ee09 404-module 1
TRANSCRIPT
-
7/26/2019 Ee09 404-Module 1
1/20
EE09 404-DC MACHINES AND
TRANSFORMERS
Prof. THANKACHEN P.V
-
7/26/2019 Ee09 404-Module 1
2/20
EE09 404-DC MACHINES AND
TRANSFORMERS
MODULE I
1.1 Magnetic Circuit
A magnetic circuitis made up of one or more closed loop paths containing a magnetic flux.
The flux is usually generated bypermanent magnetsor electromagnetsand confined to the path by
magnetic coresconsisting offerromagneticmaterials like iron, although there may be air gaps or
other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fieldsin
many devices such as electric motors, generators, transformers, relays, lifting electromagnets,
SQU!s,galvanometers,and magneticrecording heads.
"ig #.#.#$ A simple magnetic circuit %ith an air gap
"igure #.#.# sho%s a simple magnetic circuit %ith an air gap of length &lg cut in the middle of
a leg. The %inding providesNI ampere'turn. The spreading of the magnetic flux lines outside the
common area of the core for the air gap is kno%n as fringing field (figure #.#.) *a+. "or simplicity,
this effect is negligible and the flux distribution is assumed to be as in figure #.#.) *b+. t can be
sho%n that the magnetic flux generated in the air gap is e-ual to the magneto motive force NI divided
by the sum of the reluctances of the core and of the air gap.
*a+ *b+
"igure #.#.)$ Air gaps *a+ %ith fringing and *b+ ideal
Dept. Of EEE 1 SIMAT,Vavanoor
http://en.wikipedia.org/wiki/Magnetic_fluxhttp://en.wikipedia.org/wiki/Magnetic_fluxhttp://en.wikipedia.org/wiki/Permanent_magnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Magnetic_corehttp://en.wikipedia.org/wiki/Ferromagnetichttp://en.wikipedia.org/wiki/Ferromagnetichttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_motorhttp://en.wikipedia.org/wiki/Electric_generatorhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Relayhttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/SQUIDhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Recording_headhttp://en.wikipedia.org/wiki/Recording_headhttp://en.wikipedia.org/wiki/Permanent_magnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Magnetic_corehttp://en.wikipedia.org/wiki/Ferromagnetichttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_motorhttp://en.wikipedia.org/wiki/Electric_generatorhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Relayhttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/SQUIDhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Recording_headhttp://en.wikipedia.org/wiki/Magnetic_flux -
7/26/2019 Ee09 404-Module 1
3/20
EE09 404-DC MACHINES AND
TRANSFORMERS
Some corresponding -uantities in electric and magnetic circuit are listed as belo%$
Electric quantity Magnetic quantity
urrent in ampere *+ Magnetic flux in %ebers */+
urrent density 0 Magnetic flux density 1
onductivity 2 3ermeability 4
5lectromotive force in volt6resistance x Magneto motive force in ampere
turns6reluctance x /
5lectric field intensity 5 Magnetic field intensity 7
onductance6#8resistance 3ermeance6#8reluctance
9esistance6#82A. 9eluctance6#84A
The differences bet%een electric and magnetic circuits are as belo%$
: The path of the magnetic flux flo%s is perpendicular to the current flo%s in the circuit. n other
%ords, the directions of 1 and 0 are perpendicular.
: "or a given temperature, electric resistance is constant and does not depend on current density.
7o%ever, the magnetic reluctance depends on magnetic field and flux intensity since the
permeability is not constant.
: urrent flo%ing in an electric circuit involves dissipation of energy, but for magnetic circuit, energy
is needed to generate magnetic flux.
1.2 Magneto-Motive Force
The amount of flux density setup in the core is dependent upon five factors'the current,number of turns, material of the magnetic core, length of core and the cross'sectional area of the
core. More current and the more turns of %ire %e use, the greater %ill be the magneti;ing effect.
-
7/26/2019 Ee09 404-Module 1
4/20
EE09 404-DC MACHINES AND
TRANSFORMERS
reluctance. t is a scalar, extensive -uantity, akin to electrical resistance. The units for magnetic
reluctance are inverse 7enries, 7>#.
n a ! field, the reluctance is the ratio of the ?magneto motive force@ *MM"+ in a magnetic
circuitto the magnetic fluxin this circuit.
The definition can be expressed as follo%s$
S = mmf/ *#..#+
-
7/26/2019 Ee09 404-Module 1
5/20
EE09 404-DC MACHINES AND
TRANSFORMERS
applied field 7. This property is called magnetic hysteresis. The 1'7 loop is called hysteresis loop.
The shape and area of the loop are different for different materials .
1.5.1 ysteresis loo!"
Get us take an unmagnified bar of iron A1 and magneti;e in by placing it %ithin the magneti;ing
field of a solenoid *7+. The field can be increased or decreased by increasing or decreasing current
through it. Get &7B be increased in step from ;ero up to a certain maximum value and the
corresponding of induction flux density *1+ is noted. f %e plot the relation bet%een 7 and 1, a curve
like DA, as sho%n in fig, is obtained. The material becomes magnetically saturated at 76DM and
has, at that time, a maximum flux density, established through it.
*a+ *b+
"ig #.F.#$ *a+ magneti;ation of an iron bar *b+ hysteresis loop.
f 7 is no% decreased gradually *by decreasing solenoid current+ flux density 1 %ill not
decrease along AD *as might be expected+ but %ill decrease less rapidly along A.
-
7/26/2019 Ee09 404-Module 1
6/20
EE09 404-DC MACHINES AND
TRANSFORMERS
t is seen that 1 al%ays lags behind 7 the t%o ne%er attain ;ero value simultaneously. This
lagging of 1, behind 7 is given the name hysteresis %hich literally means &to lag behind.B The closed
loop A!5"HA, %hich is obtained %hen iron bar is taken through one complete cycle of reversal of
magneti;ation is kno%n as 7ysteresis loop.
1.5.2 ysteresis loss"
7ysteresis loss is %hen the effect of a cause lags behind the cause itself. This is noticed %hen
changes in magnetism of a body lag behind the changes in the magnetic field. ron, for example,
depends not only on the magnetic field, but also any previous exposures. !eformations in the shapes
of substances that continue indefinitely, once the deforming force has been removed, are an example
of hysteresis.ysteresis lossis energy %asted in the form of heat %hen alternating current reversesrapidly and molecular dipoles lag the magneti;ing force.
n other %ords %e can say that, if the magnetic field applied to a magnetic material isincreased and then decreased back to its original value, the magnetic field inside the material does
not return to its original value. The internal field &lagsB behind the external field. This behaviour
results in a loss of energy, called the hysteresis loss, %hen a sample is repeatedly magneti;ed and
demagneti;ed.
5nergy loss in 08m8cycle 6 Area of hysteresis loop.
7ysteresis po%er loss, Ph= kh(volume) f Bmn *#.F.).#+
3h 6 7ysteresis loss in %atts
f 6 "re-uency in 7;.
1m 6 Maximum flux density, T
&nB varies from #.F to ).F depending on the material used. The constant khalso depends on the
material. "or a particular machine, the volume of material also constant, so that 3hcan be %ritten as
Ph= Khf Bmn *#.F.).)+
-
7/26/2019 Ee09 404-Module 1
7/20
EE09 404-DC MACHINES AND
TRANSFORMERS
The bar magnet represents the armature and the coil of %ire represents the field. The arro%
sho%s the direction of the armatureBs rotation. =otice that the arro% sho%s the armature starting to
rotate in the clock%ise direction. The north pole of the field coil is repelling the north pole of the
armature, and the south pole the field coil is repelling the south pole of the armature.
"ig #.J.#$ *a+ magnetic diagram that explains the operation of a ! motor. The rotating
magnets moves clock%ise because like poles repel. *b+ The rotating magnet being attracted because
the poles are unlike. *c+ The rotating magnet is no% sho%n as the armature coil, and its polarity is
determined by the brushes and commutator segments.
As the armature begins to move, the north pole of the armature comes closer to the armature
comes closer to the south pole of the field, and the south pole of the armature is coming closer to the
north pole of the field. As the t%o unlike poles near each other, they begin to attract. This attraction
becomes stronger until the armatureBs north pole moves directly in line %ith the fieldBs south pole,and its south pole moves directly in line %ith the fieldBs north pole *fig #.J.# *b++.
-
7/26/2019 Ee09 404-Module 1
8/20
EE09 404-DC MACHINES AND
TRANSFORMERS
Since the armature is no% a coil of %ire, it %ill need ! current flo%ing through it to
become magneti;ed. This presence another problemL since the armature %ill be rotating, the !c
voltage %ires cannot be connected directly to the armature coil. A stationary set of carbon brushes is
used to make contact to the rotating armature. The brushes ride on the commutator segments to make
contact so that current %ill flo% through the armature coil.
n fig #.J.# *c+ you can see that the ! voltage applied to the field and to the brushes. Since
negative ! voltage is connected to one of the brushes, the commutator segment the negative brush
rides on %ill also be negative. The armatureBs magnetic field causes the armature to begin to rotate.
This time %hen the armature gets to the point %here it becomes locked up %ith the magnetic field,
the negative brush begin to touch the end of the armature coil that %as negative. This action s%itches
the direction of current flo% through the armature, %hich also s%itches the polarity of the armature
coilBs magnetic field at Eust the right time so that the repelling and attracting continues. The armature
continues to s%itch its magnetic polarity t%ice during each rotation, %hich causes it to continually be
attracted and repelled %ith the field poles.
This is a simple t%o pole motor that is used primarily for instructional purposes. Since the
motor has only t%o poles, the motor %ill operate rather roughly and not provide too much tor-ue.
Additional field poles and armature poles must be added to the motor for it to become useful for
industry.
An electrical current in a magnetic field *produced by some other currents+ experiences a
force perpendicular to both the direction of the current and the direction of the magnetic field, and
reverses if either of these reverses in direction. The force is proportional to the current and to the
strength of the magnetic field *fig #.J.)+. This principle can be called Kmotor action.@
"ig #.J.)$ A force is exerted on a current in a magnetic field perpendicular to the plane of themagnetic field and the current.
1.) *evelo!e& torque
"ig #. sho%s a coil carrying a current and lying in a magnetic field of flux density 1. t is
seen that an up%ard force is exerted on the left hand conductor and a do%n%ard force on the right
hand conductor.
Dept. Of EEE 7 SIMAT,Vavanoor
-
7/26/2019 Ee09 404-Module 1
9/20
EE09 404-DC MACHINES AND
TRANSFORMERS
"ig #.$ Tor-ue on a coil in a magnetic field
"orce on each conductor, F = B I l=e%ton *#..#+
-
7/26/2019 Ee09 404-Module 1
10/20
EE09 404-DC MACHINES AND
TRANSFORMERS
n #P# Michael "araday discovered that if a conductor is moved through a magnetic field, an
electrical voltage is induced in the conductor.
The magnitude of this generated voltage is directly proportional to the strength of the
magnetic field and the rate at %hich the conductor crosses the magnetic field. The induced voltagehas a polarity that %ill oppose the change causing the induction'Gen;Bs la%
This natural phenomenon is kno%n as generator action and is described today by "aradayBs
la% of electromagnetic induction$ *ind6 R/8Rt+, %here ind6 induced voltage, R/ 6 change in flux
density, Rt 6 change in time.
All rotary generators built use the basic principles of Henerator Action.
An electrical conductor, such as a copper %ire, moving in a magnetic field has an electrical
current induced in it. This is expressed by the creation of an electromotive force or voltage, %hich
causes current to flo% Eust as the voltage of a battery does. The effect is maximum %hen the %ire, the
motion, and the magnetic field are all mutually perpendicular *fig #.P.#+. This principle can be called
Kgenerator action.@
"ig #.P.#$ A voltage is induced in a conductor moved in a magnetic field. =ote that the voltage is
opposite to the current causing a force in the direction of motion.
1., Energy conversion in rotating electrical machines
onverters that are used to continuously translate electrical input to mechanical output or viceversa are called electric machines. The process of translation is kno%n as electromechanical energy
conversion. 5lectro mechanical energy conversion occurs %hen there is a change in magnetic flux
linking a coil, associated %ith mechanical motion. An electric machine is therefore a link bet%een an
electrical system and a mechanical system. n these machines the conversion is reversible. f the
conversion is from mechanical to electrical energy, the machine is said to act as a generator. f the
conversion is from electrical to mechanical energy, the machine is said to act as a motor. These t%o
effects are sho%n in fig #.. n these machines, conversion of energy from electrical to mechanical
form or vice versa results from the follo%ing t%o electromagnetic phenomena$
-
7/26/2019 Ee09 404-Module 1
11/20
EE09 404-DC MACHINES AND
TRANSFORMERS
"ig #.$ The energy directions in generator and motor actions.
These t%o effect occur simultaneously %henever energy conversion takes place from
electrical to mechanical or vice versa. n motoring action, the electrical system makes current flo%
through conductors that are placed in the magnetic field. A force is produced on each conductor. f
the conductors are placed on a structure free to rotate, an electromagnetic tor-ue %ill be produced,
tending to make the rotating structure rotate at some speed. f the conductors rotate in a magnetic
field, a voltage %ill also be induced in each conductor. n generating action, the process is reversed.
n this case, the rotating structure, the rotor, is driven by a prime mover *such as a steam turbine or
diesel engine+. A voltage %ill be induced in the conductors that are rotating %ith the rotor. f an
electrical load is connected the %inding formed by these conductors, a current %ill flo%, delivering
electrical po%er to the load. Moreover, the current flo%ing through the conductor %ill interact %ith
the magnetic field to produce a reaction tor-ue, %hich %ill tend to oppose the tor-ue applied by the
prime mover. =ote that in both motor and generator actions, the coupling magnetic field is involved
in producing a tor-ue and an induced voltage.
1.1 E&&y currents an& e&&y current losses
-
7/26/2019 Ee09 404-Module 1
12/20
EE09 404-DC MACHINES AND
TRANSFORMERS
This circulating current creates a magnetic field that opposes the external magnetic field. The
direction of the eddy current is described by Gen;Bs la%. The stronger of the external magnetic field
or the greater of the electrical conductivity of the material, the eddy current that is developed %ill be
stronger and also yields stronger opposing force.
5ddy current creates losses through 0oule heating, and it reduces the efficiency of device that
operates under alternating magnetic field condition such as iron core of transformers and alternating
current motors. This po%er loss is kno%n as eddy current loss due to the induced eddy current in the
metal or magnetic materials.
n order to reduce the eddy current loss, the resistivity of the material is increased by adding
silicon in the metal or ferromagnetic materials. Another effective %ay to achieve lo% eddy current
loss is by using lamination of electrical metal sheets. These metal sheets are coated %ith insulator
%hich breaks the eddy currents path as illustrated in the diagram belo%.
"igure #.#.)$ 5ddy currents in a laminated toroidal core.
The po%er due to the eddy current loss is given asL
e/ 0e t
2 %2 m2'volume( , unit$
-
7/26/2019 Ee09 404-Module 1
13/20
EE09 404-DC MACHINES AND
TRANSFORMERS
parts, one stationary and one moving, called the field and the armature. An essential example of a !
machine is a copper coil spinning on its o%n axis bet%een t%o magnets. A practical ! machine also
needs a commutator, brushes, poles and bearings.
The construction of ! machines is discussed here. An actual generator consists of the follo%ingparts$
magnetic frame or yoke
pole cores and pole shoes
armature core
armature %indings or conductors
field %inding
commutator
brushes
bearing
The yoke, pole cores, armature core and air gaps bet%een the poles and the armature core
form the magnetic field. The rest form the electrical circuit. "igure #.## sho%s the construction of a
! machine in %hich the above parts have been depicted.
"igure #.##$ Sectional vie% of a O pole ! Machine
"agnetic frame or #o$e: The magnetic frame or yoke gives mechanical support for poles as
%ell as protects the %hole machine as a protecting cover. t also carries the magnetic flux
produced by the poles. n small generators yokes are made of cast iron, %hereas for largemachines cast steel is used. The yoke carries F per cent of total flux per pole.
Dept. Of EEE 12 SIMAT,Vavanoor
-
7/26/2019 Ee09 404-Module 1
14/20
EE09 404-DC MACHINES AND
TRANSFORMERS
%ole cores and pole soes:The pole core and pole shoe stacked together under hydraulic
pressure and then attached to the yoke. These t%o structures are assigned for different
purposes, the pole core is of small cross sectional area and its function is to Eust hold the pole
shoe over the yoke, %hereas the pole shoe having a relatively larger cross'sectional area
spreads the flux produced over the air gap bet%een the stator and rotor to reduce the loss dueto reluctance. The pole shoe also carries slots for the field %indings that produce the field
flux.
&rmature core:The armature or rotor core, %hich carries the armature or rotor %inding, is
made of sheet'steel laminations, and as a result is subEected to altering magnetic field in the
path of its rotation %hich directly results in magnetic losses. "or this reason the rotor is made
of armature core, thatBs made %ith several lo%'hysteresis silicon steel laminations, to reduce
the magnetic losses like hysteresis and eddy current loss respectively. The laminations are
stacked together to form a cylindrical structure.
&rmature 'inding or conductors:Armature %inding is an arrangement of conductors to
develop desired emfs by relative motion in a magnetic field. These %indings are first %ound
in the form of flat rectangular coils and are pulled into proper shape in a coil puller. The
conductors are placed in the armature slots %hich are lined %ith a tough insulating material
called Gatheroide paper. 7ere normally t%o layer %inding %ith diamond shaped coils are
used.
ield 'inding:The field %inding of dc motor are made %ith field coils *copper %ire+ %ound
over the slots of the pole shoes in such a manner that %hen field current flo%s through it, then
adEacent poles have opposite polarity are produced. The field %indings basically form an
electromagnet, that produces field flux %ithin %hich the rotor armature of the dc motor
rotates, and results in the effective flux cutting.
ommutator: The commutator is cylindrical structure and is built up of %edge shaped
segments of high conductivity hard dra%n copper. These segments are insulated from each
other by thin layers of mica usually .F to # mm thickness. The commutator is a form of
rotating s%itch placed bet%een the armature and the external circuit. "ollo%ing purposes are
served by the commutator$
t provides electrical connections bet%een rotating armature coils and stationary external
circuit.
t collects current from armature conductors. t rectifies alternating current induced in the
armature conductors into unidirectional current for external load circuit
*ruses: The brushes of dc motor are made %ith carbon or graphite structures, making
sliding contact over the rotating commutator. The function of brush is to collect current from
the armature conductors and supply it to the external load circuit. The brushes are rectangular
in shape and rests on commutator.
*earings: n small motors ball bearings are used at both ends. "or larger motor, roller
bearings are used at driving end and ball bearing at commutator end.
-
7/26/2019 Ee09 404-Module 1
15/20
EE09 404-DC MACHINES AND
TRANSFORMERS
1.12 Flu &istriution curve in the air ga!
To estimate the correct reluctance of the air gap, the magnetic field distribution in the
space bet%een the pole shoes and the armature is plotted. onsider a smooth armature, the half pole
pitch of it is divided into suitable number of sections. ts flux lines are plotted by method of
curvilinear s-uares. All these lines must leave and enter the surface at right angle.
-
7/26/2019 Ee09 404-Module 1
16/20
EE09 404-DC MACHINES AND
TRANSFORMERS
The !c armature %indings are al%ays of the closed continuous type of double layer
lap or %ave %inding. "or small machines, the coils are directly %ound in the armature slots using
automatic %inders. n large machines, the coils are performed and then inserted into the armature
slots. 5ach coil consists of a number of turns of %ire, each turn taped and insulated from the other
turns and form the rotor slots. 5ach side of the turn is called the con&uctor. The number of the
conductors on a machineVs armature is given by
"= 2#N
*#.#.#+
%here $
W6 numbers of conductors on rotor
6 numbers of coils on rotor=6 number of turns per coil
Since the voltage generated in conductor under the south pole opposite the voltage
generated in the conductor under the =orth pole, the coil span is e-ual to #P electrical
degrees, one pole pitch. n a ) pole machine #P electrical degrees is e-ual to #P mechanical
degrees, %hereas in a O'pole machine #P electrical degrees is e-ual to mechanical
degrees. n general, the relationship bet%een the electrical angle and mechanical angle is
electrical angle 6 *38)+ mechanical angle
%here 3 is the number of poles.
1.14 7a! an& 6ave
T%o types of %inding mostly employed are kno%n as lap %inding and %ave %inding.
1.14.1 7a! 6in&ing"
n lap %inding, the finishing end of one coil is connected to a commutator segment
and to the starting end of the adEacent coil situated under the same pole and so on, till all the
coils have been connected. This type of %inding derives its name from the fact it doubles or
laps back %ith its succeeding coils.
"or a progressive lap %inding the commutator pitch y 6 #.
A typical coil of = turns for a simplex lap %inding is sho%n in fig #.#O.#
Dept. Of EEE 14 SIMAT,Vavanoor
-
7/26/2019 Ee09 404-Module 1
17/20
EE09 404-DC MACHINES AND
TRANSFORMERS
"ig #.#O.#.a$ Simplex lap %inding
n the simplex lap %inding the number of parallel path is e-ual to the number of poles and
also to the number of brushes.
-
7/26/2019 Ee09 404-Module 1
18/20
EE09 404-DC MACHINES AND
TRANSFORMERS
n the %ave %inding, the t%o ends of a coil are connected to a commutator segments
that are approximately J degrees apart. This %ay all the coils carrying current in the same
direction are connected in series. Therefore, there are only t%o parallel paths bet%een the brushes,
a6) independent of the number of poles. This type of %inding is used lo%'current, high voltage
application.
"ig #.#O.).a$ Simplex %ave %inding
"ig #.#O.).b represents an unrolled %ave %inding of a dc armature, along %ith the
commutator segments *bars+ and stationary brushes. oils are laid out in a %ave pattern and cross all
the poles. n %ave %indings, the number of parallel paths, a, is al%ays t%o *)+, and there may be t%o
or more brush positions.
-
7/26/2019 Ee09 404-Module 1
19/20
EE09 404-DC MACHINES AND
TRANSFORMERS
"ig #.#O.).b$ unrolled %ave %inding and e-uivalent coil representation
1.15 Equalizer rings
The existence of many parallel paths, in a lap %inding, can lead to the serious
problem of circulating currents. The fluxes from all the poles are not exactly e-ual. 1ecause
of %ear on the bearings, the air gap does not remain uniform around the %hole periphery. Asthe armature conductor rotate, the voltage induced in some conductors may be slightly more
than that in the others. Since all the parallel paths are in parallel, a resultant emf acting
around a closed path may cause circulating current in the %inding. The resistance of %inding
being very small, even a small imbalance in the emfs can give rise to a large circulating
current. 5vidently these circulating currents cause energy loss and heating. Therefore the
points %hich should be the same potential, in different parallel paths, are connected together
by a ring made of copper. 5ach ring is insulated from the other. These rings, kno%n as
e-uali;er rings or bars, help in keeping the circulating currents inside the small sections
shorted together, so that these circulating currents may not flo% through the brushes.
1.1# *ummy coils
Dept. Of EEE 17 SIMAT,Vavanoor
-
7/26/2019 Ee09 404-Module 1
20/20
EE09 404-DC MACHINES AND
TRANSFORMERS
These coils are used %ith %ave %inding and restored to %hen the re-uirement of the
%inding are not met by the standard armature punching available in armature %inding shops, these
dummy coils does not influence the electrical character of the %inding. 1ecause, they are not
connected to the commutator. They are exactly similar to the other coils except that their ends are
short and tapped. The dummy coils inserted into the slots in the same %ay as the others to make the
armature dynamically *an armature having some slots %ithout %indings %ould be out of balance
mechanically+ balanced but it is not a part of the armature %inding.