chp1 electromagnetic
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IntroductionIntroduction(Chapter 1)(Chapter 1)
BEE3163BEE3163ELECTROMECHANICALELECTROMECHANICAL
SYSTEMSSYSTEMS
BEE3163BEE3163ELECTROMECHANICALELECTROMECHANICAL
SYSTEMSSYSTEMS
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BASIC FOUNDATIONELECTROMAGNETICS
The basic concept of electromagnetic field theory constitute thefoundation of electrical motion devices (motor, generators, and
transducers), as well as electromechanical analysis and design
ELECTROMAGNETICSELECTROMAGNETICS
CIRCUITS AND DEVICESCIRCUITS AND DEVICES
Iron or ferromagnetic material as pathway
Magnetic flux as energy carrier
Current pass through turns of wire wrapped around the closedpathway---- electromagnetic circuit is energized
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BASIC FOUNDATIONMagnetic Flux
If AC current passes through the coil then flux alternating back andforth in the core
If DC current passes through the coil then flux moves in only 1direction in the core
SI units = Wb= webers
Flux Density, BAbility of magnetic core to conduct flux is limited to cross section of
the pathway
Ferromagnetic magnetic material of the core that conduct magneticflux is limited in capacity to carry flux
Saturated: core is operating at its maximum capacity and no more fluxcan be carried in the core
Force of the magnetic flux is proportional to the flux density
BFg
J
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BASIC FOUNDATION
AB
J!
B= flux density in T or Wb/m2
(Wb)corein thelux!J2
marea,!A
B
H
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BASIC FOUNDATION Total magnetic flux through the surface
! sdBTT
.J
!
l s
sdJdlBTTT
..0
Q spacereeotypermeabili0 !Q Ampere circuit law states that
n
l
ildB ..0
Q!TTand
Faradays law of induction states that
=
!!!!l s
dt
d
dt
dNsdtB
dt
ddltEemf
JTTT..
linkagesflux
turnsofnumber
!
!
]
N
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BASIC FOUNDATION
The current flow in the opposite direction of the flux linkages.
The emf represent the magnitude of the potential difference in acircuit carrying current
dtdire firV =!!
][volts,isemsorunit V
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BASIC FOUNDATION
Is the result of the electric current circulating in
the coil wrapped around the core
mmf in the magnetic circuit is multivalued,because its magnitude (amount) increase with
each turn of wire added to the coil
1-turn coil with 2A of electric current circulating
in it has mmf of 2 amp-turn
magnetomotive force, mmf
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BASIC FOUNDATION
10-turns coil with 2A of electric current circulating in it has mmf of 20amp-turn
mmf = NImmf = NImmf = magnetomotive force
N = number of turn
I = electric current, A
!l
dltHf .
mmf is the line integral of the time- varying magnetic field intensity
!ssl
sddt
tDdsdtJldt
TT
TTTT...
Using second Maxwells equation
ctordensity vecurrentvarying-time!J
T
mmf is the sum of induced current and the rate of change of the fluxpenetrating the surface of the contour
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BASIC FOUNDATION
Magnetic circuit has a core cross sectional area
of 24cm2 (A=LxW= 4cm x 6cm) and flux of
1.80mWb circulating in it. The flu result from a
6Hz alternating current of 0.75A passing througha 200 turns coil wrapped around the core of the
magnetic circuit. Determine
Flux density in the core
mmf used to set up the flux in the core
Example
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BASIC FOUNDATION
If a circuit is made from the same
Cross sectional area
mmf
Ferromagnetic material
but different in the average length of the magnetic path, therefore themagnetic strength (H) is greater in shorter path
magnetic field strength, H
l
mmf
l
NI!!
)
m
A(pathmagnetictheofstrengthfieldmagnetic!H
turn)-(ampA!mmfAcurrent,electric!I
Nturn,oNumber!Ncmdl 311 !! T
cmdl 472 !!T
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BASIC FOUNDATION
HB .Q!
magnetic field strength, H Example
2 cast iron of magnetic circuits have length of 31cm and 47cm. Each are
magnetized by winding 50 turns of wire around the core and passing 4A of
electric current through the turns. Determine magnetic field strength, H
Permeability of a substance is an indication of its ability to carry magnetic
flux when acted on by a magnetomotive force, mmf.
If H, varies, then B caries
Wb/A.mcore,magneticin thematerialtheoftypermeabili!Q
ExampleExample
Determine of the permeability of mild steel core of the series
magnetic circuit when the magnetic field strength of the circuit is
250A/m. Find the permeability using B=uH and the B-H curve for
the mild steel
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BASIC FOUNDATION
Reluctance, Is a measure of the opposition the magnetic circuit offers to the flux
Analogies to the resistance in electric circuit
!
!NImmf
J
A
l
AHB
l
lAB
H
l
lINNI
).()./(/./
/.
QJJ!!!!!
Relative Permeability, rQ
Is the ratio of the permeability of the material to the permeability of free space
0Q
QQ !r
)t.m-Wb/A(,104space,reeotypermeabili
t.m-Wb/Amaterial,otypermeabili
typermeabilirelative
7-
0TQ
Q
Q
!
!
!r
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BASIC FOUNDATION
Duality of the mmf and emf !
l
dltHmmf . !l
ldtEemfTT
.
Inductance and reluctance
I
NL
J!
J
mmf!
Is the ratio of the total flux linkages to thecurrent which they link
Is the ratio of the mmf to the flux
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BASIC FOUNDATION
Self inductance
dtdLI
dtdiL
dtLId
dtde f !!! )(]
Inductance and reluctanceI
L]
!
dt
diLemf !
If L is constant
ExampleFind the self inductance of a long solenoid with air core and iron core
( ). The solenoid has 100 turns ( ), thelength is 0.2m ( ), and the uniform circular cross
sectional area is 0.005m2 ( ).
02000QQ ! 100!N
ml 2.0! 2005.0 mA !
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BASIC FOUNDATIONBASIC FOUNDATIONAnalogies between Electric and Magnetic
Circuit
!
mmf
J RIE.
!!
tongcorrspondi
tongcorrspondi
tongcorrspondi
R
I
For magnetic circuit For electric circuit
J
mmf
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BASIC FOUNDATION
Electrostatic
20
21
4 x
qq
F TI!
Electrostatic interaction was investigated by Charles coulomb
For charges q1 and q2 separated by a distance x in free space,
the magnitude of the electric force is
112
01085.8space,freeoftypermittivi
v! FmI
xaxqqFT
2
0
21
4TI!
chargestwothesejoininglinethealongdirectedrunit vectotheisa x
In vector form
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BASIC FOUNDATION
Electrostatic
.,. EDQdsDs
s
TTTIJ !!!
Gauss Law states that
surfacebyenclosedchargetotalQ
areasurfacevectorsd
fluxelectrictotal[C]
mediumtheoftypermittivi
intensityfieldelectricE
densityfluxelectric][FmD 1
!
!
!
!
!
!
s
T
T
T
J
Ohms Law states that
EJTT.W!
Wmaterial,otyconductivi
intensityieldelectric
Jdensitychargevolume T
T
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BASIC FOUNDATION
Electrostatic
J
ET
T
!V
resistivity
Resistance, resistivity and conductivity relationship
A
l
A
lr
.rand
.
W
V!!
areasectionalcrossisA
lengthisl
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BASIC FOUNDATIONEnergy
Energy stored in magnetostatic field
densityvolumemagneticis][.2
1 3JmHB!
v
m dvHBWTT
.2
1
Ex: Energy stored in inductor is stored in the magnetic field within the coil
2.
2
1
ILWm !
mmec dWdW !
ldFdW mmecTT
.!
z
WF
y
WF
x
WF
mmz
mmy
mmx
x
x!
x
x!
x
x! ,,
For the lossless conservative system, the differential change of the mechanicalenergy is equal to the differential change of magnetic energy
For translational motion
In Cartesian coordinates
UdTdW emec !For rotational motion, Torque
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BASIC FOUNDATION
Example
Consider the electromagnet that has N turns. The distance between
the stationary and moveable members is denoted as x (t). The mean
length of the stationary and moveable members are l1
and l2respectively and the cross sectional area is A. neglecting the
leakage flux, find the force exerted on the moveable member if the
time varying current ia(t) is supplied. The permeability of stationary
and moveable members are 1 and 2 respectively.
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