slide #1 - introduction to machinary - sem 1, 2012-2013
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MCT 2337
Electrical Machines
Lecture Slide #1
Introduction to Machinery
Principles
1
Dr. Iskandar Al-Thani bin Mahmood
Department of Mechatronics Engineering
Faculty of Engineering
International Islamic University Malaysia
E-mail: am.iskandar@iium.edu.my
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ELECTRICAL MACHINES
An electrical machine is a device that can convert either:Mechanical energy to Electrical energy, or
Electrical energy to Mechanical energy.
When it converts:
Mechanical energy to Electrical energy GeneratorElectrical energy to Mechanical energy Motor
Since, any electrical machine can convert power in any direction,
any machine can be used as motor or generator.
Transformer is a electrical device that is closely related
to electrical machine. It operate on the same principle as
motors and generators magnetic field.2
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Why motor and generator are so common?
The answer are:Electrical power is a clean, efficient, easy to transmit over long
distances and easy to control. This is unlike internal-
combustion engine.
3
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ROTATIONAL MOTION, NEWTONS LAW AND
POWER RELATIONSHIPS
Almost all electric machine rotate about an axis shaft.
Because of the rotational nature of machinery, it is
important to have basic understanding of rotational
motion.
In general, a 3-dimensional vector is required to
describe a rotation of an object, but since machines turn
on a fixed shaft, one angular dimension is enough,
In this course, clockwise(CW) is assumed to be +ve, and
counterclockwise(CCW) is assumed to be ve.4
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ROTATIONAL MOTION
Angular position,,of an object is the angle at which
it is oriented from some ref. point and normallymeasure in radians or degrees.
The following symbols are used to describe angular
velocity and angular acceleration , Angular Velocity, radians/second;
fm, Angular Velocity, revolution/second
nm, Angular Velocity, revolution/minute
, Angular Acceleration, radians/second2;
The subscriptmis to indicate mechanical quantity.
5
= m
m
d
dt
m
=d
dt
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Shaft speed are related to each other by the following
equations
6
2
60
mm
mm
f
fn
=
=
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TORQUE
In linear motion, a force applied to an object causes its velocity to change.
There exists a similar concept in rotation i.e. torque.
The torque on an object is the product of force applied and the smallest
distance between the line of action of the force and the objects axis of
rotation.
Figure 1-1
(a)A force applied to a cylinder so that it passes through the axis of rotation.
(b)A force applied to a cylinder so that the line of action misses the axis of rotation.7
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More formally,
Figure 1-2
Derivation of the equation for the torque on an object 8
rxF
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NEWTONS LAW OF ROTATION
In linear motion, the Newtons law is given by the equation
A similar equation describes the relationship between the torque
applied to an object and its resulting angular acceleration call
Newtons law of rotation
is the net applied torque (Newton-meters)
is the resulting angular acceleration (radians/second2)
Jis the moment of inertia of the object (kilogram-meters2)
9
J=
maF=
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WORK
For linear motion, work is defined as the application of a force
through distance. In equation form
For a constant force that is collinear with the direction of motion
For rotational motion, work is the application of a torque through an
angle. In equation form
For constant torque
10
= FdrW
= dW
FrW=
=W
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POWER
Power is the rate of doing work, or the increase in work per unit time.
The equation for power is
By this definition, and assuming that force is constant and collinear
with the direction of motion, power is given by
Similarly, assuming constant torque, power in rotational motion is
given by
11
dtdWP=
( ) Fvdt
drFFt
dt
d
dt
dWP =
===
( ) =
===dt
d
dt
d
dt
dWP
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THE MAGNETIC FIELD
Magnetic fields are the fundamental mechanism in
electrical machineries. Four basic principles below describehow magnetic field are used in these devices:
A current-carrying wire produced a magnetic field in the area
around it. (Magnetic field is measured by H magnetic field
intensity.)
A time changing magnetic field induces a voltage in a coil of wire if
it passes through that coil - Transformer action.
A current-carrying wire in the presence of a magnetic field has aforce induced on it - Motor action.
A moving wire in the presence of a magnetic field has a voltage
induced in it - Generator action.. 12
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Magnetic field intensity is governed by Amperes Law
whereHis the magnetic field intensity produced by the currentInet
dlis a differential element of length along path of integration.
To better understand the meaning of this equation, let
us look at the following example:
13
= netIdIH.
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EXAMPLE 1 Consider this rectangular core withNturn wire winding wrapped about
one leg of the core.
Assuming the core is made of ferromagnetic materials, all the magneticfield produced by the current will remain inside the core, so the path of
integration in Amperes law is the mean path length of the corelc.
The current passing within the path of
integrationInettis thenNior magnetomo-
tive force (mmf).
Thus, Amperes law becomes
Therefore, the magnitude of the magnetic
field intensity in the core due
to the applied current is
14Fig.1: A simple magneticcore
NiHlc=
cl
NiH=
=== netc IHldlHdIH.
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Magnetic field intensityHis in a sense a measure of the effortthat a current is putting into the establishment of a magnetic field.
The strength of the magnetic field flux produced in the core alsodepends on the material of the core.
The relationship between theHand the resulting magnetic fluxdensityBwithin a material is given by
where
H= magnetic field intensity (ampere-turns per meter, A/m)
= magnetic permeability of material. (henrys per meter,H/m)
B= resulting magnetic flux density produced (tesla, T)
The permeability of free space is called0, and its value is
H/m 15
HB =
7
0 104
=
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The permeability of any other material compared to the0is called its
relative permeability
In the core shown in Fig. 1, the magnitude of the flux density is given
by
The total flux in a given area is given by
wheredAis the differential unit of area.
If the flux density vector is perpendicular to a plane of areaA, and fluxdensity is constant throughout the area
16
0
=r
cl
NiABA
==
cl
NiHB
==
=A
dAB.
MAGNETICPROPERTIESOFFERROMAGNETIC
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MAGNETIC PROPERTIES OF FERROMAGNETIC
MATERIALS
The relative permeability of ferromagnetic
material is very high, up to 6000 times the
permeability of free space.
Although permeability is constant in free space,
it is not true for ferromagnetic materials.
Consider a direct current applied to the core inFig. 1 starting from 0 A and slowly working up
to the maximum permissible current.
Fig. 2(a) illustrate theproduced in the coreversus mmf producing it.
Note that theproduced in the core is linear inthe unsaturated region, and approaches a
constant regardless of mmf in the saturated
region. 17
Fig. 2: Saturation Curve or
Magnetizing curve or B-H curve.
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From these equations
it can be found that the relationship ofBandHwould be the same asbetweenand mmf as illustrated in Fig. 2 (b).
Thus in electrical machines, ferromagnetic material is used as core in order
to produce as much as flux as possible in order to produced voltage
(generator) or torque (motor), i.e. 6000 time more as compared to air core.
In most real machines, they operates near knee (nonlinear region) of
magnetization curve in order to maximize flux. This nonlinearity account for
many peculiar behavior explained in future lectures.
Discuss:Example 1-5
18
BAl
NiH
c
== ,
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MAGNETIC CIRCUIT
The following equation show that the current in a coil wrapped
around a core produces a magnetic flux in the core.
This is in some sense analogous to voltage in electric circuit (EC)
producing a current flow. Hence, its possible to define magnetic
circuits (MC).
In EC (V = IR), its the voltage that drives currentI.Byanalogous, the corresponding quantity in MC is called
magnetomotive force (mmf).
Magnetomotive force is measured in ampere-turns is equal to
effective current flow applied to the core, or
19
cl
NiABA ==
NiF=
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Like voltage source, mmf has polarity. The polarity can be determined as
in Fig. 3.
In an EC, the applied voltage causes a currentIto flow. In MC, theapplied mmf causes fluxto be produced.
The relationship between voltage and current is , similarly, the
relationship between mmf andis
where = reluctance of circuit,
and measured in ampere-turns/weber.
Just like in EC, conductance is recipr-
ocal of resistance, permeancePis
the reciprocal of .
Thus, flux can be expressed as 20Fig. 2: Determining the polarity of
a mmf in a magnetic circuit.
IRV=
=F
PFmmf=
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Reluctance in a MC obey the same rules as resistance in an EC.
Reluctance is series
and in parallel
The reluctance of the core in Fig. 1:
By comparing with ,
Discuss:Example 1-121
.....321 +++= RRRReq
.....1111
321
+++=RRRReq
=
===
c
cc
l
AF
lANi
lNiABA
=FA
lc
=
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ENERGY LOSSES IN A FERROMAGNETIC CORE
HYSTERESIS LOSSES
Consider alternating current as shown in Fig. 4(a)
applied to the winding on the core.
By referring to Fig. 4(b), assuming the initial flux
is zero (pointa), as the current increases for the 1st
time pathab.
When the current falls, the flux traces a different
pathbcdand later when the current increases
again, the flux traces out pathdeb.
Note that the amount of flux present in the core
depends on applied current and previous history offlux.
This dependence on the preceding flux history and
the resulting failure to retrace flux path is called
hysteresis.22
Fig. 4:The hysteresis loop
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Note in Fig. 4(b), when mmf is removed, the flux does not go to zero.
Instead, a magnetic field is left in the core residual flux.
To force the flux to zero, an amount of mmf known as thecoercive mmfmust be applied in the opposite direction.
The fact that turning domains requires energy leads to a common type of
energy loss hysteresis loss.
23
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Why does hysteresis occur
As the strength of mmf is increased, nearly all the atom and domains in
the iron are lined up with the external field, any further increase in the
mmf can cause only the same flux increase that it would be in free space.
At this point, the iron issaturatedwith flux. 24
Fig. 5: (a) Magnetic domain orientated randomly
(b) Magnetic domain lined up in the presence of
external magnetic field.
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FARADAYS LAW
Faradays law states that if a flux passes through a turn of coil of wire,
a voltage will be induced in the turn of wire that is directly proportional
to the rate of change in the flux with respect to time or in equation form
This equation assumes that exactly the same flux is present in each
turn of the coil, no flux leaking out.
Faradays law is the fundamental property of magnetic field involved in
transformer operation.
25
dt
dNeind
=
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EDDY CURRENT LOSSES
A time-changing flux within a ferromagnetic core also induced voltage ,
just the same manner as it would in a wire wrapped around that core.
These voltages cause swirls of current to flow within the core, much like
the eddies seen at the edges of a river. It is the shape of these current
that gives rise to the nameeddy currents.
These eddy currents are flowing in a resistive material, so energy isdissipated which lead into heating the iron core.
The amount of energy lost due to eddy current depend on: Size of current swirls
Resistivity of the material
Thus, eddy current losses can be reduces by Broken up the ferromagnetic core into parallel laminations to reduced the current
swirl size. An thin insulating layer is used between lamination to limit eddy
current to small area.
Adding silicon to the steel core in increase the resistivity.
26
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27
Fig. 6: (a) Solid iron core
carrying an ac flux.
(b) Eddy currents are reduced by
splitting the core in half.
(c) Core built up of thin,
insulated laminations.
Fig. 7: (a) Voltage induced in a revolvingarmature. (b) Large eddy currents are induced.
Fig. 8: (a) Armature built up of thin laminations.(b) Much smaller eddy currents are induced.
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PRODUCTION OF INDUCED FORCE ON A WIREA second major effect of a magnetic field on its surrounding is that it
induces a force on a current-carrying wire within the field.
Consider a conductor (wire) present in a uniform magnetic field of flux
densityB, pointing into the page. The force induced on the wire is given
by
The magnitude of the force is given by the equation
where is the angle between the wire and the
flux density vector.
The direction of the force is given by the right
-hand rule: Index finger points in the direction ofl.
Middle finger points in the direction ofB.
Thumb points in the direction of resultant forceF.
DiscussExample 1-7
28
Fig. 8: Force on a current-carrying
wire in a magnetic field
sinilBF=
( )BliF =
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INDUCED VOLTAGE ON A CONDUCTOR MOVING IN A MAGNETIC FIELD
The third major way in which a magnetic field interacts with its
surrounding is that if a wire with the proper orientation moves through a
magnetic field, a voltage is induced in it as shown in Fig. 9.
The voltage induced in the wire is given by
where
v= velocity of the wireB= magnetic flu density vector
l= length of conductor in the magnetic field
Vectorlpoint along the direction of the wire
towards the end making the smallest anglew.r.t. the vectorv x B.
The voltage in the wire will be built up so
that the positive end is in the direction of the
vectorv x B.
29
Fig. 9: A conductor moving in thepresence of a magnetic field.
( ) IBveind =
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DiscussExample 1-8, 1-9.
30
Fig. 10: The conductor of Example 1-9
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REAL, REACTIVE AND APPARENT POWER IN SINGLE-PHASE AC CIRCUITS
In DC circuit, the power supplied to the DC load is simply the product of
the voltage across the load and the current flowing through it.
However in AC circuits, power is more complex, because there can be a
phase difference (angle) between the AC voltage and the AC current
supplied to the load.
The instantaneous power is still the product of the instantaneous
voltage and the instantaneous current, but the average power supplied
to the load is affected by the phase angle.
Consider, a single-phase voltage source supplying power to a single-phase load
31
VIP=
= ZZ
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Consider, a single-phase voltage source supplying power to a single-
phase load
The voltage applied to this load is
whereVis the rms value of the voltage applied to the load.
The resulting current flow is
whereIis the rms value of the current flowing through the load.
The instantaneous power supplied to this load at any time is 32
Fig. 11: An AC voltage source
supplying a load Z.
( ) tVtv cos2
=
( ) ( ) = tIti cos2
( ) ( ) ( ) ( ) == ttVItitvtp coscos2
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The eqn. can be rewrite as
the first term represent the power supplied to the load by component of
current that is in phase with voltage,
while the second term represents the power supplied to the load by the
component of current that is 90oout of phase with voltage.
33
Fig. 12: The component of power
supplied to a single-phase load.
( ) ( )[ ] [ ]tVItVItp 2sinsin2cos1cos ++=
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Note that the first term is always positive and produces pulses of power
instead of a constant value. This power is known as real power (P) and
the unit is watts (W).
The second term is positive half of the time and negative half of thetime. So, the average power supplied by this source is zero. This power
is known as reactive power (Q) and the unit is volt-amperes reactive
(VAR).
Reactive power represents the energy that is first stored and thenreleased in the magnetic field of an inductor, or in electric field of a
capacitor.
By convention, Q is positive for inductive loads and negative for
capacitive loads.
The apparent power S is the power that appears to be supplied to the
load if the phase angle are ignored.
The unit is volt-amperes (VA).
34
cosVIP=
sinVIQ=
VIS=
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Other form of power equations
Consider
35
Fig. 13: An inductive load has a
positive impedance angle .
*VIS
jQPS
=
+=
== IIVV and
( ) ( ) ( )
( ) ( )
( ) ( )
jQP
jVIVI
jVIVI
VIIVVIS
+=+=
+====
sincos
sincos
*
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The real, reactive and apparent power supplied to a load are related by
the power triangle.
The quantity of is usually known as the power factor of a load.
Its defined as the fraction of the power S that is actually supplying real
power to a load.
36
Fig. 14: The power triangle
222
QPS +=cos
S
P
PF == cos
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DiscussExample 1-11.
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