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Electric Motors

How electric motors work, the main motor types, and DC motor load curves.

  1. Electric Motor Principles
  2. Electric Motor Types
  3. DC Motor Torque, Speed, and Power
Engineering Fundamentals/Electrical Systems

Electric Motor Principles

Find the stator and rotor, then follow the changing magnetic field that keeps a motor turning.

The stator stays still; the rotor turns

The stator stays still; the rotor turns

An electric motor turns electrical input into mechanical motion. In a rotary motor, the stator is the stationary part and the rotor is the rotating part. An air gap separates them. Bearings support the rotating assembly; the shaft carries motion to the load.

Two simplified motor cross-sections: the rotor field follows the stator field, then the stator field advances again. The outer stator is stationary while its magnetic field changes direction.

The stator is often outside the rotor, but it does not have to be. The names describe motion, not inside versus outside. See Electric Motor Types for both arrangements.

Keep the magnetic target moving: carrot on a stick

Keep the magnetic target moving: carrot on a stick

Picture the rotor turning to align its magnetic field with the stator's field. If the fields simply settled into alignment, that turning effect would disappear. To keep turning, the motor switches a field or keeps the stator field rotating. Think carrot on a stick: keep moving the target ahead.

Commutation means switching current between windings at the right time. Brushes and a commutator can do it mechanically, or a drive can do it electronically. A winding is a coil of wire that creates a magnetic field when current flows through it.

Supporting detail: Addendum 1 — Where the alignment picture needs care.

Why a DC motor keeps turning: coil, field and commutator; Interactive

Why a DC motor keeps turning: coil, field and commutator

The simplest brushed DC motor is one rectangular coil on a shaft between two magnet poles. Turn the coil, find where the field stops pushing it, and see how a split-ring commutator keeps the push going one way.

Predict first: a coil carrying current sits between a north and a south pole. At which angles does the field give it no turning push at all, and where is the push largest?

Torque on the coil. For an ideal rectangular coil in a uniform field, the torque about the shaft is τ = N·B·I·A·sin θ. N is the number of turns, B the field (T), I the current (A) and A the coil's area (m²), so τ is in N·m. θ is the angle from the field B to the coil's normal n, the line perpendicular to the coil's face. The coil's magnetic moment lies along n or against it, depending on which way the current circulates. That sets the direction of the torque, not its size.

SB12+−DC supplysplit ringN, cut awayNSBneutral plane12nτθ = 30°
One coil at θ = 30°. Left, a cutaway side view: the N pole in front is cut away, the S pole is behind the coil, and B points away from you. Right, the end view from the commutator end, with the top brush positive. In the end view, current runs away from you along side 1 (⊗) and back toward you along side 2 (⊙). F = BIL pushes side 1 down and side 2 up. The two forces are equal and opposite, so there is no net force, but they form a couple. Each acts at a lever arm of r·sin 30° = 0.5r from the shaft, where r is half the coil width. So τ = 0.5·NBIA, counter-clockwise as seen from the commutator end.

Why the angle matters. Whenever current flows, each long side of the coil feels a force F = BIL, the same size at every angle. What changes is its lever arm about the shaft, r·sin θ, where r is half the coil's width. As the coil approaches θ = 0° or 180°, with its face across the field in the neutral plane, the forces point almost straight through the shaft. The lever arm shrinks to zero, and so does the torque. With slip rings the current still flows at those angles and the forces point straight through the shaft. With an ideal split ring the brushes sit on the gaps at that instant, so there is momentarily no current and no force at all. Either way the torque there is zero. At θ = 90° and 270° the lever arm, and the torque, are largest.

Why a commutator. If the coil were fed through slip rings, its current would never reverse. With the polarity drawn here, past 180° the torque would reverse too, pushing the coil back toward that neutral-plane position, and over a whole turn it would average zero. Reverse the supply or the magnets and the coil's resting position moves half a turn. A split-ring commutator turns with the coil. Its brushes change segments exactly as the coil crosses the neutral plane, which reverses the coil current. The torque becomes N·B·I·A·|sin θ|: it never points backward, but it still falls to zero twice a turn.

0°90°180°270°360°10−11.41Torque ÷ one coil’s peak NBIAθ, angle from B to the coil normal ntwo coils (thick)one coil, commutatorone coil, slip rings (dashed)zero
Torque against θ for one turn, as a fraction of one coil’s peak NBIA. Slip rings (dashed): the torque reverses every half turn and averages zero. Split-ring commutator (solid): the current reverses at the neutral plane, so the torque is |sin θ|, never negative, averaging 2/π ≈ 0.64; it is still zero at 0° and 180°. Two commutated coils 90° apart (thick): the sum runs from 1 to √2 ≈ 1.41, so the smallest torque is 0.71 of the largest and never zero.

Two coils. Add a second coil 90° ahead of the first, each with its own split ring. When one coil is in the neutral plane, the other is at its peak. The total, |sin θ| + |cos θ| in units of one coil's peak, runs from 1 to √2. Its smallest value is 1/√2 ≈ 0.71 of its largest, so the ripple shrinks and the zero-torque dead spot disappears.

Worked example, with illustrative numbers rather than a real motor rating: N = 50 turns, B = 0.20 T, I = 2.0 A, and a coil 40 mm × 30 mm, so A = 1.2 × 10⁻³ m². The peak torque is N·B·I·A = 50 × 0.20 × 2.0 × 0.0012 = 0.024 N·m. At θ = 30°, τ = 0.024 × sin 30° = 0.012 N·m.

Direction. Reversing the current reverses every force (F = I L × B), so the motor turns the other way. Swapping the magnets reverses B and does the same. Reversing both restores the original direction.

Model limits. This is an ideal teaching model: one or two rectangular coils, a uniform field, and current switched exactly at the neutral plane. Torque is shown as a fraction of one coil's peak, N·B·I·A. It does not model back EMF, speed, magnetic saturation or brush sparking.

For how a DC motor's speed falls as its load torque rises, see DC Motor Torque, Speed, and Power.

Supporting detail: Addendum 2 — Sources for the torque formula and the commutator.

Separate turning effort, speed, and power

Separate turning effort, speed, and power

Torque is turning effort. Angular speed tells how fast the shaft turns. Mechanical power combines the two. A stopped shaft can have torque and still deliver zero mechanical power.

Start with Current, Voltage, and Resistance for the electrical quantities, then use DC Motor Torque, Speed, and Power to see what happens when a load asks a motor for more torque.

Engineering Fundamentals/Electrical Systems

Electric Motor Types

Compare how motors switch their fields, what wears, and how they control motion.

Brushed DC: simple supply, wearing contacts

Brushed DC: simple supply, wearing contacts

A small permanent-magnet brushed DC motor has stationary magnets and rotating electromagnets. Carbon brushes press against a segmented copper commutator. As the segments rotate past the brushes, the connections change and reverse current in rotor windings. The torque keeps acting in the intended direction.

Simplified two-segment commutator: fixed positive and negative brushes touch rotating copper segments A and B. After half a turn the segments exchange brushes, reversing current in the attached coil.

Strength: inexpensive and simple to run from DC, useful in small toys, pumps, and actuators. Weak points: brushes wear through contact and electrical arcing; the commutator and spring contact system can also deteriorate. Switching current at the contacts can cause sparks and electrical noise. Permanent-magnet construction is common in small motors; some brushed motors use field windings instead.

A microcontroller can command a power driver with pulse-width modulation (PWM), switching the supply on and off rapidly to control the motor. The driver handles motor current; a logic output is not a motor power supply.

AC induction: the rotor follows a rotating field with slip

AC induction: the rotor follows a rotating field with slip

Stator windings arranged around the motor produce a rotating magnetic field. In a three-phase motor, the currents reach their peaks at different times, moving the combined field around the stator. That moving field induces current in conducting rotor bars. The rotor current and stator field interact to produce torque.

The rotor runs slightly slower than the field during normal motoring. The difference is called slip. If the rotor caught the field exactly, there would be no relative motion to induce the rotor current needed for torque. For example, a field at 1,800 rpm and a rotor at 1,740 rpm differ by 60 rpm, or 3.33% of field speed.

Strength: a squirrel-cage induction rotor needs neither brushes nor permanent magnets, making it useful for pumps, fans, and conveyors. Weak points: speed changes with load and slip; a variable-frequency drive is normally used when adjustable speed is needed.

Supporting detail: Addendum 3 — Why alternating current alone is not the full explanation.

Brushless permanent-magnet motors: switch the stator current

Brushless permanent-magnet motors: switch the stator current

Here the rotor carries permanent magnets and the stator carries windings. A drive switches the stator currents in sequence so the magnetic field turns. There are no commutator brushes to wear.

BLDC means brushless DC; PMSM means permanent-magnet synchronous motor. A DC supply can feed an inverter, an electronic circuit that creates changing phase currents. Most BLDC/PMSM drive systems use this electronic switching. The labels often distinguish waveform and control choices; they do not mean one rotor needs AC magnets and the other needs DC magnets.

A suitably designed line-fed synchronous motor instead follows a rotating field set by the AC supply frequency and pole count. It needs an appropriate starting arrangement. Do not assume an arbitrary BLDC motor can connect directly to an AC line.

Strengths: no brush contact wear and controllable speed; common uses include cooling fans, drones, and controlled machine drives. Weak points: drive electronics and correctly timed switching are needed; bearings still wear and winding temperature still limits output.

Inner-rotor and outer-rotor describe what rotates

Inner-rotor and outer-rotor describe what rotates

Side-by-side cross-sections: an inner-rotor motor has rotating magnets inside fixed windings; an outer-rotor motor has a rotating magnet ring outside fixed windings.

An inner-rotor motor, also called an inrunner, rotates inside the stator. An outer-rotor motor, or outrunner, rotates around the stator. These are the arrangements sometimes called “inboard” and “outboard.” Use inner-/outer-rotor when describing the construction.

An inner rotor can have low rotational inertia, useful for rapid speed changes. An outer rotor puts magnetic force at a larger radius, useful for producing torque in fan and propeller drives, but its rotating shell contributes inertia. Dimensions and design still decide the actual performance.

Stepper: count commanded steps, but allow for missed motion; Practice

Stepper: count commanded steps, but allow for missed motion

A stepper drive energizes stator phases in a sequence of magnetic positions. As a first approximation, picture an inner-rotor brushless motor with many magnetic poles or teeth. That helps explain the small steps; it is a simplification, since stepper constructions differ.

Open loop means the controller sends a move without measuring whether it happened. A stepper can position and hold without feedback while energized and within its torque capability. It is useful for printer axes and small indexing mechanisms. Holding position still uses current and produces heat.

The weak point is missed steps. Excessive load or acceleration can prevent commanded motion. Without feedback, the controller keeps counting commands and does not know the shaft fell behind. Step count is not a guarantee of exact position, and holding torque is not a guarantee against any load.

Practice motor selection

Servo: measure motion and correct the error

Servo: measure motion and correct the error

A servo is a motor used with feedback and closed-loop control, not one particular magnetic construction. A sensor such as an encoder measures motion. The controller compares measured position or speed with the command and adjusts the drive to reduce the error.

Strength: responds to a load disturbance and detects position error, useful for robot joints and machine axes. Weak points: adds sensor, controller, tuning, and cost. Feedback does not create extra torque; a servo can still reach its limits. A brushed, brushless, or other suitable motor can be part of a servo system.

Linear motors move directly along a track

Linear motors move directly along a track

Think of the magnetic layout of a rotary motor opened out into a straight line. A traveling field pushes or pulls a moving member along a track, producing linear force instead of shaft torque. One permanent-magnet arrangement uses a magnet track and a moving coil assembly. Linear induction designs also exist; a magnetized rail is not universal.

Strength: direct linear motion without a rotary-to-linear screw or belt, useful for positioning stages and transport systems. Weak points: the magnetic track, drive, cooling, and position measurement can add cost. Separate guides support and constrain the moving assembly; a motor does not replace the guide system.

Compare the basic field picture in Electric Motor Principles and the load calculation in DC Motor Torque, Speed, and Power.

Engineering Fundamentals/Electrical Systems

DC Motor Torque, Speed, and Power

Use an ideal linear torque-speed curve to find a load point and see why peak output power occurs halfway to no-load speed.

More load torque means less speed on this curve

More load torque means less speed on this curve

This model approximates a permanent-magnet DC motor at a fixed supply voltage with a straight line between two endpoints. Stall torque is the torque at zero speed. No-load speed is the speed at zero external shaft load. It is not a universal curve for induction motors, steppers, or regulated drives.

Let Ts be stall torque, n0 no-load speed, and T the constant resisting load torque. The steady operating point is where motor torque equals load torque:

n = n0(1 − T/Ts).

This is an assumed linear approximation, not a measured motor rating. It omits acceleration, current limiting, temperature changes, and supply voltage drop. At stall it predicts zero shaft power, not zero electrical input. A stall rating is not a continuous operating rating.

Supporting detail: Addendum 4 — Manufacturer basis for the straight line.

Explore the load point and the peak-power point; Interactive

Explore the load point and the peak-power point

Predict first: a model motor has 0.8 N·m stall torque and 3,000 rpm no-load speed. A constant load asks for 0.2 N·m. Does the motor run above or below half speed?

Normalized torque falls from one at stall to zero at no-load speed. Normalized output power peaks at half no-load speed. A load of one-quarter stall torque operates at three-quarters no-load speed.

Static example: n = 3,000(1 − 0.2/0.8) = 2,250 rpm. Angular speed is 2,250 × 2π/60 = 235.6 rad/s, so output power is 47.12 W. Peak power is 62.83 W at 1,500 rpm and 0.4 N·m.

Peak power is halfway, not at either endpoint; Practice

Peak power is halfway, not at either endpoint

Use P = Tω, with torque in N·m and angular speed in rad/s. Convert rpm using ω = 2πn/60. The definitions and units are on Power and Efficiency and Angular Motion.

At stall there is torque but no speed. At no load there is speed but no external load torque. Both endpoints therefore have zero shaft output power. Between them, torque times speed reaches a maximum.

Supporting detail: Addendum 5 — Derive the halfway result from the straight line.

Supporting detail: Addendum 6 — Manufacturer check on peak power.

Practice operating speed Practice output power

Peak efficiency needs electrical input as well as shaft output

Peak efficiency needs electrical input as well as shaft output

Efficiency is output power divided by input power. Peak output power and peak efficiency answer different questions. The torque-speed line alone does not give electrical input or losses, so this explorer deliberately does not calculate efficiency.

For the brushed coreless DC motors described by Portescap, peak efficiency occurs at a lighter load and higher speed than peak output power. Its exact position needs loss or current data. No external load means no useful shaft output, even though a real motor draws current to overcome its internal losses. Consult the actual motor's efficiency and continuous-operation data before selecting a load point.

Supporting detail: Addendum 7 — Manufacturer basis for the efficiency comparison.

Match the motor, reduction, and the same output load; Interactive; Practice

Match the motor, reduction, and the same output load

A gearbox changes the torque demanded at the motor shaft for the same output load. That can move the motor to a different point on its torque–speed curve. Predict both operating points before revealing them.

Static example: a motor has 0.8 N·m stall torque and 120 rpm no-load speed. The output load resists with 0.6 N·m. Compare direct drive with a 20-tooth driver, 40-tooth driven gear, and a stated 90% running mesh efficiency.

The same motor and output load, two connections
ConnectionTorque required at motorMotor speedOutput speedMotor shaft powerModeled output power
Direct0.600 N·m30.0 rpm30.0 rpm1.885 W1.885 W
2:1 reduction, 90%0.3333 N·m70.0 rpm35.0 rpm2.443 W2.199 W

Result: the reduction runs the output faster under this load, even though it divides motor speed. It reflects less load torque to the motor, so the motor reaches a higher speed. The gearbox did not create power: motor shaft power changed before the 10% modeled mesh loss.

This is a fixed-voltage steady-running comparison with a constant resisting torque. It does not establish starting ability, acceleration, thermal or continuous rating, back-driving, electrical input, or gear strength. At stall, speed and shaft output power are zero; if required motor torque exceeds stall torque, the model reports no forward steady operating point instead of assigning a fictitious speed.

Supporting detail: Addendum 8 — Source and the standstill boundary.

Real loads may demand different torque at different speeds. Their operating point is an intersection of a load curve and a motor curve. Practice reflected load Practice output power

Supporting detail

Addendum

Additional evidence, standards context, and background referenced from the main text.

  1. Engineering Fundamentals/Electrical Systems/Electric Motor Principles

    Addendum 1. Where the alignment picture needs care

    This is a first picture, not a description of every motor's internal timing. A synchronous motor can rotate at the same speed as the stator field while keeping an angular offset that produces torque. An induction rotor runs slower than the field during normal motoring; that relative motion induces rotor current. A stepper can deliberately stop and hold a commanded position.

    Back to reference 1

  2. Engineering Fundamentals/Electrical Systems/Electric Motor Principles

    Addendum 2. Sources for the torque formula and the commutator

    OpenStax, University Physics Volume 2, section 11.5, Force and Torque on a Current Loop, derives the torque on a rectangular loop in a uniform field (equations 11.19 to 11.22). It defines the magnetic moment of an N-turn loop as N·I·A along the loop's normal and describes brushes and a commutator reversing the current. HyperPhysics (Georgia State University), Commutator and Brushes on DC Motor, describes a split-ring device called a commutator that reverses the current as the coil passes the plane perpendicular to the field. Its Torque on a Current Loop page gives the same torque in terms of the magnetic moment.

    Back to reference 2

  3. Engineering Fundamentals/Electrical Systems/Electric Motor Types

    Addendum 3. Why alternating current alone is not the full explanation

    A single winding supplied by single-phase AC makes a field that pulses back and forth; that alone does not establish a starting direction. Single-phase induction motors use an additional starting arrangement. The rotating field, rotor current, and relative speed explain rotation more clearly than saying the rotor field simply opposes the stator field.

    Back to reference 3

  5. Engineering Fundamentals/Electrical Systems/DC Motor Torque, Speed, and Power

    Addendum 5. Derive the halfway result from the straight line

    Put x = n/n0. Then T = Ts(1 − x), so P = Tsω0x(1 − x). Since x(1 − x) = 1/4 − (x − 1/2)2, the largest value is 1/4 at x = 1/2. Thus peak power = Tsω0/4, at half no-load speed and half stall torque. The two endpoint maxima cannot occur at the same time.

    Back to reference 5

  8. Engineering Fundamentals/Electrical Systems/DC Motor Torque, Speed, and Power

    Addendum 8. Source and the standstill boundary

    The running conversion follows maxon's gear conversion note: motor speed equals reduction multiplied by load speed, while motor torque equals load torque divided by reduction and gear efficiency. The note also requires checking actual gear torque and speed limits. A separate maxon standstill note explains that power efficiency is undefined when both input and output power are zero. This lesson therefore treats stall as a boundary; it does not calculate blocked-state efficiency or a permissible output torque.

    Back to reference 8