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Magnetic materials
− In engineering applications the ferromagnets are used because of
their high μ, which enable high magnetic induction to be obtained
with only modest magnetic field.
(Their ability to retain magnetization and thereby act as a source of
field and of course the torque on a magnetic dipole in a field can be
used in electric motors.)
− Important magnetic properties of ferromagnets
(1) Permeability (what is the most important single property of ferromagnets for
application?)
high relative
permeability(μr)

B
H
To characterize the properties of a given ferromagnetic materials, it is
necessary to measure the B as a function H over a continuous range of H to
obtain a hysteresis curve.
− The permeability of a ferromagnet is not constant as a function of H
(μ of paramagnet is constant as a function of H)
− (μr) in(the initial reactive permeability) : 10~105 (for ferromagnet)
− The highest values of (μr)in occur for
permalloy (78% Ni, 22% Fe)
supermalloy (80% Ni, 15% Fe, 5% Mo)
− These materials are useful as flux concentrators.
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(2) Retentivity (保磁性)
What is the most characteristic property of ferromagnet ?
• Permanent magnet materials don’t have a high permeability, but
their applications depend on their retentivity.
• The retention of magnetization distinguishes ferromagnets from
paramagnets which although they acquire a magnetic moment in an
applied field H, can not maintain the magnetization after the file is
removed.
(It is well known that ferromagnets can be magnetized. This is to say
that once exposed to a magnetic field they retain their magnetization
even when the field is removed.)
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(How can we best represent the magnetic properties of ferromagnet? )
(3) Hyteresis - The most common way to represent the bulk magnetic properties
of a ferromagetic materials is by a plot of B – H curve
M–H
M
B
H
H
B

H
contain
the
same
sinceB=μ0(H + M)
information
The term hysteresis, meaning to lag behind
M

H
−
The suitability of ferromagnetic materials for applications is determined
principally from characteristics shown by their hysteresis loops.
−
(i) For transformer application
high permeability
low hysteresis loss
(because of the need for efficient conversion of electrical energy)
−
(ii) For electromagnet application
low remanence
low coercivity
(to ensure that M can easily be reduced to zero as needed)
−
(iii) For permanent materials
high remanence
high coercivity
( to retain M as much as possible )
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(4) Saturation magnetization (M0)
(Is there an upper limit to the magnetization of a ferromagnet ?)
•From the hysteresis plot, it can be seen that the ferromagnet in its
initial state is not magnetized.
•Application of a field H causes B to increase in the field direction.
M0 : all the magnetic dipoles within the material are aligned in the
direction of the magnetic field H (M0 is dependent only on the
magnitude of m and n)
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(5) Remanence(剩磁) (What happens to the magnetic induction of a
ferromagnet when the magnetic field is switched off? )
− When the field is reduced to zero after magnetizing a magnetic
material
(i) The remaining magnetic induction is called the remanent(殘存的)
induction (BR)
(ii) The remaining magnetic magnetization is called the remanent
magnetization(MR)
BR  0 M R
− The remanence is used to describe the value of either the remaining
induction or magnetization when the field has been removed after
the magnetic material has been magnetized to saturation.
− The remanent induction or magnetization is used to describe the
remaining induction or magnetization when the field has been
removed after magnetizing to an arbitrary level.
− The remanence become the upper limit for all remanent inductions
or magnetizations.
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(6) Coercivity (How is the magnetic induction reduced to zero?)
−B can be reduced to zero by applying a reverse magnetic field of
strength Hc. This field strength is known as the corectivity.
−Hc strongly depend on the condition of the
sample being affected by: heat treatment
deformation
−The intrisic coercivity (Hic) is defined as the field strength at which
the M is reduced to zero.
In soft magnetic materials Hic ≈ Hc
In hard magnetic materials Hic > Hc
−The coercive field (or coercive force), which is the magnetic field
needed to reduce the magnetization to zero from an arbitrary level.
−The coercivity which is the magnetic field needed to reduce the
magnetization to zero from saturation.
−The coercivity become an upper limit for all values of coercive force.
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(7) Differential permeability
(How useful is permeability when considering ferromagnets?)
− The permeability μ is not a particularly useful parameter for
characterization of ferromagnet, since by virtue of the hysteresis
loop almost any value of μ can be obtained.
(1) μ = ∞ at the remanance B = Br, H = 0
(2) μ = 0 at the coercivity B = 0, H = Hc
dB
− The differential permeability  ' 
is a more useful quantity (this
dH
value also varies with field).
− The maximum μ’max, which occurs at the coercive point
H = Hc; B = 0.
− The initial μ’in, which is the slop of the initial magnetization curve at
the origin.
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(8) Curie temperature (what happens if a ferromagnets heated?)
− The transition temperature from ferromagnetic to paramagnetic
behavior is called the Curie temperature (Tc).
− At Tc, the permeability of material drops suddenly and Hc, Br
become zero
Material
Tc
Fe
770oC
Co
358oC
Ni
1130oC
Nd2Fe14B
312oC
Gd
20oC
Hard ferrite
400-700oC
Barium ferrite
450oC
− Classification of hard or soft magnetic materials
(Is there a simple method of classification of the various ferromagnetic
materials?)
 Ferromagne tic  Coercivity hard

 

magnetic materials
 materials

soft
− Coercivity is a structure –sensitive magnet property
it can be altered by
different thermal
treatment
different mechanical
(In a way that for example saturation magnetization cannot.)
Hard magnetic material
Soft magnetic material
Hc > 10 kA/m (125 Oe)
Hc < 1 kA/m (12.5 Oe)
Metglas
μr
(See in fig 4.2)
Hc
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Electromagnets (Where do soft magnetic materials find uses?)
− Soft magnetic materials find applications in electromagnet, motors,
transformers, and relays.
− The criteria for consideration of materials for electromagnets are that
the core materials should have (1) high permeability, to enable high
magnetic induction to be achieved, while a having a (2) low
coercivity so that the induction can easily be reversed.
− The electromagnets soft iron is used almost exclusively.
coercivity : 80A/m (10 Oe)
saturation magnetization : 1.7 × 106 A/m
make it the ideal material
− Electromagnets are used in the lab for generating high magnetic
fields.
− A typical lab electromagnet is capable of generating field of up to 2
tesla without any special configuration and, with small air gaps,
fields of up to 2.5 tesla can be produced.
− Sometimes the pole tips of the electromagnet are made from a
cobalt-iron alloy which has a higher saturation magnetization in
order to achieve slightly higher fields in the air gap
(Ms = 1.95 × 106 A/m, for an alloy of 35% Co, 65% Fe
Ms = 1.7 × 106 A/m, for iron)
− For magnetic induction above 3 tesla, electromagnets are not very
usefully because the iron cannot contribute much additional field.
Therefore for higher field strength either water-cooled iron-free
magnets(Bitter magnets) or superconducting magnet are used.
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Electromagnet
Electromagnets produce static, or DC, magnetic fields normally in the
range 0-20 kOe, It consists of a magnetic circuit composed by a yoke
and two cores made of high permeability carbon steel. Two coils of wire
having hundreds, or even thousands, of windings are allocated around
the cores.
The useful magnetic field is created in the air gap between the pole
caps. This magnetic field depends on the current, the permeability and
saturation induction of the core and the physical dimensions of the
magnetic circuit (in particular, the air gap distance).
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The following figure shows a typical horizontal electromagnet, but in
some cases costumers also request vertical electromagnets. For instance,
companies that commercialise BH meters and DC hysteresigraphs for
the characterization of permanent magnets prefer a vertically designed
electromagnet.
The most important specifications of an electromagnets are:
maximum magnetic field produced in useful air gap distances (one-inch
or one and half inches air gap, for instance), magnetic field uniformity,
power consumption, maximum current per coil, magnets resistance,
cooling water, or air, flow required and air gap range.
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Transformer (what are the characteristics of ferromagnetic materials
needed in power generation?)
− At first sight it would appear that the requirements for transformer
material were identical to those for electromagnet. However, this not
quite true.
− Transformers operate under a.c. conditions and therefore although
high permeability of the core material is desirable it is also necessary
to reduce the eddy current losses by employing as low conductivity
material as possible.
−Transformer core material:
(1) Grain-oriented silicon-iron, which contain 3~4wt% Si to reduce
conductivity.
(2) The material is usually hot-rolled then cold-worked twice followed
by an annealed to improve the grain orientation, increasing permeability
along the rolling direction.
(3) Core loss unit: watts/kilogram
(4) Losses decrease with increasing Si content but material also become
more brittle.
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− Table 4.3 show core loss at a frequency of 60Hz for sheets
of thickness 0.3~0.5mm.
− These thickness are equal or less than skip depth δ in the
material, which at 60Hz is typically δ = 0.3~0.7mm
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• A transformer makes use of Faraday's law and the ferromagnetic
properties of an iron core to efficiently raise or lower AC voltages.
It of course cannot increase power so that if the voltage is raised,
the current is proportionally lowered and vice versa.
Core form and shell form transformers
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Energy losses
An ideal transformer would have no energy losses, and would be
100% efficient. In practical transformers, energy is dissipated in the
windings, core, and surrounding structures.
Larger transformers are generally more efficient, and those rated for
electricity distribution usually perform better than 98%.
Designing transformers for lower loss requires a larger core, goodquality silicon steel, or even amorphous steel for the core and thicker
wire, increasing initial cost so that there is a trade-off between initial
cost and running cost.
Transformer losses arise from:
(1)Winding joule losses
Current flowing through winding conductors causes joule heating. As
frequency increases, skin effect and proximity effect causes winding
resistance and hence losses to increase.
(2) Hysteresis losses
Each time the magnetic field is reversed, a small amount of energy is
lost due to hysteresis within the core. According to Steinmetz's formula,
the heat energy due to hysteresis is given by
hysteresis loss is thus given by
where, f is the frequency, η is the hysteresis coefficient and βmax is the
maximum flux density, the empirical exponent of which varies from
about 1.4 to 1 .8 but is often given as 1.6 for iron.
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(3) Eddy current losses
Eddy currents therefore circulate within the core in a plane normal to
the flux, and are responsible for resistive heating of the core material.
The eddy current loss is a complex function of the square of supply
frequency and inverse square of the material thickness.
Eddy current losses can be reduced by making the core of a stack of
plates electrically insulated from each other, rather than a solid block; all
transformers operating at low frequencies use laminated or similar cores.
Core Characteristics
A transformer whose core is constructed of laminated sheets of steel
dissipates heat readily; thus it provides for the efficient transfer of power.
These steel laminations are insulated with a nonconducting material,
such as varnish, and then formed into a core. It takes about 50 such
laminations to make a core an inch thick.
The purpose of the laminations is to reduce eddy current losses. An
important point to remember is that the most efficient transformer core
is one that offers the best path for the most lines of flux with the least
loss in magnetic and electrical energy.
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Electromagnetic relays (what magnetic properties are useful in magnetic
switches and control devices?)
− A relay is a form of electromagnet
Opening
− Relay can be used as a switch for Closing an electrical circuit.
− A very weak current in the control circuit can be used to control a
much larger current in the operating circuit.
− The control circuit of the relay consists of
a coil with magnetizable
core
a moveable component
(armature, 轉子)
− The yoke(軛鐵) and core(芯) materials of relays have much the
same requirements as electromagnets
low coercivity
low remanence
high magnetic induction
leading
low core loss
high permeability
Iron
or
Iron-based alloy (Fe-Si, Fe-Ni)
− Relay materials
− The addition of Si
from 100A/m to n A/m
to
Fe
reduces
the
coercivity
− The addition
as low as 1 A/m
to
Fe
reduces
the
coercivity
of
Ni
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Relay
繼電器(Relay)，也稱電驛，是一種電子控制器件，它具有控
制系統（又稱輸入迴路）和被控制系統（又稱輸出迴路），通常應
用於自動控制電路中，它實際上是用較小的電流去控制較大電流的
一種「自動開關」。故在電路中起著自動調節、安全保護、轉換電
路等作用。
電磁繼電器的工作原理和特性:
電磁式繼電器一般由鐵芯、線圈、銜鐵、觸點簧片等組成的。
只要在線圈兩端加上一定的電壓，線圈中就會流過一定的電流，從
而產生電磁效應，銜鐵就會在電磁力吸引的作用下克服返回彈簧的
拉力吸向鐵芯，從而帶動銜鐵的動觸點與靜觸點（常閉觸點）吸合
。當線圈斷電後，電磁的吸力也隨之消失，銜鐵就會在彈簧的反作
用力返回原來的位置，使動觸點與原來的靜觸點（常開觸點）吸合
。這樣吸合、釋放，從而達到了在電路中的導通、切斷的目的。
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