Feeds and Speeds

Six quantities connect the cutting data, machine and cut

Start by separating six quantities. Cutting speed and feed per tooth describe what the cutting edges should experience. Spindle speed and table feed are the corresponding machine settings. Width of cut and axial depth describe how much of the cutter is engaged. The exact starting values come from cutting data for the tool, material and operation.

Cutting speed

How fast the cutting edge moves through the material: the speed at the outside of the cutter. Written in surface feet per minute (SFM) or metres per minute (m/min). Also called surface speed. Comes from cutting data.

Feed per tooth

How far the work moves while the cutter turns from one tooth to the next, in inches or millimetres per tooth. Also called chip load, because it sets the size of the bite each tooth takes. Comes from cutting data.

Spindle speed

How many turns the cutter makes each minute, in revolutions per minute (rev/min, usually said RPM). Set on the machine.

Table feed

How fast the work moves past the cutter, in inches or millimetres per minute. Also called the feed rate. On a machine that moves the cutter instead, it is how fast the cutter travels. Set on the machine.

Width of cut, a_e

The cutter’s radial engagement in the work, measured across the cutter in inches or millimetres. It is also called radial depth of cut; those names describe the same quantity, not two separate settings.

Axial depth of cut, a_p

The distance engaged along the cutter’s axis, in inches or millimetres: the difference between the uncut and cut surfaces in that axial direction.

Spindle speed: the turns it takes to reach the cutting speed

Cutting speed is a distance per minute, measured at the edge of the cutter. In one turn, a point on that edge travels once around the cutter: its circumference, π × D. So the spindle speed is the cutting speed divided by the distance one turn covers, once the two are in the same units.

Spindle speed (rev/min) = 12 × cutting speed (SFM) ÷ (π × cutter diameter in inches)

The 12 is there because cutting speed is in feet and the diameter is in inches: 12 inches to the foot. In metric units the same idea needs a 1000, millimetres to the metre:

Spindle speed (rev/min) = 1000 × cutting speed (m/min) ÷ (π × cutter diameter in mm)

Worked example, with illustrative numbers. A 0.5 in cutter, with cutting data that calls for 300 SFM: 12 × 300 ÷ (π × 0.5) = 2,292 rev/min. The 300 SFM is there to make the arithmetic concrete. It is not a recommendation for any tool or any material. The feed value below is illustrative too; use the later material guide for the carbide starting bands.

Look at where the diameter sits: underneath. Halve the diameter and the spindle speed doubles. A small cutter has to turn faster to give its edge the same cutting speed, which is why small cutters so often ask for more speed than a machine has. That case has its own card below.

Table feed: each tooth takes one chip load as it passes

Each time a tooth passes, the work should have moved one feed per tooth. The number of teeth passing each minute is the spindle speed times the number of flutes, so:

Table feed = spindle speed × flutes × feed per tooth

Worked example, continued. A 4-flute cutter at 2,292 rev/min, with a feed per tooth of 0.002 in: 2,292 × 4 × 0.002 = 18.3 in/min. The units work out on their own: turns per minute, times teeth per turn, times inches per tooth, leaves inches per minute.

Turned around, the same relation tells you what chip load a feed gives. That is the way to check a feed someone else has set:

Feed per tooth = table feed ÷ (spindle speed × flutes)

Flutes here means the teeth that actually take a chip in each turn. For an ordinary end mill that is simply the number of flutes.

Removal rate: width × depth × table feed

Two more numbers describe the cut itself. The width of cut is how far the cutter reaches sideways into the work, across the direction of feed. The depth of cut is how far down its side the cutter is buried, along its axis. A side cut can be no wider than the cutter; a wider path takes more than one pass.

While the table feeds, the cutter sweeps through the work and leaves a channel behind it. In a stretch of time the cutter travels table feed × time, and the solid metal it takes out in that stretch is a slab as wide as the cut, as deep as the cut, and as long as that travel. Per minute, that is the material removal rate:

Removal rate (in³/min) = width of cut (in) × depth of cut (in) × table feed (in/min)

The front of the cut is curved, because it is the cutter’s own shape. The slab’s two ends are the same curve, one travel apart, so whatever the curve, the slab holds exactly width × depth × travel.

Worked example, continued. The same cutter, 0.1 in wide (20% of its diameter) and 0.5 in deep, at 18.3 in/min: 0.1 × 0.5 × 18.3 ≈ 0.917 in³/min, or 15.0 cm³/min. In 5 seconds the cutter travels 1.53 in and removes 0.0764 in³.

That is the volume of solid metal. Once it is chips, the same metal lies loose and takes up far more space, so the removal rate is not the size of the chip pile.

Cutting power: removal rate times the energy each cubic inch takes

Cutting a cubic inch of a given material takes roughly a given amount of energy. That is its specific cutting energy, and it is why the same cut needs more power in steel than in aluminum. Written as power per unit of removal rate, it turns a removal rate straight into power:

Cutting power (hp) = removal rate (in³/min) × unit power (hp per in³/min)

Cutting power (W) = removal rate (mm³/min) × specific energy (J/mm³) ÷ 60

The 60 turns minutes into seconds, because a watt is a joule per second. One mechanical horsepower is 745.7 W.

Worked example, continued. For 6061-T6 aluminum the guide in the calculator gives a band of 0.16 to 0.30 hp per in³/min. At 0.917 in³/min that is about 0.15 to 0.28 hp, or 110 to 210 W. The same cut in 304 stainless steel, whose band is 0.65 to 1.3 hp per in³/min, needs about 0.60 to 1.2 hp.

The answer is usually a band. Some table rows give one factor; that still produces an estimate, not a measured certainty. Published bands cover a family of materials over a range of hardness, and the energy a real cut takes also depends on chip thickness and cutting-edge geometry. Treat the band as the size of the job, not a prediction to the watt.

Three different powers get called “the power”, and they are not the same:

• Cutting power is what the cutting edge spends. That is the estimate above.
• Motor shaft power is more, because the belts, gears and bearings between the motor and the cutter lose some on the way. If the drivetrain passes on 80% of what the motor delivers, the motor must deliver the cutting power ÷ 0.8.
• Electrical power drawn from the supply is more again, because the motor and its drive lose some too.

None of these tells you whether a machine can take the cut. A spindle motor’s rating is not necessarily available at every speed, and power is only one limit: the tool, the holding and the machine’s stiffness are others. Use the estimate to compare cuts and to see why a cut is heavy, not to approve one.

When the machine cannot turn as fast as the formula asks

Because small cutters ask for high spindle speeds, the formula can easily give more than a machine’s top speed. A 0.125 in cutter at 300 SFM asks for 9,167 rev/min. On a machine that stops at 4,000, it runs at 4,000.

• Work the feed from the speed the spindle really turns. At 4,000 rev/min, with 2 flutes and 0.0008 in per tooth, that is 4,000 × 2 × 0.0008 = 6.4 in/min. Each tooth then takes the chip load you meant it to.
• The cutting speed is what you give up. At 4,000 rev/min the edge of a 0.125 in cutter moves at π × 0.125 × 4,000 ÷ 12 = 131 SFM, not the 300 the data asked for.

Working the feed from the speed that was asked for, rather than the one the spindle is turning, gets the chip load wrong by the same ratio. A feed worked from 9,167 rev/min would give each tooth 9,167 ÷ 4,000 = 2.3 times the chip load intended.

The same applies to a machine that offers only certain speeds, through belts or gears: set the nearest speed it has, and work the feed from that one. The calculator’s machine top speed box does this for a top speed.