unit 4 correct syllabus

8/12/2019 Unit 4 Correct Syllabus

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4.1 Elementary Concepts

Voltages can be induced by time-varying magnetic fields. In rotating machines,voltages are generated in windings or groups of coils by rotating these windings mechanicallythrough a magnetic field, by mechanically rotating a magnetic field past the winding, or bydesigning the magnetic circuit so that the reluctance varies with rotation of the rotor.

he flu! lin"ing a specific coil is changed cyclically, and time-varying voltage isgenerated. Electromagnetic energy conversion occurs when changes in the flu! lin"age resultfrom mechanical motion. # set of such coils connected together is typically referred to as anarmature winding, a winding or a set of windings carrying ac currents. In ac machines such assynchronous or induction machines, the armature winding is typically on the stator. $the stator

winding% In dc machines, the armature winding is found on the rotor. $he rotor winding%&ynchronous and dc machines typically include a second winding $or set of windings%, referredto as the field winding, which carries dc current and which are used to produce the mainoperating flu! in the machine. In dc machines, the field winding is found on the stator. Insynchronous machines, the field winding is found on the rotor. 'ermanent magnets can beused in the place of field windings. In most rotating machines, the stator and rotor are made of

electrical steel, and the windings are installed in slots on these structures. he stator and rotorstructures are typically built from thin laminations of electrical steel, insulated from each other,to reduce eddy-current losses.

4.( Introduction to #C and )C *achines

4.(.1 #C *achines

raditional ac machines fall into one of two categories+ synchronous andinduction.

In synchronous machines, rotor-winding currents are supplied directly from the

stationary frame through a rotating contact. In induction machines, rotor currents are induced inthe rotor windings by a combination of the time-variation of the stator currents and the motion of


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the rotor relative to the stator. &ynchronous *achines

ig. 4.1+ a simplified salient-pole ac synchronous generator with two poles.

he armature winding is on the stator, and the field winding is on the rotor. he field winding ise!cited by direct current conducted to it by means of stationary carbon brushes that contactrotating slip rings or collector rings. It is advantages to have the single, low-power field windingon the rotor while having the high-power, typically multiple-phase, and armature winding on thestator. #rmature winding $a,a% consists of a single coil of turns. Conductors forming these coilsides are connected in series by end connections. he rotor is turned at a constant speed by asource of mechanical power connected to its shaft. lu! paths are shown schematically by

dashed lines.

#ssume a sinusoidal distribution of magnetic flu! in the air gap of the machine in ig.4.1.

he radial distribution of air-gap flu! density is shown in ig. 4.($a% as a function of thespatial angle / around the rotor periphery. #s the rotor rotates, the flu! 0lin"ages of thearmature winding change with time and the resulting coil voltage will be sinusoidal in time asshown in ig 4.($b%. he freuency in cycles per second $23% is the same as the speed of therotor in revolutions in second $rps%. # two-pole synchronous machine must revolve at 566 rpmto produce a 5623 voltage. ote the terms 7rpm8 and 7rps8.


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the generated voltage for the single-phase generator of ig. 4.1.

# great many synchronous machines have more than two poles. ig 4. shows in schematicform a four-pole single-phase generator. he field coils are connected so that the poles are of

alternate polarity. he armature winding consists of two coils $a1,9a1%and $a(,9a(%connected inseries by their end connections. here are two complete wavelengths, or cycles, in the flu!distribution around the periphery, as shown in ig. 4.4. he generated voltage goes through twocomplete cycles per revolution of the rotor. he freuency in 23 is thus twice the speed in rps.

igure 4. &chematic view of a simple, four-pole, single-phase synchronous generator.


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igure 4.4 &pace distribution of the air-gap flu! density in an ideali3ed,

four-pole synchronous generator.

:hen a machine has more than two poles, it is convenient to concentrate on a single pair ofpoles and to e!press angles in electrical degrees or electrical radians rather than in physical

units.

;ne pair of poles euals 56 electrical degrees or (

< electrical radians. &ince there are poles=( wavelengths, or cycles, in one revolution, it followsthat

:here

s the angle in electrical units and /ais the spatial angle.

he coil voltage of a multipole machine passes through a complete cycle every time a pair ofpoles sweeps by, or $poles=(% times each revolution. he electrical freuency

fe of the voltage generated is therefore

where n is the mechanical speed in rpm.ote that

he rotors shown in igs.4.1 and 4. have salient, or pro>ecting, poles with concentratedwindings. ig.4.? shows diagrammatically a nonsalient-pole, or cylindrical, rotor.

he field winding is a two-pole distributed winding@ the coil sides are distributed in

multiple slots around the rotor periphery and arranged to produce an appro!imatelysinusoidal distribution of radial air-gap flu!.


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*ost power systems in the world operate at freuencies of either ?6 or 56 23.

# salient-pole construction is characteristic of hydroelectric generators because

hydraulic turbines operate at relatively low speeds, and hence a relatively large numberof poles is reuired to produce the desired freuency.

&team turbines and gas turbines operate best at relatively high speeds, and turbine-driven alternators or turbine generators are commonly two- or four-pole cylindrical- rotormachines.

igure 4.? Elementary two-pole cylindrical-rotor field winding.

*ost of the worldAs power systems are three-phase systems. :ith very few e!ceptions,

synchronous generators are three-phase machines.

# simplified schematic view of a three-phase, two-pole machine with one coil per phase

is shown in ig. 4.5 $a%

ig. 4.5$b% depicts a simplified three-phase, four-pole machine. ote that a minimum of

two sets of coils must be used. In an elementary multipole machine, the minimumnumber of coils sets is given by one half the number of poles.

ote that coils $a,a% and $aB,9aB% can be connected in series or in parallel. hen the coils

of the three phases may then be either - or D-connected. &ee ig. 4.5$c%.


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igure 4.5 &chematic views of three-phase generators+ $a% two-pole, $b% four-pole, and

$c% connection of the windings.

he electromechanical torue is the mechanism through which a synchronous generator

converts mechanical to electric energy.

:hen a synchronous generator supplies electric power to a load, the armature current

creates a magnetic flu! wave in the air gap that rotates at synchronous speed.

his flu! reacts with the flu! created by the field current, and an electromechanical

torue results from the tendency of these two magnetic fields to align.

In a generator this torue opposes rotation, and mechanical torue must be applied from

the prime mover to sustain rotation.

he counterpart of the synchronous generator is the synchronous motor.

#c current supplied to the armature winding on the stator, and dc e!citation is

supplied to the field winding on the rotor. he magnetic field produced by thearmature currents rotates at synchronous speed.

o produce a steady electromechanical torue, the magnetic fields of the stator

and rotor must be constant in amplitude and stationary with respect to each other.

In both generators and motors, an electromechanical torue and a rotational

voltage are produced which are the essential phenomena for electromechanical

energy conversion.

ote that the flu! produced by currents in the armature of a synchronous motor

rotates ahead of that produced by the field, thus pulling on the field $and hence onthe rotor% and doing wor". his is the opposite of the situation in a synchronousgenerator, where the field does wor" as its flu! pulls on that of the armature,

which is lagging behind.


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igure 4.F ypical induction-motor speed-torue characteristic.

4.(.( )C *achines

)C *achines

here are two sets of windings in a dc machine.

he armature winding is on the rotor with current conducted from it by

means of carbon brushes.

he field winding is on the stator and is e!cited by direct current.

#n elementary two-pole dc generator is shown in ig. 4.G.

#rmature winding+ $a,a% , pitch factor + 1G6o

he rotor is normally turned at a constant speed by a source of

mechanical power connected the shaft.


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igure 4.G Elementary dc machine with commutator.

he air-gap flu! distribution usually appro!imates a flat-topped wave,

rather

than the sine wave found in ac machines, and is shown in ig. 4.H$a%.

otation of the coil generates a coil voltage which is a time function

having the same waveform as the spatial flu!-density distribution.

he voltage induced in an individual armature coil is an alternating

voltage and rectification is produced mechanically by means of acommutator. &tationary carbon brushes held against the commutatorsurface connect the winding to the e!ternal armature terminal.

he need for commutation is the reason why the armature windings are

placed on the rotor.

he commutator provides full-wave rectification, and the voltage

waveform between brushes is shown in ig. 4.H$b%.


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igure 4.H $a% &pace distribution of air-gap flu! density in an elementarydc machine@ $b% waveform of voltage between brushes.

It is the interaction of the two flu! distributions created by the direct

currents in the field and the armature windings that creates anelectromechanical torue.

If the machine is acting as a generator, the torue opposes rotation.

If the machine is acting as a motor, the torue acts in the direction of the

rotation.

4. ** of )istributed :indings

*ost armatures have distributed windings, i.e. windings which are spread over a

number of slots around the air-gap periphery.

he individual coils are interconnected so that the result is a magnetic field

having the same number of poles as the field winding.

Consider ig. 4.16$a%.

ull-pitch coil+ a coil which spans 1G6 electrical degrees.

In ig. 4.16$b%, the air gap and winding are in developed form $laid out flat% and

the air-gap mmf distribution is shown by the stepli"e distribution of amplitude


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igure 4.16 $a% &chematic view of flu! produced by a concentrated, full-pitchwinding in a machine with a uniform air gap. $b% he air-gap mmf produced bycurrent in this winding.

4..1 #C *achines

It is appropriate to focus our attention on the space-fundamental

sinusoidal component of the air-gap mmf.

In the design of ac machines, serious efforts are made to distribute the

coils ma"ing up the windings so as to minimi3e the higher-order harmonic

components.

he rectangular air-gap mmf wave of the concentrated two-pole, full-pitch

coil of ig.4.16$b% can be resolved to a ourier series comprising afundamental component and a series of odd harmonics.

he fundamental component


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ig. 4.11$a% shows phase a of the armature winding of a simplified two-

pole, three-phase ac machine and phases b and c occupy the empty slots.

he windings of the three phases are identical and are located with their

magnetic a!es 1(6 degrees apart. he winding is arranged in two layers,

each full-pitch coil of c turns having one side in the top of a slot and theother coil side in the bottom of a slot a pole pitch away.


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igure 4.11 he mmf of one phase of a distributed two-pole, three-phase windingwith full-pitch coils.

he modified form of $4.% for a distributed multipole winding is

+ number of series turns per phase,

kw+ winding factor, a reduction factor ta"ing into account the distribution of

the winding, typically in the range of 6.G? to 6.H?, hepea" amplitude of this mmf wave is

E. $4.?% describes the space-fundamental component of the mmf wave

produced by current in phase a of a distributed winding.

If the result will be an mmf wave which is stationary in space

and varies sinusoidally both with respect to aand in time.

he application of three-phase currents will produce a rotating mmf wave.

otor windings are often distributed in slots to reduce the effects of space

harmonics.


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ig. 4.1($a% shows the rotor of a typical two-pole round-rotor generator.

#s shown in ig. 4.1($b%, there are fewer turns in the slots nearest the pole

face.

he fundamental air-gap mmf wave of a multipole rotor winding is

igure 4.1( he air-gap mmf of a distributed winding on the rotor of a round-rotor

generator.

4..( )C *achines

ecause of the restrictions imposed on the winding arrangement by the

commutator, the mmf wave of a dc machine armature appro!imates asawtooth waveform more nearly than the sine wave of ac machines.

ig. 4.1 shows diagrammatically in cross section the armature of a two-pole

dc

machine.


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he armature coil connections are such that the armature winding produces a

magnetic field whose a!is is vertical and thus is perpendicular to the a!is ofthe field winding.

#s the armature rotates, the magnetic field of the armature remains vertical

due to commutator action and a continuous unidirectional torue results.

he mmf wave is illustrated and analy3ed in ig. 4.14.

igure 4.1 Cross section of a two-pole dc machine.


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igure 4.14 $a% )eveloped s"etch of the dc machine of ig. 4.((@ $b% mmf

wave@ $c% euivalent sawtooth mmf wave, its fundamental component, andeuivalent rectangular current sheet.

)C machines often have a magnetic structure with more than two poles.

he machine is shown in laid-out form in ig. 4.1?$b%.


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igure 4.1? $a% Cross section of a four-pole dc machine@ $b% development of

current sheet and mmf wave.

he pea" value of the sawtooth armature mmf wave can be written as

Ca total number of conductors in armature winding

m number of parallel paths through armature winding.

ia armature current, #

4.4 *agnetic ields In otating *achinery

he behavior of electric machinery is determined by the magnetic fields

created by currents in the various windings of the machine.

he investigations of both ac and dc machines are based on the assumption

of sinusoidal spatial distribution of mmf.

esults from e!amining a two-pole machine can immediately be e!trapolated

to a multipole machine.

4.? otating ** :aves in #C *achines

o understand the theory and operation of polyphase ac machines, it isnecessary to study the nature of the mmf wave produced by a polyphase

winding.

4.?.1 ** :ave of a &ingle-'hase :inding

ote that from E. $4.?%,


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:hen the winding is e!icted by a current

MMF pattern for alternating and rotatingmagnetic field

Consider a 2-pole machine or one pair of poles of a

P-pole winding. The analysis presented can easily be

extended to a poly phase winding with any number of

phases.

In a 3-phase machine the windings of the

individual phases are displaced from each other by 2!

electrical degrees in space around the inner

circumference of the stator" as shown by the coils a-a#" b-

b#" c-c# in $igure3.2% . Consider a 2 pole machine with

concentrated full-pitch coils which represent distributed

windings.


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&a' . (implified 2-pole 3-phase &b' Instantaneous 3-phase currents

stator winding

$ig.3.2%

)hen a current flows through a phase coil" it

produces a sinusoidally distributed m.m.f wave centered

on the axis of the coil representing the phase winding.

If an alternating current flows through the

coil" it produces a pulsating m.m.f wave " whose

amplitude and direction depend on the instantaneous

value of the current flowing through the winding. *ach

phase winding will produce similar sinusoidally

distributed mmf waves " displaced by 2! electrical

degrees in space from each other.

+et us now consider a balanced 3-phase current

flowing through the 3-phase windings. The instantaneous

currents are

, cos t --- 3.

, cos t - 2! ' ----- 3.

, cos t -2%! ' , cos

t/ ' ---3.!

These instantaneous currents are shown in $igure

3.2% &b'.The reference directions" when positive-phase

currents flow through the windings" are shown by dots


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and crosses in the coil sides in $igure 3.0.&a'. )hen

these currents flow through the respective phase

windings" each produces a sinusoidally distributed m.m.f

wave in space " pulsating along its axis and having a pea1

located along the axis.

*ach m.m.f wave can be represented by a space

vector along the axis of its phase with magnitude

proportional to the instantaneous value of the current.

The resultant m.m.f wave is the net effect of the three

component m.m.f waves" which can be computed either

graphically or analytically.

n analytical expression will be obtained for

the resultant m.m.f wave a t any point in the air gap"

defined by an angle. The origin of the angle can be

chosen be the axis of phase a" as shown in $igure 3.22.

&a'. t any instant of time " all three phases contribute to

the air gap m.m.f along the path defined by & or t'. The

mmf along is

$&' , $a&' / $b&' / $c&' --- 2


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$ig.3.24. 5otion of the resultant mmf

t any instant of time" each phase winding

produces a sinusoidally distributed mmf wave with its

pea1 along the axis of the phase winding and amplitude

proportional to the instsntaneous value of the phase

current. The contribution from phase a along

$a&' , 6 iacos ----3.

)here 6 is the effective number of turns in

phase 7a#8 ia is the current in phase a 9ecause the phase axes are shifted from

each other by 2! electrical degrees" the contributions

from phase b and c are" respectively


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$b&' , 6 ib cos & - 2! --- 3.2

$c&' , 6 iccos& / 2! ----

3.3

The resultant m.m.f a t point is

$&' , 6 iacos / 6 ib cos & - 2! / 6 ic

cos& / 2! ---3.%

The currents ia " ib and ic are functions of

time and are defined *:uations

nd thus

$&" t' , 6Imcos cos / 6Imcoscos & -2! / 6Imcos cos & /2! ----;

+et us define6Im , $m " and using the

following trigonometric identity

cos.cos9 , < coa &-9' /=2 cos&/9'

----3.4

*ach term on the right-hand side of e:uation

3.% can be expressed as the sum of two cosine

functions" one involving the difference and the other the

sum of the two angles which can be arranged to have

$& " t' , /

, $m cos & ' --- 3.0

*:uation &' shows that the resultant wave in

the air gap has two components> the first component is


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termed forward-rotating component whereas the second

term the bac1ward ? rotating component.

The forward rotating rotates at the constant

angular velocity given by speed rotates

" f , supply fre:uency

t any instant of time" say t" the wave is

distributed sinusoidally around the air gap &fig .2' with

the positive pea1 acting along , t a later

instant" say t2" the positive pea1 of the sinusoidally

distributes wave is along > that is " the wave

has moved by around the air-gap.

3.11 Space Phasor Model

The space phasor model of ac machine can

be developed using the concept of @space vectorsA. In ac

machines the stator has a distributed winding with

several coils distributed around the periphery.

The 55$ distribution in space therefore "has

a stepped waveform" which can be approximated to a

sine wave. $or dc current flowing in the 7a# phase of the

stator winding" there is sinusoidal distribution of the55$ and the flux density in space. The pea1 value of

this flux density is along the axis of the coil which is

considered here as reference axis &,!'.

Bowever "if the 55$ wave of phase 7a# of

stator is described by an e:uivalent current phasor ias> it

will be assumed to have a magnitude of Ias and direction

along the axis of the winding&,!'.(ince the distributionof 55$ is sinusoidal the effect of this current at an angle

will be Ias cos .

In three phase induction motor the three

phase windings are identical with 2! degree phase

displacement between them. Thus if axis 7a# current is

ta1en as reference" the current space phasor for phase 7b#

and 7c# will have /2! degree and /2%! degrees &-2!


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degree' from phase 7a#. If dc current is flowing in all the

three windings" the current space vectors will have their

position

$ig 3.20. Current space vectors with dc

current in a"b and c windings

as shown in fig 3.20. The combined stator

currents as given by *:uation is also a current vector"

called resultant stator current space

Vector Is, which can be obtained as

= 0 + + = {

+a + } --3.17

Where

a= ; cos = [a ! cos =

---- 3.1"

The current vector can be resolved along d-:

axes as

, / ---3

The current space vector of a three-phase

machine has a fixed direction in space for each phase that


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is along the axis of the magnetic flux density produced

by the 55$ of respective winding. The magnitude of

each phase currentspace vector is the magnitude of the

current" and the angle is the angle of the axis of the

phase winding with the reference axis. If instead of dc "

ac current is applied to the three phase windings of the

stator" the magnitude of the current space vector will be

varying sinusoidally with time" In order to obtain the

resultant current spac e vector" the time v ariation of the

current is also considered. (uppose

= cos t;

= cos t #;

= cos t #----3.$0

Then the resultant current space vector is

given as

, / + =

+% ----- 3.$1

or = -----3.$$

This means that the stator current space

vector has a constant magnitude e:ual to and it

rotates with a constant angular speed e:ual to

Dad=sec.

The current"voltage or flux space phasors are

the resultant stator or rotor current" voltage or flux:uantities obtained by ta1ing vector sum of these

:uantities in appropriate axes frame.


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(imilarly the complex rotor current phasor

= +a + } -----3.$3

In a similar way sinusoidal flux density wave

can be described bya pace vector. It is however preferred

to choose the corresponding distribution of the flux

lin1age with a particular three phase winding as the

characteriEing :uantity.

2 ARMATURE W!"!#

The armature winding is a vital part of a dc

machine. This is where emf is induced and force is

developed that results in the turning of the rotor. The

design of the armature winding is more critical than the

design of other parts of a dc machine. The armature

winding is housed on slots made on the armature

surface. $ormed coils are placed on slots. The ends of

the coils are oined with commutator segments.

3.2.1 Materials Re$%ired for Armat%re Winding

Coils for the armature winding are made from insulated

copper conductors. Bard-drawn annealed higher

conductivity copper is used. luminum wires are not used

because of the restriction on winding space in slots and a


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Class G Cotton" sil1" paper"press board" wood" etcH notimpregnated nor oil immersed" PCwith or without plasticiEer"vulcaniEed natural rubber" etc.

Class Cotton" sil1" paper" etc.when impregnated or immersed in ali:uid dielectric such as oil" &in classG material impregnated with naturalresins" cellulose esters" insulatingoils" etc.'" also laminated wood"varnished paper" cellulose" acetatefilm" etc.

Class * (ynthetic resinenamels" cotton and paper

laminates with

formaldehyde bonding" etc.

Class 9 5ica" glass fibre"asbestos" etc. with suitable

bonding substances"built-up mica" glass-fibre

and asbestos laminates

Class $ Class 9 materials withthermally resistant

bonding materials.

Class B Jlass fibre" asbestos"built-up mica" etc. with silicon resinbinder

Class C Jlass fibre" asbestos"built-up mica" etc.

with silicon resinbinder.

&ond%ctor ns%lation $or small-siEe machines double-cotton-covered

copper wires are used. $or medium-siEe machines the conductors are rectangular in

shape. *ach conductor is machine-taped with superfine cotton tape" whereas for


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large-siEe machines each conductor is machine-taped with one layer of !.2 mm

thic1 impregnated cotton tape with half overlap.

Slot ns%lation$or slot insulation" leatheroid" manila paper or

mica folium of appropriate thic1nesses are used. Kverhangs" i.e. the

bac1 portions of the coils not lying in slots" are insulated with

varnished and impregnated cotton tape.

$ig.3.%. &a' Cross-sectional view of thearmature of

a %-pole dc machine

&b' Incomplete developed diagram of the armature

winding

&omm%tator The commutator is made up of a number of

commutator segments. Coil-ends are connected to each commutator

segment.

The segments of the commutator are made of hard-drawn copper

and are separated by thin sheets of mica or micanite.

The induced emf per conductor in a dc machine is small. The problem is how

these conductors are to be connected together so as to form a complete winding.

$igure 3.%&a' shows the cross-sectional view of the armature of a four-pole machine.


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$or ease of understanding" a developed diagram of armature of $ig.

3.% &a' is drawn as shown in $ig. 3.%&b'. Conductors should be so

connected that the total emf is maximum. Therefore" conductor

should be connected to conductor 0 shown by dotted line as conductor

0 is placed below conductor 4 so that they occupy identical positions

under two adacent poles. (imilarly conductor 3 should be connected

with conductor and so on. $ig. 3.4 shows the developed winding

diagram of the 0 armature conductors of $ig. 3.% &a'. The average

pitch LaYbac1 pitch LbY and the front pitch fY are calculated as>

0%

%aY = =

2

b f

a

Y YY

+

=

2b fY Y =

$or progressive lap winding

2b f

Y Y =

4" 3b fY Y =

$igure 3.4 gives the details of end

connections of the conductors" connection of coils with

commutator segments" and the position of brushes on thecommutator surface with their polarities. This type of

winding is called lap winding. In the winding shown in

$ig.3.4" single-turn conductors are used. s many as 0

conductors ma1e eight coils. The coils are -0" 3-" 4-!"


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;-2" -%" -0" 3-2 and 4-%. The design of a lap

winding of the type shown in $ig. 2. is described as

follows.

Fig 3.' Armat%re (inding of a dc machine

3.2.2 )ap Winding

In a lap winding" the finishing end of one coil is

connected via the commutator segment to the starting end of the

adacent coil situated under the same pole. In this way all the coils

are connected. The winding is 1nown as lap winding because the sides

of successive coils overlap each other &see $ig.3.4'. coil may

consist of any number of turns. The number of slots re:uired on the

armature is e:ual to the number of coil-sides if two coil-sides are

placed in each slot. )ith two coil-sides in each slot" a two-layer

winding is obtained. )hile ma1ing a winding diagram in a two-layer

winding" all top coil-sides are numbered odd whereas the bottom

coil-sides are numbered even &shown by dotted lines' as shown in

$ig.3.0 . $or an eight-coil armature" therefore" eight slots are re:uired


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on the armature surface. The following terminologies are re:uired to

be understood for preparing an armature winding diagram.

Fig. 3.* Position of coil+sides in slots of a t(o+la,er armat%re (inding

Pole Pitch It is e:ual to the number of coil-sides perpole. $or a single turn" eight-coil" four-pole armature pole pitch is

calculated as>

Pole pitch ,. 2 - 2

%. %

No of coils

No of poles

= =

&oils and &oil+sides The dc armature

windings are double-layer type having at least twocoil-sides per slot. *ach coil consists of an upper coil-

side at the top of one slot and a lower coil-side

situated at the bottom of another slot. The distance

between the two coil-sides of a coil is approximately

e:ual to the pole pitch. coil may be of single turn

or of many turns. If two coil-sides are placed in one

slot " then the number of slots re:uired on the

armature of housing the coils is e:ual to the number

of coils of the winding. $or low-speed high-voltage

winding" however" the number of coil-sides per slot is


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more than two. This is because the winding will have

a large number of coils and it may not be possible to

have an e:ual number of slots on the armature.

-acPitch The distance measured in terms of the number of armature

conductors &coil sides' between the two coil-sides of a coil measured around the

bac1 of the armature" i.e. away from the commutator end of the armature is called

the bac1 pitch" Yb&see $ig.3.;'.

Front PitchThe distance between two coil-sides connected to the

same commutator segment is called the front pitch".

Res%ltant PitchIt is defined as the distance in terms of the number of

coil-sides between the start of one coil and the start of the next coil to which it is

connected.

&omm%tator PitchIt is defined as the

distance measured in terms of commutator segments

between the segment is to which the two ends of a coil are

connected.


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E/ample 3.1

Prepare a layout winding diagram for a

simplex lap-type dc armature winding. The winding is for

four poles. The armature has 0 slots and 0 commutator

segments.

(olution

6umber of armature coils , 6umber of

commutator segments

, 0

6umber of coil,sides &conductors'

0 2 32Z = =

9ac1 Pitch32

%

b

ZY

P= =

, or ;

2b fY Y =

2f bY Y

, - 2 &using bY ,'

, ;

.bY =

;fY =

(ince b fY Y> the winding is a progressive one.

s there are 32 coil-sides and 0 slots" the

number of coil-sides per slot is 2. The connection scheme

of the coil-slides is shown in $ig.3..


36/65

Coil-side is connected to coil-side ! on the

other side of the commutator &since bY is " coil- side is

connected to coil - side /" i.e. !'.

Coil -side ! is connected to coil-side /"

i.e. !'. Coil-side ! is connected to coil side 3 on the

commutator end &(ince Gfis ;" coil-side ! is connected

to coil-side !-;"i.e. 3' The winding progresses according

to the above scheme. It may be noted that each coil is

used once and the winding is a closed one.

$ig 3. (cheme for connections of the coil-sides of a

dc armature windings

The layout diagram of the winding along with commutator connections and brush

positions is shown in $ig.3.. Connections of the coil-sides are made as follows> for

connections at the bac1 end of the armature" add the bac1 pitch with the coil-side

which is to be connected.


37/65

Thus coil-side is to be connected with coil-side / Yb, i.e. / , !. Kn the

commutator end side" coil-side ! is connected to coil-side 3.

This is achieved by subtracting Gf"i.e. ; from coil-side number ! &! -; , 3'.

Coil-side 3 is now connected to 3 / Yb, 3 / , 2. In this way the winding is

completed.

The positions of the four poles are also shown in $ig. 3.. *ight coil-sides

placed in four slots are under each pole. ssuming a direction of rotation of the

armature" say anti-cloc1wise in $ig. 3." the direction of the induced emf in the

armature conductors is determined by applying $lemingLs right-hand rule. The

direction of the current in the coil-sides under north poles will be downward and

under southL poles upward as shown in $ig. 3..

The position of brushes can be determined by tracing the directions of

current in various coil-sides. $rom $ig. 3." it can be observed that directions of

current in coil-sides and are downward and they are connected to commutator

segment . brush placed on commutator segment will have positive polarity.(imilarly in coil-sides and 0" the current is upwards. The two coil-sides are

connected to commutator segment 4. The brush placed on commutator segment

4 will have negative polarity. (imilarly the positions of the other two brushes

are fixed. Two positive brushes and two negative brushes are oined together to

output terminalsA andB respectively.

The number of parallel paths of the armature winding across the outputterminals is four &e:ual-to the number of poles' which can be examined as

follows> Dedraw the armature winding of $ig. 3. in a simplified manner as

shown in fig. 3.!.


38/65

9etween terminalsA andB there are four parallel paths shown asM, N,K and

P. The total emf generated in the machine is e:ual to the emf generated in one

parallel path.

Fig.3.0.The layout diagram of the windingalong with commutator connections


39/65

$ig.3.! . &a' rmature winding of a dc

machine shown in a simplified manner

&b' (hows the number of parallel

paths in the armature

*:ualiser Connections in +ap )indings> s

mentioned earlier" a simplex lap winding has as many

number of parallel paths as there are poles. The emf

induced in each parallel path may not be exactly e:ual

due to a number of reasons" such as the difference in the

lengths of the air-gap under each pole" the difference in

the lengths of the air-gap under each pole" the difference

in the field strength due to some error in putting field

windings. etc.

Fne:ual values of emf generated in the

parallel paths will circulate a considerable amount of

current in the armature circuit without doing any useful

wor1. This circulating current will be large as the

armature circuit resistance is generally very low.

This circulating current will generate heat and while circulating

through the brush contacts will cause commutation difficulties &li1e

spar1ing on the commutator surface'.

To overcome this problem arising from the

circulating current" e:ualiEer connections are made in lap

wound armatures. These e:ualiEer connections or

e:ualiEers are low-resistance copper conductors which

connect those points in the winding which under ideal


40/65

conditions should be at e:ual potential. The difference in

potential between these points created due to reasons

mentioned earlier will be e:ualiEed as a result of flow of

current through these low resistance conductors which

will bypass the current from flowing through the brushes.

3.2.3 Wae Winding

In a wave winding a coil-side under

one pole is connected to a second coil-side which

occupies approximately the same position under the next

pole through bac1 connection. The second coil-side is

then connected forward to another coil-side under the

next pole &in the case of lap winding the second coil is

connected bac1 through the commutator segment to a

coil-side under the original pole'. The difference in lap

and wave winding connections has been illustrated in

$ig. 3.; &a' and &b'.

The characteristics of a wave winding are

&i' verage pitch"2

2

b f

a

Y Y ZY

P

= =

If Ya is ta1en e:ual toZ/P, as is the case in a lap winding the winding after one

round will close itself without including all the coils which is not desirable. Bence

the product of the average pitch and the number of pairs of poles must be two

greater or less than the number of coil-sides.

verage pitch should be a whole number.


41/65

&ii' 9oth bac1 pitch and front pitch should he odd

numbers.

&iii' To ma1e the average pitch a whole number" wave winding is not possible

with any number of coil-sides. $or example if M , 32 andP , %"

2 32 2 - ;2 2%

a

ZY or

P

= = =

Thus wave winding is not possible with 32 coil-sides. In this case

the number of effective coil-sides needs to be 3!.

E/ample 3.2

Prepare a winding diagram for a four-pole wave-connected armature of

a dc generator having 22 coil sides.

2 22 20 4

%a

ZY or

P

= = =

If aY is ta1en to be odd" i.e. 4" then the front pitch and

bac1 pitch will be e:ual. Thus" 4a b fY Y Y= = =

Connections of the coil sides will be as shown in $ig.3..

The connection diagram is achieved by adding Yband Y with the coil num-

bers progressing in the forward direction. Coil-side is connected at the bac1

with coil-side 0 & / Yb= 0'. Coil side 0 is connected at the front with coil-side

&0/Gf, ' and so on.


42/65

$ig 3..Connection diagram of the coil-

sides for a dc wave winding

In $ig. 3. it is to be noted that coil-side

is connected with coil-side 2. This is obtained by

adding bY to which gives 2%. Coil-side 2% does not

exist as there are in all in all 22 coil-sides.

Therefore after 22 count two more numbers

starting from . This gives coil-side 2. (imilarly it can be

seen that coil-side 2! is connected in the front with coil-

side 3. 9y adding & 4'fY = to 2!" the number 24 is


43/65

$ig. 3.2.+ayout diagram for a wave winding

obtained. fter 2! five numbers are counted as 2" 22" "

2" and 3. Thus coil-side 2! should be connected to coil-side 3. In this

way the whole winding is completed by connecting all the coil-sides

with one another. The actual layout diagram of the winding along with

the position of the poles and the direction of induced emf in the coil-

sides for a particular direction of rotation of the armature are shown in

$ig.3.2..

The positions of the four brushes are also shown in the

figure.

The positions of brushes are fixed as follows> for ease in

understanding" the connection diagram of $ig. 3. is reproduced in

$ig.3.3. The directions of current in the coil-sides are also shown

by observing the directions from $ig.3.2.

9y carefully examining the directions of current in the coil-

sides it is seen that between points P and Q current gets divided in

two parallel paths. $rom point P the current flows to Q via two

paths" viE. through -0-2- ...

0---3-

The pointP in $ig. 2. is the separating point ofthe emf in the two sections of the winding and therefore

corresponds to the position of one of the brushes" viE.

the negative brush. $or placing of the positive brush" it is

seen from $ig. 3.3 that at point N current is coming out


44/65

from both the coil-sides. Therefore" point Q corresponds

to the position of the positive brush.

$ig 3.3 Connection diagram for armature

winding of figure 3.2

It may be noted from $ig. 3.2that coil-sides 0

and ; lie in the interpolar region. The direction of

current in these coil-sides will depend upon the

direction of current in the other coil side of the

respective coils" viE. coils -0 and ;-22. Dummy Coils

s mentioned earlier wave winding is possible with a

particular number of coil-sides. 9ut if standard stampings

with a definite number of slots are to be used" the number

of coil-sides needed to be placed in all the slots may be

more than the re:uired number. In such a case" the extra

coils are left unconnected. These coils are called dummy

coils. Oummy coils are used so as to ma1e the armature

dynamically.

A"A!TA#ES F WAE ER )AP

W!"!#

. wave winding does not usually re:uire

e:ualiEer rings.


45/65

2. Though wave winding re:uires only two

brushes" it is usually fitted with as many brushes as there

are poles. s such poor contact at any brush does not

impair satisfactory operation of the machine.

3. 5ost of the machines are wave wound.

+ap windings may be used in high power machines

&above 4!!)' to reduce the current per armature path.

E/ample 3.3

The armature core of a 0-poles machine has

% slots. The commutator has 242 segments. The

windings are to have six coil ? sides per slot. )hat must

be the front and bac1 pitches so that the elements may be

insulated in groups of three &i.e." symmetrical winding'

a. If the winding is to be a simplex lap.

b. If it is to be simplex wave.

Sol%tion4

. The number of coil sidesZ , 242x2 , 4!%

6umber of coil-sides per slot u , 0 " 6umber

of slots 4!%=0 , %

a. Simple lap4

yav , , % " yb, % / , 4 as

is an integer to satisfy the condition of symmetrical. Gf ,

3

b. Simple (ae4

yav , is not an integer. Therefore with

one dummy coil of two sides"


46/65

the number of the active coil-sides , 4!2.

yav , , %" yb , 4" yf , 3 will

ma1e the winding symmetrical.

E/ample 3.5

Calculate the winding pitches and draw

developed and se:uence diagrams of the winding for a

four-pole wave connected armature winding of a dc

generator having seven coils. In the diagram" show the

position of poles and the position and polarity of brushes.

(olution 6umber of coil-sides ; 2 %= =

2 % 23 %

%a

ZY or

P

= = =

aY (hould be an integer" bY and fY should be

odd numbers.Therefore we choose

aY , bY , fY ,3

The se:uence and layout diagrams of the

winding are shown in $ig". 2.2!.

3.3 Field (indings

3.3.1 MMF pattern of comm%tator(inding

characteristic of poly-phase windings is

that the phase windings are" in principle"


47/65

galvanically separated. The phase windings are

connected via terminals to each other" in a star or

in a polygon. The armature winding of commutator

machines does not start or end at terminals.

The winding comprises turns of conductor

soldered as a continuum and wound in the slots

of the rotor so that the sum of induced voltage s is

always Eero in the continuum. This is possible i f the sum

of s lo t vo l tages i s Ee ro . l l t he co i l s ides o f

such a winding can be connected in ser ies to

form a continuum without causing a current to

Qow in the closed ring as a result of the voltages inthe coil sides.

Fig%re 3.15. T(o e/amples of comm%tator

(inding coil sides mo%nted in the slots. 6a7 T(o coil sides in a

slot8 one side in a la,er8U 91. 6:7 Fo%r coil sides in a

slot8 t(o coil sides in a la,er8 % 92 Een+n%m:ered coil


48/65

sides are located at the :ottom of the slots. There has

to :e a large eno%gh n%m:er of coils and comm%tator

segments to eep the oltage :et(een comm%tator segments

small eno%gh.

n external electric circuit is created by

coupling the connection pints of the coils to the

commutator segments. current is fed to the

winding via brushes dragging along the

commutator.

The commutator switches the coils in turns

to the brushes thus acting as a mechanical inverter

or rectiRer depending on the operating mode of the

ma-chine. This is called commutating. In the

design of a winding" the construction of a reliable

commutating arrangement is a demanding tas1

Commutator windings are always double-layer

windings.

Kne coil side of each coil is al-ways in the

upper layer and the other in the bottom layer

approximately at the distance of a pole pair from

each other. 9ecause of problems in commutating"

the voltage difference between the commutatorsegments must not be too high" and thus the

number of segments and coils has always to be

h igh enough . Kn the o the r hand " t he number

of s lots is rest r ic ted by the minimum width of


49/65

the teeth. Therefore" usually more than two coil

sides are placed in each slot. In the slot of the

upper diagram of $igure 2.%%" there are two coil

sides" and in the lower diagram the number of coil

sides is four. The coil sides are often numbered so

that the sides of the bot tom layer a re even

numbers" and the slots of the upper layer are odd

numbers. If the number of coi ls is Mc"2Mc coi l

sides have to be mounted in N slots" and thus there

are 2u , 2Mc=N sides in a slot.

The symbol u gives the number of coil sides

in one layer. In each side" there are 6v conductors.

The total number of conductors E in the armature is

M , N , 2 u N , 2 ----

3.

Bere

N is the number of slots

is the number of conductors in a slot

u is the number of coil sides in a layer"

is the number of coils"

is the number of conductors in a coilside"

2 u ,


50/65

9ecause , E=N , 2u N=N ,

2u

Fig%re 3.1'. 6a7 Princ iple of a t(o+pole8

do%:le+la,er comm%tator armat%re. The armat%re

rotates at an ang%lar speed ; cloc(ise generating an

emf in the conductors in the slots.

The emf tends to create the current directions

illustrated in the Rgure. &b' coil voltage phasor diagram

of the armature. It is afull-pitch winding" which does not


51/65

normally occur as a commutator winding. 6evertheless" a

fu ll-p itch winding is given here as a clarifying example. N , 0"

u, &one coil side per layer'

Commutator windings may be used both in C

and OC machines. 5ulti-phase commutator C

machines are " however " becoming rare. OC

machines" instead" are built and used also in the

present-day indust ry even though OC dr ives are

gradually being replaced by powere lectronic C

drives. 6evertheless" it is advisable to loo1 brieQy also at

the OC windings.

The C and OC commutator windings are in

principle e:ual. $or simplicity" the conRguration of the

winding is investigated with the voltage phasor

diagram of a OC machine. Bere" i t sufRces to

investigate a two-pole machine" since the winding ofmachines with multiple poles is repeated unchanged

with each pole pair. The rotor of $igure 3.4" with

N , 0" u ," is assumed to rotate cloc1wise at an

angular speed S in a constant magnet ic Reld

between the poles 6 and (.

The magnetic Reld rotates in the positivedirection with respect to the conductors in the

slots" That is countercloc1wise. 6ow" a coil voltage

phasor diagram is constructed for a winding" in which

we have already calculated the difference of the


52/65

coil side voltages given by thec oil voltage phasor

diagram. 9y applying the numbering system of

$igure 3.%.

)e have in slot the coil sides and 32" and

in slo t the coil sides 0 and ;. )ith this

system" the coil voltage phasor diagram can be

illustrated as in $igure 3.4 b.

$igure 3.4 shows that if the induced emf decides

the direction of the armature current" the produced tor:ue

is opposite to the direction of rotation &countercloc1wise

in $igure 3.4'" and mechanical power has to be

supplied to the machine" which is acting as a

generator. 6ow" if the armature current is forced to

Qow against the emf with the assistance of an external

voltage or current source" the tor:ue is in the

direction of rotation" and the machine acts as a

motor.

There are Mc , Nu , 0 , 0 coils in the

winding" the ends of which should next bec

onnected to the commutator. Oepending on the

way

they are connected different 1inds

of w i n d i n g s a re p r o d u c e d . * a c h c o n n e c t i o n p o i n t o f

t h e c o i l e n d s i s c o n n e c t e d t o t h e c o m m uta tor .There

are two main types of commutator windings> lap


53/65

windings and wave windings. lap winding has

coils" creating loop-li1e patterns. The ends of the coils

a re con nected t o ad acent commutator segments.

wave winding has a waveli1e drawing pattern

when presented in a plane.

The number of commutator segments is

given by ,uN " ---- 3.2

because each co i l s ide begins and

ends a t the commuta tor segment .

The number of commutator segments"

therefore" depends on the conductor arrangement

in the slot" and eventually on the number of coil

sides in one layer. $urther important parameters of

commutator windings are>

yN -coil span expressed as the number

of slots per pole

y - bac1-end connector pitch" which is a coil

span expressed as the number of coil sides.

$or the winding" the coil sides of which

are numbered with odd Rgures in the top layer and

with even Rgures in the bottom layer" this is

y,2uyN /" ----- 3.3


54/65

where the minus sign stands for the coil side numbering as seen

in $igure 2.%%" and the plus sign for the numbering where in

slot there are coil sides " 2" in slot 2 there are coil sides3" %"

and so on" if u,8 or in the top layer of slot there are coil

sides " 3 and in the bottom layer there are coil sides 2" %" and

so on" if u,2.

y2 - front-end connector pitch8 it is a

pitch expressed as the number of coil sides

between the right coil side of one coi l and the left

coil side of the next coil.

y - total winding pitch expressed as the

number of coil sides between two left coil sides

of two adacent coils.

yc - commutator pi tch between the

beginning and end of one coil expressed as the

number of commutator segments. The e:uation for

commutator pitch is a basic e:uation for winding design

because this pitch must be an integer

yc , n U a =p ----- 3.%

)here a is the number of parallel paths

per half armature in a commutator winding" which

means 2a parallel paths for the whole armature. The

windings that are most o ften employed are

characteriEed on the basis of n>


55/65

. I f n ,! " i t r e sul ts in a l ap

wind ing . The commuta tor p i t ch wi l l be yc ,

Ua= p" wh ic h means that 7a 7 is an integer multiple

of p to give an integer for the commutating pitch.

$or a l a p w i n di n g 2 a,2 p" th is means a,p" yc,

U . (uch a w ind ing i s ca l l ed a pa ra l l e l one .

T h e p l us s i gn i s f o r a p rog res s iv e w i nd i ng

moving f rom lef t to r igh t " and the minus sign

for a retrogressive winding moving from right to

left. If a is a 1 -multiple of the pole pair number"

a,1p " then it is a 1 -multiplex parallel winding.

$or example" for

a,2 p" the commuta tor p i tch i s yc,

U2 " a nd t his wi ndi ng i s c al l ed a d up le x

para l le l winding.

2 . I f n," it results in a wave winding

and a commutator pitch" that is

yc, Ua= p ,uN U a =p ---- 3.4

must be an integer. The plus sign is for

progressive and the minus sign for ret rogressive

winding. In the wave winding the number of

paral le l paths is always 28

there is only one pair of parallel paths"

irrespective of the number of poles> 2a ,2 " a,.


56/65

6ot al l the combinat ions of " a" p

result in an integer. It is a designer#s tas1 to choose a

proper number of slots" coil sides" number of poles and

type of winding to ensure an integer commutator pitch.

If the number of coils e:uals the number of

commutator segments" then" if the coil sides are

numbered with odd Rgures in the top layer and

even Rgures in the bottom layer" we can write

y,y/ y2,2 yc ----- 3.0

Therefore" if the commutator pitch is

determined" the total pitch expressed as a number

of coil sides is given by

y,2 yc ---- 3.;

and after y is determined from the numbers

of slots per pole yN and number of coil sides in a

layer u

The front-end connector pitch can be determined as

G2 , y-y

3.12 EMF E$%ation


57/65

The :uantitative expression will now be derived for the generated emf in

synchronous and dc machines armatures. (ome idea of ac windings will be

advanced here and certain sweeping statements made.

#enerated oltage of A& Winding4

The 9-wave of a synchronous machine &in general multipolar' assumed

sinusoidal is drawn in figure 3.2;" and a single full pitched coil cross sectional

form.

$ig 3.2; (inusoidal )ave form

The 9-wave moves towards left with a speed ! of elect.rad=sec or mechanical

rad=sec.

t the orgin of time the coil sides are located in the inter polar region where the

full pole flux lin1s the coil. t any time t the coil has relatively moved by,t elect.rad ---3.2%

to the right of the 9-wave. The 9-wave can be expressed as in figure. Delative

localtion of the 9-wave and armature coil at any time

-9 sin


58/65

9 sin6 7

)here 9Pea1 flux density

(ince the flux is physically spread over the mechanical angle" the flux lin1age

the coil can be computed by integrating over the mechanical angle. Thus"

9 sin6 7lrd ++++ 3.2'

)here"

l, active coil-side length&axial stator length'

r, mean radius of the stator at the air-gap.

(ince

9

*:uation % modifies to

, lrsin d

, 2 lrcos

9 2 lrcost, cos t

It is therefore seen that the flux lin1ing the coil varies sinusoidally and has a

maximum value of

9 lr 6flux=pole7


59/65

t ,t,!" which indeed is flux =pole. The flux lin1ages of the coil at any time t are

,6,6cost

)here 6,6umber of turns of coil

Bence the coil induced emf is

e, ,6sin t

The negative sign in the e:uation accounts for the fact that the assumed positive

direction of emf and the current in the coil produces flux along the coil axis

causing positive flux lin1ages. In case of transformer the positive direction of emf

was assumed such as to cause a current which would produce negative flux

lin1ages and therefore the induced emf law used was e, .

It may be absorbed that the spatial flux density wave up on rotation causes time

varying flux lin1ages with the coil and hence the production of emf and effect

which is produced by a fixed axis time varying flux in a transformer. The time

variation factor is introduced by rotation causing the phenomenon ofelectromechanical energy conversion.

The rms value of emf induced in the coil

,

The rms value of the generated emf in a full pitched coil is

* , " where , 6 = $&'( [=)*

* , , &f6, %.%% f6


60/65

3.13 Tor$%e e$%ation

)hen the stator and rotor windings of a machine both carry current they

produce their own magnetic fields along their respective axis which are

sinusoidally distributed along the air gap. Tor:ue results from the tendency of

these two fields to align them. The flux components setup by the stator and rotor

current cross the air gap twice and complete their circuits through the stator and

rotor iron. These component fields cause the appearance of 6orth and (outh poles

on the stator and rotor surface.

$if.3.2 . The field axis

The field axes being along north-south and out of the 6orth Pole" This is shown in

$ig 3.2 $or a 2 pole structure.

The tor:ue tending to align the two fields is produced only if the two fields havesame number of poles and are stationary with respect to each other. Two relatively

rotating fields will produce alternating tor:ue as they cross each other so that the

average tor:ue is Eero. ll rotating machines are therefore devised to produce

interacting fields with Eero relative velocity.


61/65

&ertain %nderl,ing ass%mptions are made at this stage 4

. (tator and other mmf#s are sinusoidally space moves" this is sufficiently

ensured by distributed windings.

2. Dotor is cylindrical &non salient pole' so that the air gap is uniform

throughout.

3. The airgap is narrow so that flux established in it radial and further the flux

density does not vary significantly&because the cylindrical area presented to

flux does not vary appreciably with radius' along a radial path in the gap. s

a result" the field intensity B" along any radial path is constant in the airgap.

The mmf across the airgap at any space point is $air-gap,Bg where g is the

radial airgap length.

%. Deluctance of the iron path of flux is assumed negligible. s a conse:uence of

a assumption to 3" a sinusoidal space mmf wave produces a sinusoidal flux

density wave in space in phase with it.

4. 5ost of the resultant flux is common to both stator and rotor windings i.e. it

is mutual flux. The lea1age flux lin1ing either winding produces lea1age

inductance as in a transformer. These affect only the net voltage applied to

the ideal machine.

+et and be the pea1 values of the spatial sinusoidal mmf of the stator and

rotor respectively as shown in fig.3.2 for a 2 pole machine the angle between their

respective positive pea1s being denoted by .


62/65

s stated earlier" these mmf can be represented as space vectors with magnitudes

corresponding to their pea1 values and angles corresponding to their positive

pea1s. The resultant space mmf can be obtained by the vector summation.

$ig.3"2

The pea1 value of the resultant mmf is

, / / 2 cos ----3.20

(ince the reluctance of the iron path is negligible the pea1 value of the resultant

field intensity is

,

The co energy density is , -----3.2;

The average value of the co energy over the airgap volume is

, ' ----- 3.2

$or a sinusoidal distribution

verage value of , -----3.2

verage value of co energy density , -----3.3!


63/65

olume of air gap , V Olg

)here O is the mean diameter at airgap. The total co energy of the field is then

, Olg

, 2 Olg -----3.3

, -----3.32

(ubstituting for

, & / / 2 cos ' -----3.33

The tor:ue developed is given by

T , , - sin -----3.3%

$or a machine with poles

T , - sin -----3.34

$rom e:uation ! it is seen that tor:ue developed is proportional to the pea1 values

of the stator and rotor mmf#s and is proportional to the sine of the angle between

the axes of the two fields. The negative sign indicates that the tor:ue acts in a

direction to reduce i.e. to align the two fields.

Kbviously e:ual and opposite tor:ue will act on the stator and rotor" )ith

reference to the vector diagram shown

sin, sin ------ 3.30

sin, sin ----- 3.3;

The tor:ue e:uation ! can be expressed in two alternative forms


64/65

T , - sin -----3.3

T , - sin -----3.3

PART+A

. Oefine the term pole pitch

2. Oefine pitch factor

3. Oefine the term breadth factor

%. )rite down the advantages of short

pitched coil.

4. )hat is distributed windingW

0. *xplain the following terms with respect

to rotating electrical machines.

;. )rite the expressions for the synchronous

speed.

. )rite the mmf e:uation of dc machine.

. )hat is meant by electromagnetic tor:ueW

!. (tate the tor:ue e:uation for round rotor

machine.

. Oefine rotating magnetic field.

PART+-

. Oerive the expression for the r.m.s value

of emf induced in a.c. machines. &0'

2. Prove that mmf wave of a single phase ac

winding is pulsating or standing. &0'


65/65

3. Prove that the resultant mmf wave of three

phase ac winding is rotating in space with

speed but its magnitude is constant. &0'

%. Oerive the tor:ue e:uation for round rotor

machine. &0'

4. *xplain the various concepts of magnetic

fields in rotating machines. &0'

0. *xplain with neat diagram the concept of

mmf space wave of a single coil. &0'

;. )rite in detail about mmf space wave of

three phase distributed winding. &0'

unit 4 correct syllabus

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