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CHAPTER 2 Electromagnetism and magnetic circuit
7th week
This property of ferrromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.
Hysteresis When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed.
It must be driven back to zero by a field in the opposite direction
If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop.
The lack of re-traceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material.
Once the magnetic domains are reoriented, it takes some energy to turn them back again.
Hysteresis Loop
It is customary to plot the magnetization M of the sample as a function of
the magnetic field strength H, since H is a measure of the externally
applied field which drives the magnetization .
Variations in Hysteresis Curves
Variations in Hysteresis Curves There is considerable variation in the hysteresis of different magnetic materials
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Hysteresis Loss
• Hysteresis loop
Uniform distribution
• From Faraday's law
Where A is the cross section area
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Hysteresis Loss
• Field energy
Input power :
Input energy from t1 to t2
where Vcore is the volume of the core
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Hysteresis Loss
• One cycle energy loss
where is the closed area of B-H hysteresis loop
• Hysteresis power loss
where f is the operating frequency and T is the period
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Hysteresis Loss
• Empirical equation
Summary : Hysteresis loss is proportional to f and ABH
Eddy currents are currents induced in conductors to oppose the
change in flux that generated them.
It is caused when a conductor is exposed to a changing magnetic field
due to relative motion of the field source and conductor; or due to
variations of the field with time.
This can cause a circulating flow of electrons, or a current, within the
body of the conductor.
These circulating eddies of current create induced magnetic fields that
oppose the change of the original magnetic field due to Lenz's law,
causing repulsive or drag forces between the conductor and the
magnet.
Eddy Current Loss
To reduce amount of eddy current loss, the iron core has to be made in laminated sheets.
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Eddy Current Loss
• Eddy current Along the closed path, apply Faraday's law
where A is the closed area Changes in B → = BA changes
→induce emf along the closed path →produce circulating circuit (eddy current) in the core • Eddy current loss where R is the equivalent resistance along the closed path
me BkfP 22 W/m3
Empirical equation of eddy current loss
K = characteristic constant of the core material Bm = maximum flux density n = steinmetz exponent; vary form 1.5 to 2.5
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Core Loss
• Core Loss
losscurrenteddyP
losshysteresisPwhere
PPP
e
h
ehc
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Magnetizing Characteristics
• Behavior of flux density compared with magnetic field strength
• B-H curve or magnetizing curve
• Increased current to the coil measured the flux
B(T)
H(A/m)
Magnetization curve (B-H characteristic)
Saturation
Figure 2. : Example of BH curve NIH
AB
;
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Hysteresis
• The relationship between B and H is complicated by non-linearity and “hysteresis”
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