Motor sizing terms

The motor that drives the axis: pick one from the list, or type a catalogue line in by hand and keep it under "my motors".

Typical

a generic 3000 rpm servo of 50 W to 3 kW to start; your own motors, saved in this browser; the catalogues later

The checks below the list say whether it makes the move, and with how much to spare.

In the calculator: step 4 →

What sort of motor it is — the type decides what its numbers mean, the shape of its torque over speed, and which checks apply.

Typical

a servo for positioning; a stepper for small, cheap, open-loop axes; a BLDC motor for speed control; an AC induction motor on a VFD for big, slow axes

A servo gives its rated torque to the rated speed and its peak for a short while, at constant power above. A stepper holds its pull-out torque to a corner speed and loses it fast beyond; the page uses that torque over a safety factor and watches the duty cycle. A BLDC motor keeps its rated torque over the whole speed range, with a limited-duty torque for a few seconds. An AC induction motor on a drive gives its rated torque to the base speed and weakens beyond, its breakdown torque falling with the square of the speed.

In the calculator: step 4 →

The torque the motor can give continuously without overheating — the line the RMS torque is checked against.

Unit

N·m

Typical

0.3 N·m (100 W) to 10 N·m (3 kW) at 3000 rpm

For a servo it is the rated power divided by the rated angular speed: P / (2π·n/60).

In the calculator: step 4 →

The torque the motor can give for a short while — the line the peak of the move is checked against.

Unit

N·m

Typical

about three times the rated torque

Above the rated speed it falls off; the page derates it at constant power unless the motor carries its own curve.

In the calculator: step 4 →

The speed up to which the motor gives its full torque.

Unit

rpm

Typical

3000 rpm for most servos; 1500 or 2000 for big ones

Beyond it the available torque drops, roughly as rated speed over actual speed.

In the calculator: step 4 →

The speed the motor must never exceed — mechanically and for its feedback.

Unit

rpm

Typical

5000 – 6000 rpm

The move's top motor speed is checked against it.

In the calculator: step 4 →

The inertia of the motor's own rotor, as the catalogue states it.

Unit

kg·m²

Typical

3 × 10⁻⁶ (50 W) to 6 × 10⁻⁴ (3 kW)

It sets the inertia ratio, load over rotor, which decides how well the servo loop can be tuned. Type it as 2.6e-5 for 2.6 × 10⁻⁵.

In the calculator: step 4 →

The supply the motor and its drive are built for.

Unit

V

Typical

230 V single-phase up to about 750 W; 400 V three-phase above

It does not enter the sizing; it is kept so the saved motor is complete.

In the calculator: step 4 →

Whether the motor has a holding brake — a spring-applied brake that holds the shaft when the power is off.

Typical

on vertical axes; off elsewhere

Needed on a vertical axis, so the load does not fall when the drive is disabled. With a brake, the dwell can be held by it instead of by the motor's torque.

In the calculator: step 4 →

During the dwell the brake holds the load, so the motor carries no torque then.

Typical

on, when the brake may be engaged during the dwell

That lowers the RMS torque on a vertical axis. Engaging the brake every cycle wears it; check the brake's cycle rating.

In the calculator: step 4 →

The largest load-over-rotor inertia ratio you accept.

Typical

10 for standard servos; 5 for very dynamic axes; up to 30 with a stiff coupling and good tuning

Below it the servo loop settles quickly; above it the motor can only tune slowly or oscillates.

In the calculator: step 4 →

The torque a stepper holds at standstill with its rated current — the figure on the catalogue's first line.

Unit

N·m

Typical

0.4 N·m (NEMA 17) to 8.5 N·m (NEMA 34)

Its pull-out torque, what it gives while turning, starts near the holding torque and falls with speed; the page takes it flat to the corner speed and falling as 1/n beyond unless a curve is given, and uses it over the safety factor.

In the calculator: step 4 →

The speed up to which the stepper's pull-out torque stays near its holding torque; beyond it the torque falls away, roughly as that speed over the actual speed.

Unit

rpm

Typical

200 – 600 rpm on a chopper driver; higher with more supply voltage

A catalogue's pull-out curve says exactly how; without one the page takes the corner from this field.

In the calculator: step 4 →

How much of the pull-out torque a stepper is allowed to use: the move's torque times this factor must stay under the pull-out curve.

Typical

2; 1.5 for a well-known load

Open loop forgives nothing — a stall is a lost position — so steppers are sized with twice the torque they need.

In the calculator: step 4 →

The angle of one full step; with the speed it gives the step rate the driver must deliver.

Unit

deg

Typical

1.8° (200 steps per turn); 0.9° for fine steppers

It does not change the torque the page computes — it is shown with the pull-out check as steps per second, the unit catalogue curves are drawn over.

In the calculator: step 4 →

The torque a BLDC motor's controller allows for a short while — starting, accelerating — before it limits the current.

Unit

N·m

Typical

1.5 – 2 × the rated torque, for a few seconds

The peak of the move is checked against it; the RMS against the rated torque.

In the calculator: step 4 →

The largest load inertia the maker allows at the motor shaft for the controller to hold its speed through the ramps.

Unit

kg·m²

Typical

from the catalogue; blank = the ratio rule

Given, the page checks the reflected load inertia against it; blank, it applies the inertia-ratio limit instead.

In the calculator: step 4 →

The most an induction motor can give before it stalls — the top of its torque–speed curve.

Unit

N·m

Typical

2 – 3 × the rated torque

The peak of the move is checked against it; above the base speed it falls with the square of the speed, and the drive's own current limit may sit below it.

In the calculator: step 4 →

The speed the motor reaches at its rated frequency, just under the synchronous speed; up to it the drive gives full torque.

Unit

rpm

Typical

1 400 – 1 450 rpm for a 4-pole motor at 50 Hz (1 750 at 60 Hz); 2 900 for 2-pole

Above it the drive weakens the field: constant power, the torque falling as base speed over actual speed.

In the calculator: step 4 →

Your own motors as files: drop them here and they join "My motors" in this browser; download the list to keep or share it.

Typical

one JSON file per motor, or a CSV with one motor per row; a whole folder at once

A JSON file holds one motor or a list, with the page's field names (ratedTorque_Nm, peakTorque_Nm, ratedSpeed_rpm, maxSpeed_rpm, rotorInertia_kgm2, voltage_V, kind, name, maker …); a CSV has those as column headers, with common spellings understood. A folder is read through, file by file; one with the same name and maker replaces the saved one.

In the calculator: step 4 →

What the motor can give at each speed, and what the move asks of it at each speed.

Typical

the move's peak inside the orange field, its RMS line inside the green one, with the margins step 4 asks for

The green field is the continuous region — torque the motor holds for ever without overheating; the RMS of the cycle (the dashed blue line) must stay inside it. The orange field is the intermittent region — torque for a short while; the peak of the move must stay inside it. Both fall off above the rated speed. The black curve is the move itself, speed against torque, its peak marked by a dot; the blue dot is the moment the drawing is at. For a stepper the orange line is the pull-out torque and the green one that torque over the safety factor; for an AC motor the orange line is the breakdown torque, for a BLDC motor the limited-duty torque.

In the calculator: step 4 →

The torque the motor must give at every moment of the move and the dwell.

Typical

a step up while accelerating, a small constant torque while cruising, a step down below zero while braking

The shaded fields are the phases: accelerating (blue), cruising (green), decelerating (orange), dwelling (grey). Where the black curve dips below zero the load drives the motor — it brakes — and that is the energy step 5 counts. The dashed orange line is the intermittent torque available at that moment's speed; the dashed blue line the RMS over the cycle, which the rated torque must cover.

In the calculator: step 4 →