Rotating field

This article deals with the magnetic field of electrical engineering. For the municipality part of the municipality of Reinsberg in the district of central Saxony, see rotating field (Reinsberg) .

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.

• Visualization of the rotating field in a three-phase machine
• 

  Temporal sequence of the individual phase-shifted voltages as vectors

• 

  Representation as a sum vector. The tip of the outer vector describes a circle.

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

Web links

• Do-it-yourself rotating field meter
• Video: Magnetic rotating field . Institute for Scientific Film (IWF) 2004, made available by the Technical Information Library (TIB), doi : 10.3203 / IWF / C-14889 .