How Does a DC Motor Work? Torque, Commutation and Back-EMF

A DC motor works because a conductor carrying current inside a magnetic field experiences a force, and that force acting at a distance from the shaft becomes torque. The rotor turns, the motion generates a back-EMF that opposes the supply, and current falls until the torque the motor produces exactly matches the torque the load demands. Commutation is what keeps that torque pointing the same way as the rotor turns, and the balance point is the speed the motor settles at. Almost everything a designer cares about — starting current, stall current, how the motor answers a load step — follows from this one relationship.

This article follows that chain in order. It explains where torque comes from physically, what the commutator does and how a brushless drive performs the same job electronically, why back-EMF rises with speed, and how the balance between electromagnetic torque and load torque fixes the running point. It closes with the two consequences that matter most in practice: a large inrush current at start-up, and a stall current limited by supply voltage and winding resistance rather than by the controller.

Hofon builds a DC motor series with rated voltage, no-load speed and rated torque stated for each unit, which is the frame of reference for the mechanism described below.

How torque appears in a DC motor

Torque is the product of a force and a lever arm. Current flowing through the armature conductors sits inside the field produced by the permanent magnets or the field winding, and each conductor carrying current in that field experiences a force at right angles to both the current and the field. Because those conductors are mounted at a radius from the shaft, the force acts through a lever arm and turns into torque.

Two consequences follow straight away. Torque is proportional to current, so the harder the load pushes back, the more current the motor draws in order to hold its speed, with the ceiling set by whatever the supply can deliver. Torque is also proportional to field strength, so weaker magnets produce less torque for the same current. Neither statement needs any electronics to be true; both are properties of the magnetic circuit and the winding.

How commutation keeps the torque in a DC motor pointing one way

Commutation exists to solve a single problem. As the rotor turns, a given conductor moves from under one magnetic pole to under the opposite pole, and if the current through it stayed unchanged, the force acting on it would reverse. The motor would then produce torque that pushed it forwards and then backwards, twice per revolution, and would settle into a wobble instead of rotating.

In a brushed motor the commutator and brushes solve this mechanically. The rotating segments and the stationary brushes form a rotating switch that reverses the current in each coil at the moment that coil passes between poles, so the torque keeps the same sign all the way round. The cost is a sliding electrical contact that wears, sparks and limits how fast the motor can be driven.

A brushless motor solves the identical problem electronically. The windings sit on the stator, the magnets sit on the rotor, and an inverter switches current between windings in step with rotor position. Correct timing requires knowing where the rotor is, which is why a brushless motor always carries some form of position sensing — Hall sensors, or a sensorless estimate derived from the back-EMF of the winding that is momentarily unenergised.

Back-EMF and the speed-current relationship

A rotating armature is also a generator. The same conductors moving through the same field have a voltage induced in them, and by Lenz's law that voltage opposes the supply that produced the motion. This is back-EMF, and its magnitude rises in proportion to speed.

That gives the most useful relationship in DC motor behaviour: current is set by the difference between supply voltage and back-EMF, divided by armature resistance. At standstill there is no back-EMF, so the whole supply voltage drives current through the winding and the motor draws its largest current. As speed rises, back-EMF rises with it, the difference shrinks, and current falls away.

This is why a motor running free draws very little current, why adding load increases current rather than collapsing the speed, and why a motor held at standstill draws a current limited only by supply voltage and winding resistance. If a stall persists, the heat generated in the winding is what damages the motor, not the mechanical load itself.

Where the speed settles: torque balance at steady state

At any instant the motor produces electromagnetic torque in proportion to current, while the load demands torque according to its own characteristics — friction, gravity, cutting force, aerodynamic drag. If motor torque exceeds load torque there is a net torque and the rotor accelerates. As it accelerates, back-EMF rises, current falls, and motor torque falls with it, until the two are equal, net torque is zero and the speed stops changing.

That is the operating point, and it is not fixed. Increase the load and the motor slows, back-EMF drops, current rises, torque rises to meet the new demand, and a new balance is reached at a lower speed. Remove the load and the motor speeds up until torque again matches. The slope of that adjustment is what a torque-speed curve plots. Nothing in the control loop enforces the balance — the physics does, which is why a DC motor behaves as a self-regulating drive.

Two consequences worth designing around

·Inrush at start-up. At zero speed there is no back-EMF, so current is limited only by winding resistance. The supply, fuse, connector and driver must tolerate an initial current that can be many times the running value, and current-limited or soft-start control exists largely because of it.

·Stall current is a supply question. Whether the motor survives a jam depends on how much current the supply can push into a stalled winding. A supply that cannot deliver much current limits stall torque instead, which protects the winding but may fail to hold the load.

·Duty rating follows heat. The current at the balance point generates heat in the winding, and how quickly that heat leaves decides the continuous rating — which is why the same unit is rated differently in free air and on a heatsink.

How this connects to speed control

Understanding the balance point makes the two methods of speed control obvious. Lowering the supply voltage lowers the speed at which back-EMF equals the supply, so the motor settles at a lower speed for the same load. It is simple, but wasteful, because the excess voltage is dissipated as heat in a linear regulator.

Pulse-width modulation takes the other route. The supply is switched rapidly and the winding responds to the average of the on and off periods. Because winding inductance smooths the current, the motor behaves as though it were fed a lower voltage, while the losses move out of a linear pass element and into the switching device. Both methods change the voltage available to drive current against back-EMF; neither changes the balance underneath.

A DC motor works by turning current in a magnetic field into torque, and commutation is what keeps that torque pointing in the same direction as the rotor turns. Speed is never commanded directly: it emerges from the point where the torque the motor can produce equals the torque the load demands, with back-EMF deciding how much current is available at that speed. Design around the inrush and stall currents that fall out of the same relationship, and the motor will behave in the machine the way it behaved on paper.

If you are matching a drive and a supply to a mechanism, contact us with your duty cycle, load torque and supply voltage and we will confirm which winding suits them.