slide #1 - introduction to machinary - sem 1, 2012-2013

7/21/2019 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: [email protected]


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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


27/37

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.

37

slide #1 - introduction to machinary - sem 1, 2012-2013

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