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DC Machinessecond year

University of Technology

Control and Systems Engineering Department

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References

Theraja Bl, Theraja Ak “Electrical

Technology”.

V.k mehta “Principles of Electrical Machines’’

E. Hughes “Electrical Technology”

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CHAPTER ONE: Magnetism and Electromagnetism

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Magnetic Force (Coulomb laws):

Intensity of Magnetic field (H):

Field Intensity or Field Strength or Magnetizing Force at any

point within a magnetic field is numerically equal to the force

experienced by a N-pole of one weber placed at that point.

Magnetic Flux(ɸ):

It represents the lines of magnetic force ,or flux per unit pole.

ɸ = m (Wb)

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Flux Density (B):

It is given by the flux passing per unit area through a plane at

a right angles to the flux.

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Magnetic Circuit:

It is defined as the path which is followed by the magnetic

flux.

Ferromagnetic core

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Magnetomotive Force (mmf) (F): It is given by the preduct

of the current (I) times its number of turns N,(ampere.turns)

(AT).

m.m.f. = N.I AT

or F = ɸR where, R : is Reluctance in AT/Wb

Then, the Magnetic field Intensity (H) is given by the ratio of

the mmf divided by the length of the mean magnetic path,

its unit is (ampere-turns/meter)(AT/m).

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Reluctance (R) or (S): It is the ratio of the applied

magnetic potential divided by the flux through the magnetic

path under consideration, its unit is (At/Wb)

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Comparion Between magnetic and electric circuit

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Parallel Magnetic Circuits

In magnetic circuit fig.(a),The flux produce by the coil wound on the

central core is divided equally at point A between the two outer parallel

paths. The reluctance offered by the two parallel paths = half the

reluctance of each path.

In equivalent electrical circuit, fig.(b), resistance offered to the source is

= R || R = R/2.

It should be noted that reluctance offered by the central core AB has

been neglected in the above treatment.

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Series-Parallel Magnetic Circuits

In fig. (a), two parallel magnetic circuits ACB and ADB connected across

the common magnetic path AB which contains an air-gap of length .

The reluctance of the path AB consists of (i) air gap reluctance and (ii) the

reluctance of the central core which comparatively negligible. Hence, the

reluctance of the central core AB equals only the air-gap reluctance

across which are connected two equal parallel reluctance. Hence, the

m.m.f. required for this circuit would be the sum of (i) that required for

the air-gap and (ii) that required for either of two paths.

In the equivalent electrical circuit, fig.(b), the total resistance offered to the

voltage source is RT = R1+R||, R = R1+ R/2.

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Relation between magnetism and electricityIt is well known that whenever an electric current flows through a

conductor, a magnetic field is immediately brought into existence in the

space surrounding the conductor. It can be said that when electrons are in

motion, they produce a magnetic field. The converse of this also true,

when a magnetic field embracing a conductor moves relative to the

conductor, it produces a flow of electrons in the conductor. This

phenomenon where by an e.m.f. and hence current is induced in any

conductor which is cut across or is cut by a magnetic flux is known as

electromagnetic induction.

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Faraday's Laws:

Faraday summed up two laws:

First Law: states that whenever a conductor cuts magnetic

flux, an e.m.f. is induced in that conductor.

Second Law: states that the magnitude of the induced e.m.f.

is equal to the rate of change of flux-linkages.

e = (dØ/dt) volts

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Lenz's Law

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Induced e.m.f.:

Induced e.m.f. can be either: (i) dynamically or (ii) statically

induced. In the first case, usually the field is stationary and

conductors cut across it (as in d.c. generators). But in the

second case, usually the conductors or the coil remains

stationary and flux linked with it is changed by simply

increasing or decreasing the current producing this flux (as

in transformers).

Self-Induced e.m.f.:

This is the e.m.f. induced in a coil due to the change of its

own flux linked it. If current through the coil is changed,

then the flux linked with its own turns will also change,

which will produce in it that is called self-induced e.m.f. the

direction of this e.m.f. (as given by Lenz's law) would be

such as to oppose any change of flux which is, in fact, the

very cause of its production. Hence it is induction.

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Coefficient of Self-induction (L):

(i) First Method for L

The Coefficient of Self-induction of a coil is defined as the

weber-turns per ampere in coil

(ii) Second method for L

It gives the value of self-induction in terms of the dimension

of the solenoid

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(iii) Third method for L

Hence, a coil has a self-inductance of one henry if one volt

is induced in it when current through it changes at the rate

of one ampere/second.

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Magnetic HysteresisIt may be defined as the lagging of magnetization of induction flux density (B)

behind the magnetizing force (H). Alternatively, it may be defined as that quality

of a magnetic substance, due to which energy is dissipated in it, on the reversal

of its magnetism.

It is seen that B always lag behind H. the two never attain zero value

simultaneously. This lagging of B behind H is given the name (hystereis), the

close loop ACDEFGA which is obtained when iron bar is taken through one

complete cycle of magnetisation is known as (hypothesis loop).

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CHAPTER TWO : D.C. MACHINES

One of energy can be obtained from the other form with the help of

converters. Converters that are used to continuously translate

electrical input to mechanical output or vice versa are called electric

machines. The process of translation is known as electromechanical

energy conversion.

An electrical machine is link between an electrical system and a

mechanical system.

Conversion from mechanical to electrical: generator

Conversion from electrical to mechanical: motor

D.C. Generator Principle

the essential components of a generator are:

(a) A magnetic field

(b) Conductor or a group of conductors

(c) Motion of conductor w.r.t. magnetic field.

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Simple Loop GeneratorConsider a single turn loop ABCD rotating clockwise in a uniform

magnetic field with a constant speed .As the loop rotates, the flux linking

the coil sides AB and CD changes continuously. Hence the e.m.f. induced

in these coil sides also changes but the e.m.f. induced in one coil side

adds to that induced in the other.

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Note that e.m.f. generated in the loop is alternating one, if

a load is connected across the ends of the loop, then

alternating current will flow through the load. The

alternating voltage generated in the loop can be

converted into direct voltage by a device called

commutator. We then have the a.c. generator in fact.

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Thus the alternating voltage generated in the loop will appear as directvoltage across the brushes (by Commutator). This is not a steady directvoltage but has a pulsating character. It is because the voltageappearing across the brushes varies from zero to maximum value andback to zero twice for each revolution of the loop.

if we require is the steady direct voltage. This can be achieved by using alarge number of coils connected in series. The resulting arrangement isknown as armature winding.

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Construction of d.c. GeneratorThe d.c. generators and d.c. motors have the same general

construction. Any d.c. generator can be run as a d.c. motor and vice-

versa. All d.c. machines have five principal components viz.,

(i) Field system.

(ii) Armature core.

(iii) Armature winding.

(vi) Commutator

(v) Brushes.

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(i) Field systemThe function of the field system is to produce uniform magnetic field within which

the armature rotates. It consists of a number of salient poles (of course, even

number) bolted to the inside of circular frame (generally called yoke). The yoke

is usually made of solid cast steel whereas the pole pieces are composed of

stacked laminations. Field coils are mounted on the poles and carry the d.c.

exciting current. The field coils are connected in such a way that adjacent poles

have opposite polarity.

The m.m.f. developed by the field coils produces a magnetic flux that passes

through the pole pieces, the air gap, the armature and the frame. Practical d.c.

machines have air gaps ranging from 0.5 mm to 1.5 mm. Since armature and

field systems are composed of materials that have high permeability, most of the

m.m.f. of field coils is required to set up flux in the air gap. By reducing the

length of air gap, we can reduce the size of field coils (number of turns).

(ii) Armature coreThe armature core is keyed to the machine shaft and rotates between the field

poles. It consists of slotted soft-iron laminations (about 0.4 to 0.6 mm thick) that

are stacked to form a cylindrical core. The laminations are individually coated

with a thin insulating film so that they do not come in electrical contact with each

other.

The purpose of laminating the core is to reduce the eddy current loss. The

laminations are slotted to accommodate and provide mechanical security to the

armature winding and to give shorter air gap for the flux to cross between the

pole face and the armature “teeth”.

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(iii) Armature windingThe slots of the armature core hold insulated conductors that are connected in a suitable

manner. This is known as armature winding. This is the winding in which “working” e.m.f. is

induced. The armature conductors are connected in series-parallel; the conductors being

connected in series so as to increase the voltage and in parallel paths so as to increase the

current. The armature winding of a d.c. machine is a closed-circuit winding; the

conductors being connected in a symmetrical manner forming a closed loop or series of

closed loops.

The armature conductors are connected to form coils. As shown in Fig(i) below, shows a

single-turn coil. It has two conductors or coil sides connected at the back of the armature.

fig.(ii) shows a 4-turn coil which has 8 conductors or coil sides.

One coil side of the coil is under N-pole and the other coil side is under the next S-pole at the

corresponding position. Consequently the e.m.f. of the coil sides adds together. If the e.m.f.

induced in one conductor is 2.5 volts, then the e.m.f. of a single-turn coil will be = 2 2.5 = 5

volts. For the same flux and speed, the e.m.f. of a 4-turn coil will be = 8 2.5 = 20 V

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(iv) CommutatorA commutator is a mechanical rectifier which converts the alternating voltage

generated in the armature winding into direct voltage across the brushes. it

consists of a cylindrical metal ring cut into two halves or segments C1 and C2

respectively separated by a thin sheet of mica. The commutator is mounted on

but insulated from the rotor shaft.

The ends of coil sides AB and CD are connected to the segments C1 and C2

respectively. Two stationary carbon brushes rest on the commutator and lead

current to the external load. The purpose of brushes is simply to lead current

from the rotating loop or winding to the external stationary load. With this

arrangement, the commutator at all times connects the coil side under S-pole to

the +ve brush and that under N-pole to the -ve brush.

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The armature conductors are soldered to the commutator segments in a suitable

manner to give rise to the armature winding. Depending upon the manner in

which the armature conductors are connected to the commutator segments,

there are two types of armature winding in a d.c. machine viz., (a) lap winding.

(b) wave winding.

Great care is taken in building the commutator because any eccentricities will

cause the brushes to bounce, producing unacceptable sparking. The parks may

bum the brushes and overheat and carbonize the commutator.

The number of commutator segments is equal to the number of slots or coils (or

half the number of conductors).

No. of commutator segments = No. of slots = No. of coils

It is because each coil has two ends and two coil connections are joined at

each commutator segment.

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(v) Brushes

The purpose of brushes is to ensure electrical connections between the rotating commutator

and stationary external load circuit. The brushes are made of carbon (because carbon has

good electrical conductivity and is soft enough not to scratch the commutator. To improve

the conductivity, sometimes we add a small amount of copper) and rest on the

commutator. The brush pressure is adjusted by means of adjustable springs. If the brush

pressure is very large, the friction produces heating of the commutator and the brushes.

On the other hand, if it is too weak, the imperfect contact with the commutator may

produce sparking.

Multiple machines have as many brushes as they have poles. For example, a 4-pole machine

has 4 brushes. As we go round the commutator, the successive brushes have positive and

negative polarities. Brushes having the same polarity are connected together so that we

have two terminals viz., the +ve terminal and the -ve terminal.

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Types of D.C. Armature WindingsTwo basic methods of making back connection and front connection (must be

connected in series) end connections are:

1. Simplex lap winding 2. Simplex wave winding

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Armature Resistance (Ra)

The resistance offered by the armature circuit is known as armature resistance (Ra)

and includes: (i) Resistance of armature winding (ii) Resistance of brushes

The armature resistance depends upon the construction of machine. Except for

small machines, its value is generally less than 1Ω. The armature resistance can

be found as under:

Let ℓ = length of each conductor,

a = cross-sectional area

A = number of parallel paths = P (for simplex lap winding),

A=2 (for wave winding)

Z = number of armature conductors

P = number of poles

E.M.F. generated = E.M.F. per parallel path

Total armature current, Ia = P X current per parallel path

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Applications of Lap and Wave Windings

In multiple machines, for a given number of poles (P) and armature

conductors (Z), a wave winding has a higher terminal voltage than a

lap winding because it has more conductors in series. On the other

hand, the lap winding carries more current than a wave winding

because it has more parallel paths.

In small machines, the current-carrying capacity of the armature

conductors is not critical and in order to achieve suitable voltages,

wave windings are used.

On the other hand, in large machines suitable voltages are easily

obtained because of the availability of large number of armature

conductors and the current carrying capacity is more critical. Hence in

large machines, lap windings are used.

Note: In general, a high-current armature is lap-wound to provide a large

number of parallel paths and a low-current armature is wave-wound to

provide a small number of parallel paths.

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e.m.f. of generator, Eg = e.m.f. per parallel path

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Types of D.C. Generators

Generators are generally classified according to their

methods of field excitation. On this basis, d.c. generators

are divided into the following two classes:

(i) Separately excited d.c. generators

(ii) Self-excited d.c. generators

The behaviour of a d.c. generator on load depends upon the

method of field excitation adopted.

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Separately Excited D.C. Generators

A d.c. generator whose field magnet winding is supplied from an independent

external d.c. source (a battery etc.) is called a separately excited generator.

The voltage output depends upon the speed of rotation of armature and the field

current (Eg = PɸZN / 60 A). The greater the speed and field current, greater is

the generated e.m.f. It may be noted that separately excited d.c. generators

are rarely used in practice.

Self-Excited D.C. Generators

A d.c. generators are normally of self-excited type,

whose field magnet winding is supplied current

from the output of the generator itself. There are

three types of self-excited generators depending

upon the manner in which the field winding is

connected to the armature, namely;

(i) Series generator,

(ii) Shunt generator, and

(iii) Compound generator

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(i) Series generatorIn a series wound generator, the field winding is connected in series with armature

winding so that whole armature current flows through the field winding as well as

the load. Since the field winding carries the whole of load current, it has a few

turns of thick wire having low resistance.

(ii) Shunt generatorIn a shunt generator, the field winding is connected in parallel with the armature

winding so that terminal voltage of the generator is applied across it. The shunt

field winding has many turns of fine wire having high resistance. Therefore, only

a part of armature current flows through shunt field winding and the rest flows

through the load.

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3. Mechanical lossesThese losses are due to friction and windage.

(i) Friction loss e, bearing friction, brush friction etc.

(ii) windage loss , air friction of rotating armature.

These losses depend upon the speed of the machine. But for a given speed, they

are practically constant.

Note. Iron losses and mechanical losses together are called stray or rotational

losses.

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Condition for Maximum Efficiency

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D.C. Generator Characteristics

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Open Circuit Characteristic (O.C.C.) of a D.C. Generator

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Characteristics of a Separately Excited D.C. Generator

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(ii) Internal and External Characteristics

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Voltage Build-Up in a Self-Excited Generator

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Characteristics of Series Generator

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Characteristics of a Shunt Generator

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Voltage Regulation

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CHAPTER 4 : D.C. Motors

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Working of D.C. Motor

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Back or Counter E.M.F. and Voltage Equation of D.C. Motor

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Power Equation

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Condition For Maximum Power

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Significance of Back E.M.F.

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Types of D.C. Motors

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(ii) Series-wound motor

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in which the field winding is connected in series with the armature.

(Small number of turns of thick wire and, therefore, will possess a

low resistance).

(iii) Compound-wound motor

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which has two field windings; one connected in parallel with the armature and the

other in series with it. There are two types of compound motor connections (like

generators). When the shunt field winding is directly connected across the armature

terminals, it is called short-shunt connection. When the shunt winding is so

connected that it shunts the series combination of armature and series field, it is

called long-shunt connection.

Armature Torque of D.C. Motor

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Alternative expression for Ta

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Shaft Torque (Tsh)

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Brake Horse Power (B.H.P.)

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