562 ROTATING MACHINES
Torque0ωs
SpeedFigure 13.1.7Approximate shape of
torque–speed curve for a single-phase
induction motor.Elementary Direct-Current Machines
A preliminary discussion of dc machines, including Equations (12.2.14) through (12.2.18), was
presented in Section 12.2. The location of the brushes on the commutator arrangement connected
to the armature winding ensures that the rotor and stator mmf axes are at all times at right angles
to one another, as shown in Figure 12.2.4. The expression for torque given by Equation (12.4.32)
is applicable to the dc machine, provided the constantKis adjusted for the nonsinusoidal mmf
distributions and sinδis made equal to unity. Not only are the conditions for constant torque
fulfilled, but also the condition for maximum torque and hence for maximum energy conversion
is satisfied, sinceδ=±π/2, depending upon whether generator or motor action occurs for a
given direction of rotation.
Since both armature and field circuits carry direct current in the case of a dc machine, they can
be connected either in series or in parallel. When the armature and field circuits are connected in
parallel, the machine is known as ashunt machine.In the shunt machine, the field coils are wound
with a large number of turns carrying a relatively small current. When the circuits are connected
in series, the machine is known as aseries machine. The field winding in the series machine
carries the full armature current and is wound with a smaller number of turns. A dc machine
provided with both a series-field and a shunt-field winding is known as acompound machine.In
the compound machine, the series field may be connected eithercumulatively,so that its mmf adds
to that of the shunt field, ordifferentially,so that the mmf opposes. The differential connection is
used very rarely. The voltage of both shunt and compound generators (or the speed, for motors) is
controlled over reasonable limits by means of a field rheostat in the shunt field. The machines are
said to beself-excitedwhen the machine supplies its own excitation of the field windings, as in
the cases just defined. The field windings may beexcited separatelyfrom an external dc source,
however. A small amount of power in the field circuit can control a large amount of power in
the armature circuit. The dc generator may then be viewed as a power amplifier. Some possible
field-circuit connections of dc machines are shown in Figure 13.1.8.
For self-excited generators, residual magnetism must be present in the ferromagnetic circuit
of the machine in order to start the self-excitation process. For a dcgenerator, the relationship
between steady-state generated emfEaand the terminal voltageVtis given by
Vt=Ea−IaRa (13.1.11)
whereIais the armature currentoutput,andRais the armature circuit resistance. For a dcmotor,
the relationship is given by