# Rotating field

In electrical engineering, a rotating field is a magnetic field that continuously rotates around an axis of rotation .

## Basics

Rotating fields are generated to drive the shafts of three-phase motors and independently starting AC motors. The rotating field magnetically pulls the rotor, which is fastened coaxially on the shaft of the motor .

Due to the time offset of the three alternating currents, three-phase alternating currents offer the possibility of generating a rotating field through the circular arrangement of coils. In the simplest case, six coils are arranged in a circle and the opposing coils are connected together to form a pole pair that forms the two poles of an electromagnet. Interchanging any two external conductors of the three-phase alternating current causes the direction of rotation to be reversed.

A rotating field can also be generated with two-phase alternating current. Due to the time offset of two alternating currents by 90 °, it forms a rotating field. Two-phase alternating current does not play an essential role in energy transmission, since the conductor cross-sections are poorly utilized, but it is used in some machines such as the two-phase synchronous motor to generate a rotating field.

## Mathematical approach

The pole pairs are magnetized in turn by the alternating current, so that, ideally, a rotating magnetic field results whose speed corresponds to the frequency of the alternating current: ${\ displaystyle n _ {\ text {s}}}$ ${\ displaystyle f}$

${\ displaystyle n _ {\ text {s}} \ sim f}$

By multiplying the number of pole pairs per outer conductor , the speed is reduced: ${\ displaystyle p}$

${\ displaystyle n _ {\ text {s}} = {\ frac {f} {p}}}$

The maximum speed at the usual frequency of the power grid of 50  Hz is:

${\ displaystyle n _ {\ text {s}} = {\ frac {50 \, \ mathrm {Hz}} {1}} = 50 \, \ mathrm {s} ^ {- 1}}$

This results in a rotating field speed per minute of 3000 min −1 .

### Rotating field as the sum of three alternating fields

As in the animation (above), the rotating magnetic field of a single-pole pair three-phase machine can be generated by summing three alternating fields that are phase-shifted by 120 degrees in space and time . The following applies accordingly in the space vector representation :

${\ displaystyle {\ underline {B}} _ {u} ^ {w} = {\ hat {B}} ^ {w} \ cdot \ cos (\ omega t) \ cdot \ mathrm {e} ^ {0} }$
${\ displaystyle {\ underline {B}} _ {v} ^ {w} = {\ hat {B}} ^ {w} \ cdot \ cos \ left (\ omega t - {\ frac {2} {3} } \ pi \ right) \ cdot \ mathrm {e} ^ {\ mathrm {j} {\ frac {2} {3}} \ pi}}$
${\ displaystyle {\ underline {B}} _ {w} ^ {w} = {\ hat {B}} ^ {w} \ cdot \ cos \ left (\ omega t - {\ frac {4} {3} } \ pi \ right) \ cdot \ mathrm {e} ^ {\ mathrm {j} {\ frac {4} {3}} \ pi}}$

After mathematical transformation, the sum of the three alternating fields results in the total field:

${\ displaystyle {\ underline {B}} ^ {d} = {\ underline {B}} _ {u} ^ {w} + {\ underline {B}} _ {v} ^ {w} + {\ underline {B}} _ {w} ^ {w}}$
${\ displaystyle {\ underline {B}} ^ {d} = {\ frac {3} {2}} {\ hat {B}} ^ {w} \ mathrm {e} ^ {\ mathrm {j} \ omega t}}$

The magnetic induction of the three-phase rotating field thus has a temporally constant 1.5 times the amount of the induction of the individual alternating fields and rotates with the angular frequency . ${\ displaystyle \ omega}$

## Special applications

AC motors that start up independently generate a rotating field through a phase shift . A phase shift of the electrical current is achieved by a capacitor , a phase shift of the magnetic flux by short-circuit rings on the iron core (see capacitor motor , shaded pole motor ).

## Rotating field measuring device

Historical rotating field measuring device

Rotary field measuring devices are used to identify the orientation of the field . Early models were equipped with a small electric motor , current devices work on an electronic basis and can also indicate the failure of a phase.

## Individual evidence

1. ^ Thomas Keve / Helmut Roeloffzen: Electrical machine building block Berliner Union & Kohlhammer 1978; ISBN 3-408-53529-9 , p. 188

## literature

• Horst Stöcker: Pocket book of physics. 4th edition, Verlag Harry Deutsch, Frankfurt am Main, 2000, ISBN 3-8171-1628-4
• Gregor D. Häberle, Heinz O. Häberle: Transformers and electrical machines in power engineering systems. 2nd edition, Verlag Europa-Lehrmittel, Haan-Gruiten, 1990, ISBN 3-8085-5002-3
• Günter Springer: Electrical engineering arithmetic book. 11th improved edition, Verlag Europa-Lehrmittel, Haan-Gruiten, 1992, ISBN 3-8085-3371-4