Calculation of the CNC Tour Cup Power

A tour cup is a cup-shaped turned part: a bore, an outer wall, often a flange at the open end. The cut that matters is usually the interrupted one at the flange face or the deep internal bore where the tool overhangs. When the spindle stalls, chatters or leaves a poor finish, the cause is often that nobody checked cutting power before the job was set up.

The calculation cnc tour cup power routine answers three questions. Does the spindle have enough power at the required cutting speed? Is there enough torque at that speed? And can the gearbox or belt ratio deliver both without dropping the spindle below its usable band? On a lathe with a stepped gearbox the answer changes with the ratio you select, so the check has to be repeated for each speed range.

Numbers matter more than rules of thumb here. A cut that runs fine at Ø80 mm on one machine may overload a smaller spindle at the same surface speed, because spindle speed and torque trade against each other through the ratio. Getting the arithmetic right before the first chip saves scrapped parts and broken inserts.

Cutting power on a lathe follows from the material removal rate and the specific cutting force of the workpiece material. The working form we use is NE = (ap × f × vc × ks) ÷ (60 × 1000 × η), where ap is depth of cut in mm, f is feed in mm/rev, vc is cutting speed in m/min, ks is specific cutting force in N/mm², and η is machine efficiency, typically 0.8 for a geared headstock.

Torque is the second number. The relationship is T = (ap × ks × f × r) ÷ 1000, with r as the cutting radius in mm and T in N·m. On a cup with a long overhang the effective radius is measured to the contact point, not to the nominal outside diameter, which is where many hand calculations go wrong.

Spindle speed comes from the cutting speed you want. Use n = (1000 × vc) ÷ (π × D), where D is the workpiece diameter in mm and n is in rpm. Feed per revolution stays constant when you change diameter; only the rpm changes. This is the step that links a tool supplier's recommended vc to the number you dial into the control.

Specific cutting force ks is not a single value. It rises as the chip thins, so a finishing pass at 0.1 mm/rev needs a higher ks than a roughing pass at 0.3 mm/rev. Tables give ks for a reference chip thickness, and the correction is applied by multiplying by a chip-thinning factor. For a first pass, using the table value at your feed rate gets you within about 15% of the real load.

Take a mild steel cup with an outside diameter of 120 mm. We want vc = 120 m/min, f = 0.2 mm/rev, ap = 3 mm, and ks = 2600 N/mm². Convert cutting speed to spindle speed first: n = (1000 × 120) ÷ (π × 120) = 318 rpm. That is the number the spindle has to hold.

Now the power. NE = (3 × 0.2 × 120 × 2600) ÷ (60 × 1000 × 0.8) = 3.9 kW. Torque follows: T = (3 × 2600 × 0.2 × 60) ÷ 1000 = 93.6 N·m at the cutting radius of 60 mm. Both numbers come from the same cut, and both have to be checked against the machine data sheet.

Here is where the gearbox enters. If the low range has a ratio of 1:6.54 and the spindle needs 318 rpm, the motor turns at roughly 2080 rpm. In that range the available torque is multiplied by the same ratio, minus losses, so 93.6 N·m at the spindle is easy. Run the same cut in a 1:2.15 high range and the motor speed drops, torque at the spindle falls, and the 3.9 kW may no longer be deliverable at that point on the curve.

The conclusion for this part: 3.9 kW and about 94 N·m at 318 rpm. If the machine's continuous rating at that speed is below 3.9 kW, the cut has to be split into two passes, or the tool has to be changed to one that runs at a lower ks. A heavier feed at lower speed is often the cheaper fix than a second operation.

Once you have power and torque, compare them against the machine's continuous rating, not its peak. Peak figures are quoted for short accelerations and spindle starts. A cut that sits at 95% of peak for four minutes will trip the drive or shorten its life. We keep roughing loads under about 80% of the continuous rating to leave headroom for hard spots in the material.

The ratio check comes second. A motor rated at 11 kW and 70 N·m may only deliver 3.9 kW at 318 rpm if the selected range puts the motor below its base speed. Look up the motor's base speed and constant-power range, then confirm the operating point falls inside it. On lathes with two or three ranges this is a two-minute check that prevents a stalled spindle.

Material choice shifts the numbers a lot. Aluminum at 6061 or 7075 needs roughly a third of the ks of 4140 steel, so the same cup geometry can be cut in one pass on a small lathe but needs two or three passes in alloy steel. Titanium and Inconel sit at the other end, and the calculation usually shows the limit is torque, not power.

For small cup features the calculation often says the cut is fine, but the real limit is tool overhang and chatter. A boring bar 4× as long as its diameter will deflect long before the spindle runs out of power. Power is a necessary check, not a sufficient one. If the numbers pass but the surface finish is poor, the problem is on the tool side.