The Rotating Magnetic Field
The principle of operation of the induction machine is based on the generation of a rotating magnetic field. Let us understand this idea better.
Click on the following steps in sequence to get a graphical picture. It is suggested that the reader read the text before clicking the link.
iapk = Im cos 2π.50.t (1)
ibpk = Im cos(2π.50.t — 120°) (2)
icpk = Im cos(2π.50.t — 240°) (3)
Let us see what happens if we sum up the values of these three sine waves at every angle. The result really speaks about Tesla’s genius. What we get is a constant amplitude travelling sine wave!
In a three phase induction machine, there are three sets of windings — phase A winding, phase B and phase C windings. These are excited by a balanced three-phase voltage supply. This would result in a balanced three phase current. Equations 1 — 3 represent the currents that flow in the three phase windings. Note that they have a 120° time lag between them.
Further, in an induction machine, the windings are not all located in the same place. They are distributed in the machine 120° away from each other (more about this in the section on alternators). The correct terminology would be to say that the windings have
their axes separated in space by 120°. This is the reason for using the phase A, B and C since waves separated in space as well by 120°.
When currents flow through the coils, they generate mmfs. Since mmf is proportional to current, these waveforms also represent the mmf generated by the coils and the total mmf. Further, due to magnetic material in the machine (iron), these mmfs generate magnetic flux, which is proportional to the mmf (we may assume that iron is infinitely permeable and non-linear effects such as hysterisis are neglected). Thus the waveforms seen above would also represent the flux generated within the machine. The net result as we have seen is a travelling flux wave. The x-axis would represent the space angle in the machine as one travels around the air gap. The first pulsating waveform seen earlier would then represent the a-phase flux, the second represents the b-phase flux and the third represents the c-phase.
This may be better visualized in a polar plot. The angles of the polar plot represent the space angle in the machine, i.e., angle as one travels around the stator bore of the machine. Click on the links below to see the development on a polar axes.
If / is the amplitude of the flux waveform in each phase, the travelling wave can then be represented as
It is worthwhile pondering over the following points.