SPEED CONTROL

9

The susceptance of the magnetic circuit obviously follows the
same law as when there are no eddy currents. That is:

b

V =

(10)

At a given current, ii, energizing the magnetic circuit, the in-
duced voltage, and thus also the voltage producing the eddy
currents, is proportional to the frequency. The currents are
proportional to the voltage, and the eddy-current losses, there-
fore, are proportional to the square of the voltage. The eddy-
current conductance, g, thus is independent of the frequency.

The admittance of a magnetic circuit consuming energy by
eddy currents (and other secondary currents in permanent closed
circuits), of negligible hysteresis loss, thus is represented, as
function of the slip, by the expression:

Y' = g-jb' (11)

^

Connecting such an admittance in series to the induction-
motor secondary, gives the total secondary impedance:

+i

Assuming:

(12)

(13)

That is, 45° phase angle of the exciting circuit of the magnetic
circuit at full frequency—which corresponds to complete screen-
ing of the center of the magnet core—we get:

1

Fig. 4 shows the speed curves, and Fig. 5 the load curves,
calculated in the standard manner, of a motor with eddy-current
starting device in the secondary, of the constants:

eQ = 100;
Fo = 0.03 - 0.3 j;
Z0 = 0.033 + 0.1 j;
Z, = 0.033 + 0.1 j;

6 = 3;

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