MC-C1 · Rotating magnetic field

Three-Phase Current and the Rotating Magnetic Field

An induction machine spins a magnetic field with no moving part to do it. See how three-phase current staggered in time and three windings spread in space weave one rotating field, by pinning the nature of the resultant.

What do three pulsating fields add up to?

Three windings spaced 120° apart in space carry three-phase currents staggered 120° apart in time. Each winding only pulsates a flux along its own axis. Pick what the vector sum of the three looks like. The animation shows the answer.

Phase ωt30°

Scrub the phase ωt with the slider. The three coloured vectors are the phases (one grows as another shrinks), gold is the resultant. The faint circle is its constant magnitude.

Resultant field (scrub the phase)

|B| = 1.5 Bm  ·  θ = 30°

As you move the phase the three phase currents change ceaselessly, yet the resultant stays constant at 1.5 times the peak and only its direction turns steadily. Its tip tracing a perfect circle (the faint ring) with no distortion is the proof. This is the rotating field that arises with no moving part.

A single phase only pulsates

When alternating current flows in a single-phase winding, the flux pulsates along one axis from peak to zero to the opposite peak, but it does not turn. This is an alternating field. It decomposes into the sum of two fields of equal magnitude rotating in opposite directions. That is why a single-phase induction motor has no reason to turn one way on its own and needs a separate starting device.

Observeb₁ ∝ cos ωt

A single-phase flux pulsates in time along one axis.

Three together make rotation

Three windings spaced 120° apart in space carry three-phase currents staggered 120° apart in time. At each instant the sum of the three flux vectors has a magnitude always 1.5 times the peak, with only its direction rotating. As the current advances one step in time, the resultant field turns the same amount in space. The time phase of the current becomes the space angle of the field. Swapping the connection of two phases (changing the phase sequence) reverses the direction of rotation.

Choose|B| = ?

The three-phase resultant has constant magnitude, 1.5 times the peak.

The rotation speed is the synchronous speed

While the current goes through one cycle, the rotating field makes exactly one revolution in the simplest two-pole winding. Adding poles P makes the field pattern denser, so the angle turned per cycle shrinks and the rotation slows in proportion. In revolutions per minute it is the synchronous speed Ns = 120f / P [rpm]. In terms of electrical and mechanical angle, θ_e = (P/2) θ_m. At 60 Hz a 2-pole turns at 3600, a 4-pole at 1800, and a 6-pole at 1200 rpm.

Fill inNs = 120f / ?

The synchronous speed is set by frequency over the pole number.

On your ownθe = ?

The electrical angle is the pole-pair multiple of the mechanical angle.

Back to the first screen

The sum of the three pulsating fluxes was one magnetic field rotating at constant magnitude. Each phase only pulsates on its axis, but adding three staggered 120° in time across windings spread 120° in space, the pulsating parts cancel and only the rotating part remains, turning at 1.5 times the peak. With not one moving part, the time phase of the current becomes the space angle of the field. That rotation speed is the synchronous speed Ns = 120f/P, and swapping two phases reverses it. In the next unit this rotating field drags the rotor along and becomes the principle of the induction machine.

The rotating field: feeding three-phase current staggered 120° in time into a three-phase winding spaced 120° in space makes the sum of three pulsating fluxes one rotating field of constant 1.5× magnitude. Its speed is the synchronous speed Ns = 120f / P [rpm], and electrical to mechanical angle is θ_e = (P/2) θ_m. Swapping two phases (changing the sequence) reverses the rotation.

Once you hold this rotation

The rotating field is the engine of the induction machine. Place a rotor inside this stator-made field and the rotor tries to follow it but can never catch the synchronous speed. That lag is the slip, and slip is exactly what induces rotor current and makes torque. The next unit draws the principle of the induction machine and the slip from the speed difference between the rotating field and the rotor (MC-C2).