Robertson C.R. Fundamental electrical and electronic principles

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Alternating Quantities 231

18 Determine the phasor sum of the two voltages

speci ed in Question 17 above.

19 Three currents, in an a.c. circuit, meet at a

junction. Calculate the phasor sum, if the

currents are:







sin amp

sin( / ) amp

sin( / ) amp.





20 Determine the phasor sum of the following

voltages, all of which are sinewaves of the

same frequency:

has an amplitude of 25 volt, and a phase

angle of zero.

has an amplitude of 13.5 volt, and lags v

by 25°.

has an amplitude of 7.6 volt, and leads v

by 40°.

2 1 By means of a phasor diagram, drawn to scale,

check your answer to Question 19 above.

22 Plot, on the same axes, the graphs of the

following two voltages. By adding ordinates,

determine the sum of these voltages. Express

the result in the form

Assignment Questions

vV t

 sin( ) φ

vtv t

1286

sin , and sin( / ) volt.

23 The waveform displayed on an oscilloscope

is as shown in Fig. 6.40 . The timebase is set

to 10 0 μ s/cm, and the Y-amp is set to 2 V/cm.

Determine the amplitude, r.m.s. value, periodic

time and frequency of this waveform.

Fig. 6.40

232 Fundamental Electrical and Electronic Principles

Suggested Practical Assignments

The principal practical exercise relating to this chapter is the usage of the

oscilloscope. The actual exercises carried out are left to the discretion of your

teacher. Using an oscilloscope is not di cult, but does require some practice;

particularly in obtaining a clear, stationary trace, from which measurements can

be made.

D.C. Machines

Chapter 7

Learning Outcomes

This chapter covers the operating principles of d.c. generators and motors, their characteristics

and applications. On completion you should be able to:

1 Understand and explain generator/motor duality.

2 Appreciate the need for a commutator.

3 Identify the different types of d.c. generator, and describe their characteristics. Carry out

practical tests to compare the practical and theoretical characteristics.

233

7.1 Motor/Generator Duality

An electric motor is a rotating machine which converts an electrical

input power into a mechanical power output. A generator converts a

mechanical power input into an electrical power output. Since one

process is the converse of the other, a motor may be made to operate as

a generator, and vice versa. This duality of function is not conﬁ ned to

d.c. machines. An alternator can be made to operate as a synchronous

a.c. motor, and vice versa.

To demonstrate the conversion process involved, let us reconsider

two simple cases that were met when dealing with electromagnetic

induction.

Consider a conductor being moved at constant velocity, through a

magnetic ﬁ eld of density B tesla, by some externally applied force F

newton. This situation is illustrated in Fig. 7.1 .

Work done in moving the conductor,

WF d newton metre

234

Fundamental Electrical and Electronic Principles

mechanical power input, P

 watt

so,

wattP



and since d /t is the velocity, v at which the conductor is moved,

then

PFv

1 watt.............[ ]

However, when the conductor is moved, an emf will be induced into

it. Provided that the conductor forms part of a closed circuit, then

the resulting current ﬂ ow will be as shown in Fig. 7.2 . This induced

current, i, produces its own magnetic ﬁ eld, which reacts with the main

ﬁ eld, producing a reaction force, F

, in direct opposition to the applied

force, F .

Now, F

 Bi newton

Fig. 7.2

Fig. 7.1

D.C. Machines

235

Assuming no frictional or other losses, then the applied force has only

to overcome the reaction force, such that:

FF Bi

PBiv







newton

so eqn [ ] becomes watt............1

[[2]

Also, induced emf, volt

so generated power,

eBv

Pei





watt

therefore, watt............[ ]PBiv

3 

Since [3]  [2], then the electrical power generated is equal to the

mechanical power input (assuming no losses). Now consider the

conductor returned to its original starting position. Let an external

source of emf, e volt pass a current of i ampere through the conductor.

Provided that the direction of this current is opposite to that shown in

Fig. 7.2 , then the conductor will experience a force that will propel

it across the ﬁ eld. In this case, the same basic arrangement exhibits

the motor effect, since the electrical input power is converted into

mechanical power.

Although the above examples involve linear movement of the

conductor, exactly the same principles apply to a rotating machine.

7.2 The Generation of d.c. Voltage

We have seen in Chapter 6 already that, if a single-loop coil is

rotated between a pair of magnetic poles, then an alternating emf is

induced into it. This is the principle of a simple form of alternator.

Of course, this a.c. output could be converted to d.c. by employing

a rectiﬁ er circuit. Indeed, that is exactly what is done with vehicle

electrical systems. However, in order to have a truly d.c. machine,

this rectiﬁ cation process needs to be automatically accomplished

within the machine itself. This process is achieved by means of a

commutator, the principle and action of which will now be described.

Consider a simple loop coil the two ends of which are connected to a

single ‘ split ’ slip-ring, as illustrated in Fig. 7.3 . Each half of this slip-

ring is insulated from the other half, and also from the shaft on which

it is mounted. This arrangement forms a simple commutator, where the

connections to the external circuit are via a pair of carbon brushes. The

rectifying action is demonstrated in the series of diagrams of Fig. 7.4 .

In these diagrams, one side of the coil and its associated commutator

segment are identiﬁ ed by

a thickened line edge. For the sake of

clarity, the physical connection of each end of the coil, to its associated

commutator segment, is not shown. Figure 7.4(a) shows the instant

when maximum emf is induced in the coil. The current directions

have been determined by applying Fleming ’ s right-hand rule. At this

236

Fundamental Electrical and Electronic Principles

instant current will be fed out from the coil, through the external circuit

from right to left, and back into the other side of the coil. As the coil

continues to rotate from this position, the value of induced emf and

current will decrease. Figure 7.4(b) shows the instant when the brushes

short-circuit the two commutator segments. However, the induced emf

is also zero at this instant, so no current ﬂ ows through the external

circuit. Further rotation of the coil results in an increasing emf, but of

the opposite polarity to that induced before. Figure 7.4(c) shows the

instant when the emf has reached its next maximum. Although the

generated emf is now reversed, the current through the external circuit

will be in the same direction as before. The load current will therefore

be a series of half-sinewave pulses, of the same polarity. Thus the

commutator is providing a d.c. output to the load, whereas the armature

generated emf is alternating.

A single-turn coil will generate only a very small emf. An increased

amplitude of the emf may be achieved by using a multi-turn coil.

rotation

brush

commutator

Fig. 7.3

Fig. 7.4

(a)

(b)

(c)

D.C. Machines

237

The resulting output voltage waveform is shown in Fig. 7.5 . Although

this emf is unidirectional, and may have a satisfactory amplitude,

it is not a satisfactory d.c. waveform. The problem is that we have

a concentrated winding. In a practical machine the armature has a

number of multi-turn coils. These are distributed evenly in slots around

the periphery of a laminated steel core. Each multi-turn coil has its

own pair of slots, and the two ends are connected to its own pair of

commutator segments. Figure 7.6 shows the armature construction

(before the coils have been inserted). The riser is the section of the

E (V)

t (s)0

Fig. 7.5

slot

segments

riser

Fig. 7.6

E (V)

t (s)0

Fig. 7.7

commutator to which the ends of the coils are soldered. Due to the

distribution of the coils around the armature, their maximum induced

emfs will occur one after the other, i.e. they will be out of phase with

each other. Figure 7.7 illustrates this, but for simplicity, only three coils

have been considered.

Nevertheless, the effect on the resultant machine output voltage is

apparent, and is shown by the thick line along the peaks of the waveform.

238

Fundamental Electrical and Electronic Principles

With a large number of armature coils the ripple on the resultant

waveform will be negligible, and a smooth d.c. output is produced.

7.3 Construction of d.c. Machines

The various parts of a small d.c. machine are shown separately in

Fig. 7.8 , with the exception that neither the ﬁ eld nor armature windings

have been included. The frame shell (bottom left) contains the pole

pieces, around which the ﬁ eld winding would be wound. One end

frame (top left) would simply contain a bearing for the armature shaft.

Fig. 7.8

The other end frame (bottom right) contains the brushgear assembly

in addition to the other armature shaft bearing. The armature (top

right) construction has already been described. The slots are skewed to

provide a smooth starting and slow-speed torque.

7.4 Classi cation of Generators

D.C. generators are classiﬁ ed according to whether the ﬁ eld winding

is electrically connected to the armature winding, and if it is, whether

it is connected in parallel with or in series with the armature. The ﬁ eld

current may also be referred to as the excitation current. If this current

is supplied internally, by the armature, the machine is said to be self-

excited. When the ﬁ eld current is supplied from an external d.c. source,

the machine is said to be separately excited. The circuit symbol used

D.C. Machines

239

for the ﬁ eld winding of a d.c. machine is simply the same as that used

to represent any other form of winding. The armature is represented

by a circle and two ‘ brushes ’ . The armature conductors, as such, are

not shown.

7.5 Separately Excited Generator

The circuit diagram of a separately excited generator is shown in

Fig. 7.9 . The rheostat, R

, is included so that the ﬁ eld excitation

current, I

, can be varied. This diagram also shows the armature being

driven at constant speed by some primemover. Since the armature

of any generator must be driven, this drive is not normally shown.

The load, R

, being supplied by the generator may be connected or

disconnected by switch S

. The resistance of the armature circuit is

represented by R

emf

Fig. 7.10

Fig. 7.9

Consider the generator being driven, with switches S

and S

both

open. Despite the fact that there will be zero ﬁ eld current, a small emf

would be measured. This emf is due to the small amount of residual

magnetism retained in the poles. With switch S

now closed, the ﬁ eld

current may be increased in discrete steps, and the corresponding

values of generated emf noted. A graph of generated emf versus ﬁ eld

current will be as shown in Fig. 7.10 , and is known as the open-circuit

characteristic of the machine.

240

Fundamental Electrical and Electronic Principles

It will be seen that the shape of this graph is similar to the magne-

tization curve for a magnetic material. This is to be expected, since the

emf will be directly proportional to the pole ﬂ ux. The ‘ ﬂ attening ’ of the

emf graph indicates the onset of saturation of the machine ’ s magnetic

circuit. When the machine is used in practice, the ﬁ eld current would

normally be set to some value within the range indicated by I

and

on the graph. This means that the facility exists to vary the emf

between the limits E

and E

volts, simply by adjusting rheostat R

Let the emf be set to some value E volt, within the range speciﬁ ed

above. If the load is now varied, the corresponding values of terminal

voltage, V and load current I

may be measured. Note that with this

machine the armature current is the same as the load current. The graph

of V versus I

is known as the output characteristic of the generator,

and is shown in Fig. 7.11 . The terminal p.d. of the machine will be less

than the generated emf, by the amount of internal voltage drop due to

, such that:

VEIR

 volt

(7.1)

voltage

 I

Fig. 7.11

Ideally, the graph of E versus I

would be a horizontal line. However,

an effect known as armature reaction causes this graph to ‘ droop ’ at the

higher values of current. The main advantage of this type of generator

is that there is some scope for increasing the generated emf in order

to offset the internal voltage drop, I

, as the load is increased. The

big disadvantage is the necessity for a separate d.c. supply for the ﬁ eld

excitation.

7.6 Shunt Generator

This is a self-excited machine, where the ﬁ eld winding is connected

in parallel (shunt) with the armature winding. The circuit diagram is