MAGNETIC CIRCUITS. Reluctance The resistance of a material to the flow of charge (current) is...
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Transcript of MAGNETIC CIRCUITS. Reluctance The resistance of a material to the flow of charge (current) is...
MAGNETIC CIRCUITS
Reluctance• The resistance of a material to the flow
of charge (current) is determined for electric circuits by the equation
• The reluctance of a material to the setting up of magnetic flux lines in a material is determined by the following equation
A
l
A
lR
At/Wbor rels,A
l
tyconductivi
1
Ampere-turns per weber
Ohm’s Law for Magnetic Circuits
opposition
causeeffect
• For magnetic circuits, the effect is the flux .
• The cause is the magnetomotive force (mmf) F, which is the external force (or “pressure”) required to set up the magnetic flux lines within the magnetic material.
• The opposition to the setting up of the flux is the reluctance, .
Ohm’s Law for Magnetic Circuits
• Substituting:
Ohm’s Law for Magnetic Circuits
• The magnetomotive force is proportional to the product of the number of turns around the core (in which the flux is to be established) and the current through the turns of wire AtNI
• An increase in the number of turns of the current through the wire, results in an increased “pressure” on the system to establish the flux lines through the core.
Ohm’s Law for Magnetic Circuits
Magnetizing Force• The magnetomotive force per unit
length is called the magnetizing force (H).
• Magnetizing force is independent of the type of core material.
At/ml
H
Magnetizing Force• Magnetizing force, H is determined
solely by the number of turns, N the current, I and the length of the core, l:
At/ml
NIH
Magnetizing Force• The flux density and the magnetizing
force are related by the equation:
HB
Hysteresis
• Hysteresis – The lagging effect between the flux density, B of a material and the magnetizing force, H applied.
• The curve of the flux density, (B) versus the magnetizing force, (H) is of particular interest to engineers.
Hysteresis
Series magnetic circuit used to define the hysteresis curve.
Hysteresis Curve
Hysteresis
• The entire curve (shaded) is called the hysteresis curve.
• The flux density B lagged behind the magnetizing force H during the entire plotting of the curve. When H was zero at c, B was not zero but had only begun to decline. Long after H had passed through zero and had equaled to –Hd did the flux density B finally become equal to zero
Hysteresis
• If the entire cycle is repeated, the curve obtained for the same core will be determined by the maximum H applied.
Hysteresis
Normal magnetization curve for three ferromagnetic materials.
Hysteresis
Expanded view for the low magnetizing force region.
Ampere’s Circuital Law• Ampère’s circuital law: The
algebraic sum of the rises and drops of the mmf around a closed loop of a magnetic circuit is equal to zero; that is, the sum of the rises in mmf equals the sum drops in mmf around a closed loop.
0
IRV
or Hl
Ampere’s Circuital Law• As an example:
0 cacabcbcabab lHlHlHNI
0
cacabcbcabab lHlHlHNI
Hl
Steel
Cobalt
Iron
Flux • The sum of the fluxes entering a
junction is equal to the sum of the fluxes leaving a junction
Flux acba juction at
bacb junction at or
Series Magnetic Circuits : Determining NI• Two types of problems• is given, and the impressed
mmf, NI must be computed – design of motors, generators and transformers
• NI is given, and the flux of the magnetic circuit must be found – design of magnetic amplifiers
Series Magnetic Circuits : Determining NI• Table method • A table is prepared listing in the
extreme left-hand column the various sections of the magnetic circuit. The columns on the right are reserved for the quantities to be found for each section
Series Magnetic Circuits : Determining NI
Example 1:
(a) Determine the secondary current I2 for the transformer if the resultant clockwise flux in the core is 1.5 x 10-5 Wb.
Series Magnetic Circuits : Determining NI
Example 1 – solution
Tx
x
AB 1.0
1015.0
105.13
5
At/m30abcdH
Tx
x
AB 1.0
1015.0
105.13
5
Series Magnetic Circuits : Determining NIExample 1: – solution (cont’d)
Based on B- H curve: mAtH abcd /30
Using ampere circuital law :
A 84.330
)16.0(30260
2
2
112
1122
2211
I
xx
N
lHINI
lHININ
lHININ
abcdabcd
abcdabcd
abcdabcd
abcdabcd2211 lHININ
Series Magnetic Circuits : Determining NIExample 2 – solution
3108.30470 efabefablH
Calculate Hl for each section;
At 34.21
3101271600 bcdebcdelH
At 2.203
1 Inch=0.0254m 1 Inch2=6.451x10-
4m2
Series Magnetic Circuits : Determining NIExample 2 – solution (cont’d)
The magnetic circuit equivalent
The electric circuit analogy
At 54.2242.20334.21 bcdebcdeefabefab lHlHNI
A 4.4950
54.224
N
NII
At/Wbor rels,,ReluctanceA
l
At,force iveMagnetomot NI
Summary:
]Tesla[,densityFlux A
B
IRV
At/ml
NI
lH