chp1 electromagnetic

8/8/2019 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.

chp1 electromagnetic

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