MC-B1 · DC machine principle

The DC Machine and the Commutator

The emf of a coil turning in a magnetic field is AC by nature. Choose for yourself when to switch the connection and see how the commutator flips that AC into one direction.

When must the connection switch to get DC outside?

The emf inside the coil is AC, flipping sign every half turn. Choose with the tabs among three moments at which the brushes swap their connection to the coil, and the upper waveform changes to the voltage that appears at the external terminals; at which moment the terminals see voltage of one direction only is the question of this lesson.

The tabs choose when the connection is switched. The upper waveform is the external terminal voltage.

Voltage seen at the external terminal

e_ext = sin θ

If the connection is never switched, the outside sees the AC in the coil as it is: sin θ, swinging between positive and negative every half turn, which is not DC.

Misaligned

A rotating conductor’s EMF is AC

When a coil turns in a magnetic field, the flux linking it changes with the rotation angle, and the induced emf is e = -dΦ/dt. The emf is largest when a conductor cuts across the field lines fastest, and 0 when it moves parallel to them. After half a turn, the conductor's direction of motion relative to the field reverses, so the emf reverses sign too; the emf inside the coil is AC by nature. Take it out through two slip rings instead of a commutator and this AC comes out unchanged: that is an AC generator.

Observee(θ) ∝ sin θ

The emf of a rotating conductor is AC, following the sine of the angle.

The commutator flips the connection at zero crossing

The commutator is a ring split in two that turns with the coil. The fixed brushes move onto the next segment at the moment the coil's plane is perpendicular to the field, when the linked flux is at its maximum and the emf is 0, and at exactly that moment the connection to the outside is swapped. Even as the coil's emf heads negative, the connection has already been flipped, so the external terminals always see the same polarity. Because the switch happens when the emf is 0, the sparking is small, which is why the brushes are set at this position, the neutral axis. These days many motors are brushless, doing the same switching with sensors that measure the rotor position and semiconductor switches instead of brushes and a commutator.

Chooseswitch at θ = ?

The commutator switches the connection at the zero crossing, where the emf is 0.

Fill ine_ext = ?

The external emf is rectified into the absolute value of the sine.

More conductors give smoother DC and larger EMF

A single coil pulses strongly as |sin θ|. Add more slots and commutator segments so that many coils overlap, and their pulses, each with a different phase, add up to nearly smooth DC, while the average emf grows too. In summary, the average induced emf is E = (P Φ Z N) / (60 a), where P is the number of poles, Φ the flux per pole, Z the total number of conductors, N the speed in revolutions per minute, and a the number of parallel paths.

On your ownE = ?

The average induced emf is proportional to the product of flux, number of conductors, and speed.

Back to the first screen

The outside saw voltage of one direction only when the connection was switched at the zero crossing. Without switching, the AC came straight through, and switching at the wrong moment made it dip negative. The heart of the commutator is the timing of flipping the external connection at exactly the moment the emf becomes 0; then, even as the coil goes negative, the outside stays positive, and the AC emf turns into pulsating DC. A DC machine is a device that mechanically rectifies the AC made by rotation.

DC machine: the emf of a coil turning in a magnetic field is AC (e ∝ sin θ), but the commutator swaps the brush connection at the zero crossing, where the emf is 0, so that outside it flows in one direction (pulsating DC, |sin θ|). More conductors and commutator segments smooth the pulsation, and the average induced emf is E = P Φ Z N / (60 a).

Once you hold this rectifying action

The commutator is the heart of the DC machine. Run the same machine backward and external DC enters the coil through the commutator to produce torque in one direction: a DC motor. The flux made by the armature current, however, distorts the main flux and shifts the zero crossing, and that is the problem of armature reaction in the next lesson (MC-B2). There we see how the zero crossing shifts and how it is corrected.