Eddy current loses

Eddy current lost

When a changing magnetic field cuts through a sample of metal or
magnetic materials that is not connected to a circuit, by Faraday’s law,
a circulating current is induced. This current is known as eddy current,
it is localised within that material and has a flow pattern as shown in
figure 4.9.

Figure 4.9: Eddy current (black arrows) induced within the metal or
Magnetic material and the current induced by the external magnetic field
(red arrows).


This circulating current creates a magnetic field that opposes the
external magnetic field. The direction of the eddy current is described
by Lenz’s law. The stronger of the external magnetic field or the greater
of the electrical conductivity of the material, the eddy current that is
developed will be stronger and also yields stronger opposing force.
Eddy current creates losses through Joule heating, and it reduces the
efficiency of device that operates under alternating magnetic field condition
such as iron core of transformers and alternating current motors.
This power loss is known as eddy current loss due to the induced eddy
current in the metal or magnetic materials. In order to reduce the eddy
current loss, the resistivity of the material is increased by adding silicon
in the metal or ferromagnetic materials. Another effective way to achieve
low eddy current loss is by using lamination of electrical metal sheets.
These metal sheets are coated with insulator which breaks the eddy
currents path as illustrated in the diagram below.

Figure 4.10: Eddy currents in a laminated toroidal core.


more (pdf)

http://www1.mmu.edu.my/~wslim/lecture_notes/Chapter4.pdf

Eddy current losses

If a closed loop of wire is placed in an alternating magnetic field,
the induced EMF will circulate a current round the loop. A solid
block of metal will likewise have circulating currents induced in it
by an alternating field, as shown in Fig.1.19. These are termed eddy
currents, and they are a source of energy loss in the metal. Eddy
current losses occur whenever conducting material is placed in a
changing magnetic field; the magnitude of the loss is dependent on
the properties of the material, its dimensions and the frequency of
the alternating field.

Magnetic structures carrying alternating magnetic flux are
usually made from a stack of thin plates or laminations, separated
from one another by a layer of insulation (Fig.1.20). This
construction breaks up the eddy current paths, with a consequent
reduction in the loss; qualitatively, the effect may be explained as
follows. With solid metal (Fig.1.19) the currents would flow in
approximately square paths; these paths enclose a large area for a
given perimeter, and the induced EMF is high for a path of given
resistance. When the metal is divided into laminations (Fig.1.20),
the current paths are long narrow rectangles; the area enclosed by a
given perimeter is much smaller, and the induced EMF is smaller,
giving lower currents and reduced losses.

An approximate analysis shows that in plates of thickness t
(where t is much smaller than the width or length) the eddy
Current loss per unit volume is given by

where the flux density is an alternating quantity of the form

and ρ is the resistivity of the material. Thus if the lamination
thickness is reduced by a factor x, the loss is reduced by a
factor x2. As might be expected, the loss varies inversely with
the resistivity
ρ. The addition of 3-4 percent of silicon to iron increases the
resistivity by about four times, as well as reducing the hysteresis
loss; this is the main reason for the widespread use of silicon steel
in electrical machines. The thickness of the laminations is typically
0.3-0.5 mm, which ensures that the eddy current loss will be less
than the hysteresis loss at a frequency of 50 Hz.


Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

MAGNETIC%20CIRCUITS.pdf



Eddy Current Lost of core

When the excitation field varies quickly, by the Faraday's law, an
electromotive fore (emf) and hence a current will be induced in the
conductor linking the field. Since most ferromagnetic materials are
also conductors, eddy currents will be induced as the excitation field
varies, and hence a power loss known as eddy current loss will be
caused by the induced eddy currents. The resultant B-H or l-i loop
will be fatter due to the effect of eddy currents, as illustrated in the
diagram below.

Under a sinusoidal magnetic excitation, the
average eddy current loss in a magnetic core can
be expressed by

where Ce is a constant determined by the nature of
the ferromagnetic material and the dimensions of
the core.

Since the eddy current loss is caused by the
induced eddy currents in a magnetic core., an
effective way to reduce the eddy current loss is to
increase the resistivity of the material. This can
be achieved by adding Si in steel. However, too much silicon
would make the steel brittle. Commonly used electrical steels
contain 3% silicon. Another effective way to reduce the eddy
current loss is to use laminations of electrical steels. These electrical
steel sheets are coated with electric insulation, which breaks the
eddy current path, as illustrated in the diagram below.

The above formulation for eddy current loss is obtained under
the assumption of global eddy current as illustrated schematically
in figure (a) of the following diagram. This is incorrect for materials
with magnetic domains. When the excitation field varies, the
domain walls move accordingly and local eddy currents are
induced by the fluctuation of the local flux density caused by the
domain wall motion as illustrated in figure (b) of the diagram below.
The total eddy current caused by the local eddy currents is in
general higher than that predicted by the formulation under the
global eddy current assumption. The difference is known as the
excess loss.


Source ( pdf )
http://services.eng.uts.edu.au/cempe/subjects_JGZ/ems/ems_ch7_nt.pdf