Spindle speed and torque: what you actually get
A spindle sold as 2.2 kW at 24,000 rpm delivers about 0.88 N·m at that speed. The same spindle makes roughly eight times that at 3,000 rpm. Knowing which region you cut in explains most disappointing spindle purchases.
Two regions, one sentence apart
An induction spindle driven by a VFD has two operating regions, separated by the base frequency — usually 50 or 60 Hz:
- Below base frequency: constant torque. The drive holds the voltage-to-frequency ratio constant, so the magnetic flux stays constant, so available torque stays roughly constant. Power rises in proportion to speed.
- Above base frequency: constant power. The output voltage has nowhere left to rise, so flux falls as frequency rises and torque falls proportionally. This is field weakening, and it is why high-speed spindles feel gutless at the top of their range.
The two formulae
Synchronous speed from frequency and pole count:
n = 120 × f / pn in rpm, f in Hz, p = number of poles. For a two-pole spindle this is simply n = 60 f — which is where 400 Hz = 24,000 rpm comes from.
Torque from power and speed:
T = 9550 × P / nT in N·m, P in kW, n in rpm. This is just T = P/ω with ω in rad/s, so it is exact rather than empirical.
Worked: 2.2 kW, two-pole, 50 Hz base, 24,000 rpm top
| Frequency | Speed (rpm) | Region | Torque (N·m) | Power (kW) |
|---|---|---|---|---|
| 25 Hz | 1,500 | Constant torque | ~7.0 | ~1.1 |
| 50 Hz | 3,000 | Base — both limits meet | ~7.0 | 2.2 |
| 100 Hz | 6,000 | Constant power | ~3.5 | 2.2 |
| 200 Hz | 12,000 | Constant power | ~1.75 | 2.2 |
| 300 Hz | 18,000 | Constant power | ~1.17 | 2.2 |
| 400 Hz | 24,000 | Constant power | ~0.88 | 2.2 |
Torque figures are the theoretical constant-torque / constant-power envelope. Real spindles fall short of it at the top of the range for the reasons below.
Why the real curve droops
The table above is an upper bound. Three things pull the actual figure below it, and all three get worse with speed:
- Iron losses in the stator rise faster than linearly with frequency.
- Windage and bearing friction rise steeply with speed, and some of your rated power is spent overcoming them before it reaches the tool.
- Slip. An induction motor runs slightly below synchronous speed — typically a few per cent at rated load — so actual rpm is a little under the synchronous figure above.
So the honest reading is: constant power is an approximation that holds reasonably well in the middle of the range and overstates what you get at the very top. If a maker publishes a torque curve, use it in preference to any calculation, including ours.
Torque at rated speed, by power rating
This is the number that surprises people. All rows assume two-pole and 24,000 rpm top speed.
| Rated power | At 24,000 rpm | At 3,000 rpm | Ratio |
|---|---|---|---|
| 0.8 kW | 0.32 N·m | 2.55 N·m | 8× |
| 1.5 kW | 0.60 N·m | 4.78 N·m | 8× |
| 2.2 kW | 0.88 N·m | 7.00 N·m | 8× |
| 3.0 kW | 1.19 N·m | 9.55 N·m | 8× |
| 4.5 kW | 1.79 N·m | 14.33 N·m | 8× |
| 5.5 kW | 2.19 N·m | 17.51 N·m | 8× |
The ratio is always the same for a given speed range, because it is just the ratio of the speeds. Which is the point: the speed range costs you torque, and the power figure on the box does not tell you that.
What this means for buying
- If you cut aluminium or steel, you are usually torque-limited at sensible cutter diameters, and you should care about the torque available in the speed band you actually use — not the headline power.
- If you cut wood, plastics or PCB, you are usually speed-limited and the top-end torque is rarely the constraint.
- A bigger spindle bought for more torque at high speed often disappoints, because the extra power goes into the constant-power region where torque still falls as 1/speed. Buying for torque at a given rpm means comparing torque at that rpm, not kilowatts.
Parts
Spindles
Questions
What is the base frequency?
The frequency at which the drive runs out of output voltage. Below it torque is constant; above it power is constant and torque falls as speed rises.
Why does the real curve droop below the theoretical one?
Iron losses, windage and bearing friction all grow with speed, so less of the input power reaches the tool. The gap is largest exactly where people most want the number.
Should I buy on power or on torque?
On torque at the speed you actually cut at. The power figure is measured at one point on a curve that is not flat — the calculator shows what that means for a given spindle.
Sources and method
Three kinds of statement appear on this page, and each is labelled where it occurs:
- Derived — constant torque below base frequency and constant power above it follow directly from the voltage ceiling the drive can produce.
- Rule of thumb — workshop practice, not a standard. Given with the range it is meant to hold over, and it loses to your manual wherever the two disagree.
- Maker-specific — parameter numbers, connector pin numbers, minimum brake resistance, maximum cable length, bearing speed limits. Not published here. They move between firmware revisions of the same model, and a wrong one is worse than none.
Standards and documents
- IEC 60034-1 — rotating electrical machines: rating and performance
- NEMA MG 1 — motors and generators
- ISO 1940-1 — balance quality requirements for rotors (G grades)
- The manual for your own drive and spindle — the only valid source for maker-specific values