0195136047.pdf

520 ELECTROMECHANICS

(a) (b)

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+

+

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Field Armature

coil

Field

structure

Field

Brushes on commutator

(not shown)

Quadrature axis,

rotor mmf axis

Direct axis,

stator mmf

or field axis

Armature

Figure 12.2.4Schematic representations of a dc machine.(a)Schematic arrangement.(b)Circuit represen-

tation.

whatever the rotor speedωm. The armature current in the armature winding is alternating. The

action of the commutator is to change the armature current from a frequency governed by the

mechanical speed of rotation to zero frequency at the commutator brushes connected to the

external circuit.

For the case of a dc machine with a flux per pole ofφ, the total flux cut by one conductor in

one revolution is given byφP, wherePis the number of poles of the machine. If the speed of

rotation isnr/min, the emf generated in a single conductor is given by

e=

φP n

60

(12.2.14)

For an armature withZconductors andαparallel paths, the total generated armature emfEais

given by

Ea=

PφnZ

60 α

(12.2.15)

Since the angular velocityωmis given by 2πn/60, Equation (12.2.15) becomes

Ea=

PZ

2 πα

φωm=Kaφωm (12.2.16)

whereKais the design constant given byPZ/ 2 πα. The value obtained is the speed voltage

appearing across the brush terminals in the quadrature axis (see Figure 12.2.4) due to the field

excitation producingφin the direct axis. For this reason, in the schematic circuit representation of

a dc machine, the field axis and the brush axis are shown in quadrature, i.e., perpendicular to each

other. The generated voltage, as observed from the brushes, is the sum of the rectified voltages of

all the coils in series between brushes. If the number of coils is sufficiently large, the ripple in the

waveform of the armature voltage (as a function of time) becomes very small, thereby making

the voltage direct or constant in magnitude.