MC-B1 · DC machine principle

The DC Machine and the Commutator

The EMF of a coil spinning in a magnetic field is inherently alternating. Discover how the commutator flips that AC into DC by choosing the switching instant yourself.

When must the connection switch to get DC outside?

The EMF inside the coil is alternating, flipping sign every half turn. Try three choices for when the brushes swap their connection to the coil. At which choice does the external terminal see clean DC?

Tap to pick the switching instant. The top trace is the external voltage.

Voltage seen at the external terminal

e_ext = sin θ

If the connection never switches, the outside sees the coil’s AC unchanged: sin θ swinging positive and negative every half turn — not DC.

Misaligned

A rotating conductor’s EMF is AC

As the coil rotates in the field, the linked flux varies with angle and the induced EMF is e = -dΦ/dt. The EMF peaks when the conductor cuts flux fastest and is zero when it moves along the flux. After half a turn the conductor’s motion reverses relative to the field, so the EMF reverses sign too. Hence the EMF inside the coil is inherently AC.

Observee(θ) ∝ sin θ

A rotating conductor’s EMF goes as the sine of angle — AC.

The commutator flips the connection at zero crossing

The commutator is a ring split in two that rotates with the coil. The fixed brushes cross to the next segment just as the coil aligns with the field and the EMF passes through zero. At that instant the external connection swaps. Even as the coil EMF heads negative, the reversed connection keeps the external terminal at the same polarity. Switching at the zero of EMF also keeps the sparking small.

Chooseswitch at θ = ?

The commutator switches at the zero crossing, where EMF is zero.

Fill ine_ext = ?

The external EMF is rectified to the absolute value of the sine.

More conductors give smoother DC and larger EMF

A single coil pulsates strongly as |sin θ|. Adding slots and commutator bars to overlap many coils sums pulsations of different phase into nearly smooth DC and raises the average EMF. The result is the average induced EMF 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, and a the number of parallel paths.

On your ownE = ?

The average induced EMF is the product form of flux, conductors and speed.

Back to the first screen

The outside saw clean DC only when the connection switched at the zero crossing. Never switching left it AC; switching at the wrong time dipped it negative. The heart of the commutator is the timing: it flips the external connection at the very instant the EMF is zero. Then even as the coil goes negative the outside stays positive, turning the AC EMF into pulsating DC. A DC machine is a device that mechanically rectifies the AC it makes by rotation.

The DC machine: the EMF of a coil spinning in a field is AC (e ∝ sin θ), but the commutator swaps the brush connection at the zero crossing where the EMF is zero, making it unidirectional outside (pulsating DC, |sin θ|). More conductors and bars 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 in reverse and external DC enters the coil through the commutator to make one-directional torque — a DC motor. But the flux from the armature current distorts the main flux and shifts the zero crossing, which is the problem of armature reaction in the next unit (MC-B2). There we see how the zero crossing is pushed and how it is corrected.