Cutting Power from Specific Cutting Energy

Specific cutting energy — also called unit power, or in North America unit horsepower — is the energy it takes to remove one unit volume of a given material. Multiply it by the volume removed per second and you have the power the cut demands. It is the simplest possible power model and it is accurate enough to size a machine.

The reason it works is that cutting is overwhelmingly a shearing process. The great majority of the energy goes into plastically deforming the chip along the shear plane, and only a minority into friction between the chip and the tool face. Because the shear happens in a thin zone at a strain rate that swamps ordinary tensile behaviour, the energy per unit volume comes out remarkably repeatable for a given material — near enough constant that a single number is useful.

This site takes $u$ as an input and always will. Published tables of specific cutting energy live in copyrighted handbooks, and reproducing them here would be both illegal and, more importantly, misleading — because the number belongs to your material batch, your feed, your rake angle and your tool condition, not to a general category called "steel". Get it from your tooling supplier's data for the cut you are actually making, or better still measure it: take a known cut, read the spindle load, subtract the idle draw, correct for drive efficiency, and divide by the removal rate.

Three corrections stand between this equation and the motor nameplate. The answer is power at the cut, so machine drive losses come on top — divide by the spindle efficiency, typically 0.75 to 0.9 on a geared head and better on a direct drive. Almost all of this power becomes heat, and something has to carry it away; most of it leaves in the chip, which is why a properly loaded cut runs cooler at the tool than a light one, and why blue chips are a sign of a working process rather than a failing one. And $u$ is not constant across the range of one material: it climbs steeply as the chip gets thin. That is the size effect, and it means a finishing cut costs several times more energy per cubic millimetre than a roughing cut in the same steel. A $u$ measured on a heavy cut badly understates a light one.

Run the equation backwards and it gives the removal-rate ceiling a machine's power sets, which is a genuinely useful number for planning. Use the power the spindle can hold continuously rather than its peak, take the efficiency off first, and then remember that most cuts are stopped by rigidity, chatter, chip evacuation or workholding long before the motor is the limit.