Page 55 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PR INCIPL8S 31

d ( N )
= dt "2>/>; (1-40)
,-1
The term in parentheses in Equation (1-40) is called thejlux lillkage A of the coil,
and Faraday's law can be rewritten in terms afflux linkage as

(1-41)

where (1-42)

The units of flux linkage are weber-turns.
( Faraday's law is the fundamental property of magnetic fields involved in
transfonner operation. The effect of Lenz's law in transformers is to predict the
polarity of the voltages induced in transformer windings.
Faraday's law also explains the eddy current losses mentioned previously.
A time-changing flux induces voltage within a ferromagnetic core injust the same
manner as it would in a wire wrapped around that core. These voltages cause
swirls of current to flow within the core, much like the eddies seen at the edges of
a river. It is the shape of these currents that gives rise to the name eddy currents.
These eddy currents are flowing in a resistive material (the iron of the core), so
energy is dissipated by them. The lost energy goes into heating the iron core.
The amount of energy lost due to eddy currents depends on the size of the
current swirls and the resistivity of the material in which the cun'ent flows. The
larger the size of the swirl, the greater the resulting induced voltage will be (due
to the larger flux inside the swirl). The larger the induced voltage, the larger the
current flow that resuits, and therefore the greater the / 2 R losses will be. On the
other hand, the greater the resistivity of the material containing the currents, the
lower the current flow will be for a given induced voltage in the swirl.
These facts give us two possible approaches to reduce the eddy current
losses in a uansformer or an electric machine. If a ferromagnetic core that may be
subject to alternating fluxes is broken up into many small strips. or laminations,
then the maximum size of a current swirl will be reduced, resulting in a lower in-
duced voltage, a lower current, and lower losses. This reduction is roughly pro-
portional to the width of these laminations, so smaller laminations are belter. The
core is built up alit of many of these laminations in parallel. An insulating resin is
used between the strips, so that the current paths for eddy currents are limited to
very small areas. Because the insulating layers are extremely thin, this action re-
duces eddy cutTent losses with very little effect on the core's magnetic properties.
The second approach to reducing eddy current losses is to increase the re-
sistivity of the core material. This is often done by adding some silicon to the steel
of the core. If the resistance of the core is higher, the eddy currents will be smaller
for a given flux, and the resulting / 2 R losses will be smaUer.