the axial depth, is how far the cutter is down into the work, measured along the spindle axis. $a_e$, the radial width, is how much of the cutter's diameter is buried, measured across it — the stepover. Slotting is the case where $a_e$ equals the full cutter diameter, and it is the hardest thing a mill does: the chips have nowhere to evacuate, the whole diameter is in contact at once, and the tool is loaded in two directions simultaneously.

The modern answer to a heavy job is the opposite arrangement — a small radial width with a large axial depth, fed fast. The volume per minute comes out the same, which is what this equation makes obvious, but everything else improves. The wear is spread along the full flute length instead of concentrating in one band near the tip. Each tooth is in the cut only briefly and has most of a revolution to shed its heat. The load runs along the tool's stiffest direction rather than trying to bend it. And the small engagement angle thins the chip, which is what lets the feed rate be raised to compensate. That is the whole of trochoidal, dynamic and high-efficiency milling, and this equation is why it is arithmetic rather than magic.

Removal rate is the right figure for comparing strategies and the wrong figure for judging a finishing pass, where the volume is negligible and the whole point is accuracy and surface. It is also the direct input to the power calculation, which is where a plan that looks fine on paper usually meets the spindle it has to run on.