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Introduction to D.C. Machines
D.C.
machines
are
characterized
by
their
versatility.
By
means
of
various
combinations of
shunt-, series-, and separately excited field
windings they can be designed
to
display a wide variety of volt-ampere or speed-
torque characteristics for both dynamic
and steady state operation. Because of
the ease with which they can be controlled,
systems
of D.C. machines are often used
in applications requiring a wide range of motor
speeds or
precise control of motor
output.
The
essential
features
of
a
D.C.
machine
are
shown
schematically.
The
stator
has
salient poles and is excited by one or
more field coils. The air-gap flux distribution
created
by the field winding is
symmetrical about the centerline of the field
poles. This is called the
field axis or
direct axis.
As we know, the A.C.
voltage generated in each rotating armature coil
is converted to
D.C. in the external
armature terminals by means of a rotating
commutator and stationary
brushes
to
which
the
armature
leads
are
connected.
The
commutator-brush
combination
forms a
mechanical rectifier, resulting in a D.C. armature
voltage as well as an armature
m.m.f.
Wave
then
is
90
electrical
degrees
from
the
axis
of
the
field
poles,
i.e.
in
the
quadrature
axis. In the schematic representation the brushes
are shown in quadrature axis
because
this is the position of the coils to which they
are connected. The armature m.m.f.
Wave
then is along the brush axis as shown. (The
geometrical position of the brushes in an
actual machine is approximately 90
electrical degrees from their position in the
schematic
diagram because of the shape
of the end connections to the commutator.)
The magnetic torque and the speed
voltage appearing at the brushes are independent
of
the
spatial
waveform
of
the
flux
distribution;
for
convenience
we
shall
continue
to
assume a sinusoidal flux-
density wave in the air gap.
The torque can then be found from
the magnetic field viewpoint.
The torque can be expressed in terms of
the interaction of the direct-axis air-gap flux
per
pole
?
d
and
space-fundamental
component
Fa
1
of
the
armature
.
With
the
brushes
in the quadrature axis the angle between these
fields is 90 electrical degrees, and
its sine equals unity. For a
P
pole machine
T
?
?
?
P
?
2
?
?
?
d
Fa
1
（
1-1
）
2
?
2
?
In which the minus sign gas been dropped
because the positive direction of the torque
can be determined from physical
reasoning. The space fundamental
Fa
1
of
the sawtooth
armature is
8
?
2
times its peak. Substitution in above
equation then gives
T
?
PC
a
?
a
i
a
(
N
?
m
)
（
1-2
）
2
?
m
Whe
re,
I
a
=current in
external armature circuit;
C
a
=total number
of conductors in armature winding;
m
=number of parallel paths
through winding.
And
K
a
?
PC
a
（
1-3
）
2
?
m
is a constant fixed by the design of
the winding.
The rectified voltage
generated in the armature has already been
discussed before for
an elementary
single-coil armature. The effect of distributing
the winding in several slots is
shown
in figure. In which each of the rectified sine
wave is the voltage generated in one of
the coils, commutation taking place at
the moment when the coil sides are in the neutral
zone. The generated voltage as observed
from the brushes and is the sum of the rectified
voltages of all the coils in series
between brushes and is shown by the rippling line
labeled
e
a
in figure. With a dozen or so
commutator segments per pole, the ripple becomes
very
small and the average generated
voltage observed from the brushes equals the sum
of the
average
values
of
the
rectified
coil
voltages.
The
rectified
voltage
e
a
between
brushes,
Known also as the speed voltage, is
e
a
?
PC
a
?
d
?
m
?
K
a
< br>?
d
?
m
（
1-4
）
2
?
m
where
K
a
is
the design constant. The rectified
voltage of
a distributed winding has
the
same average value as that of a
concentrated coil. The difference is that the
ripple is greatly
reduced.
From the above equations, with all
variable expressed in SI units,
e
a
i
a
?
< br>T
?
m
（
1-5
）
This
equation
simply
says
that
the
instantaneous
power
associated
with
the
speed
voltage equals the instantaneous
mechanical power with the magnetic torque. The
direction
of power flow being
determined by whether the machine is acting as a
motor or generator.
The direct-axis
air-gap flux is produced by the combined m.m.f.
?
N
f
i
f
of the field
windings. The flux-m.m.f.
Characteristic being the magnetization curve for
the particular
iron
geometry
of
the
machine.
In
the
magnetization
curve,
it
is
assumed
that
the
armature
–
m.m.f. Wave is
perpendicular to the field axis. It will be
necessary to reexamine
this assumption
later in this chapter, where the effects of
saturation are investigated more
thoroughly. Because the armature e.m.f.
is proportional
to
flux
times speed, it is
usually
more convenient to express the
magnetization curve in terms of the armature
e.m.f.
e
a
0
at
a
constant
speed
?
m
0
.
The
voltage
e
a
for
a
given
flux
at
any
other
speed
?
m
is
proportional to the speed, i.e.
?
m
e
a
?
e
a
（
1-6
）
?
m
0
0
There is the magnetization curve with
only one field winding excited. This curve can
easily be obtained by test methods, no
knowledge of any design details being required.
Over
a
fairly
wide
range
of
excitation
the
reluctance
of
the
iron
is
negligible
compared with
that of the air gap. In this region the flux is
linearly proportional to the total
m.m.f. of the field windings, the
constant of proportionality being the direct-axis
air-gap
permeance.
The
outstanding advantages of D.C. machines arise from
the wide variety of operating
characteristics
that
can
be
obtained
by
selection
of
the
method
of
excitation
of
the
field
windings.
The field windings may be separately excited from
an external D.C. source, or
they may be
self-excited; i.e. the machine may supply its own
excitation. The method of
excitation
profoundly
influences
not
only
the
steady-state
characteristics,
but
also
the
dynamic
behavior of the machine in control systems.
The connection diagram of a
separately excited generator is given. The
required field
current is a very small
fraction of the rated armature current. A small
amount of power in
the field circuit
may control a relatively large amount of power in
the armature circuit; i.e.
the
generator is a power amplifier. Separately excited
generators are often used in feedback
control systems when control of the
armature voltage over a wide range is required.
The
field windings of self-excited
generators may be supplied in three different
ways. The field
may be connected in
series with the armature, resulting in a series
generator. The field may
be connected
in shunt with the armature, resulting in a shunt
generator, or the field may be
in
two
sections,
one
of
which
is
connected
in
series
and
the
other
in
shunt
with
the
armature,
resulting
in
a
compound
generator.
With
self-excited
generators
residual
magnetism must be
present in the machine iron to get the self-
excitation process started.
In
the
typical
steady-state
volt-ampere
characteristics,
constant-
speed
prime
movers
being
assumed.
The
relation
between
the
steady
state
generated
e.m.f.
E
a
and
the
terminal voltage
V
t
is
V
t
?
E
a
?
I
a
R
a
（
1-7
）
where
I
a
is
the armature
current
output
and
R
a
is
the armature
circuit
resistance.
In
a
generator,
E
a
is
larger
than
V
t
and
the
electromagnetic
torque
T
is
a
counter
torque
opposing rotation.
The terminal voltage of a separately
excited generator decreases slightly with increase
in the load current, principally
because of the voltage drop in the armature
resistance. The
field current of a
series generator is the same as the load current,
so that the air-gap flux
and
hence
the
voltage
vary
widely
with
load.
As
a
consequence,
series
generators
are
normally connected so that the m.m.f.
of the series winding aids that of the shunt
winding.
The
advantage
is
that
through
the
action
of
the
series
winding
the
flux
per
pole
can
increase
with load, resulting in a voltage output that is
nearly usually contains many turns
of
relatively small wire. The series winding, wound
on the outside, consists of a few turns
of
comparatively
heavy
conductor
because
it
must
carry
the
full
armature
current
of
the
machine.
The
voltage
of
both
shunt
and
compound
generators
can
be
controlled
over
reasonable limits by
means of rheostats in the shunt field.
Any of the methods of excitation used
for generators can also be used for motors. In
the typical steady-state speed-torque
characteristics, it is assumed that motor
terminals are
supplied
from
a
constant-voltage
source.
In
a
motor
the
relation
between
the
e.m.f.
E
a
generated in the armature and terminal
voltage
V
t
is
V
t
?
E
a
?
I
a
R
a
（
1-8
）
where
I
a
is
now the armature current input. The generated
e.m.f.
E
a
is now smaller than
the
terminal
voltage
V
t
,
the
armature
current
is
in
the
opposite
direction
to
that
in
a
generator,
and
the
electron
magnetic
torque
is
in
the
direction
to
sustain
rotation
of
the
armature.
In shunt and separately excited motors
the field flux is nearly constant. Consequently
increased torque must be accompanied by
a very nearly proportional increase in armature
current
and
hence
by
a
small
decrease
in
counter
e.m.f.
to
allow
this
increased
current
through the small armature resistance.
Since counter e.m.f. is determined by flux and
speed,
the
speed
must
drop
slightly.
Like
the
squirrel-cage
induction
motor,
the
shunt
motor
is
substantially a constant-
speed motor having about 5% drop in speed from no
load to full
load. Starting torque and
maximum torque are limited by the armature current
that can be
commutated successfully.
An outstanding advantage of the shunt
motor is case of speed control. With a rheostat
in
the
shunt-
field
circuit,
the
field
current
and
flux
per
pole
can
be
varied
at
will,
and
variation
of
flux
causes
the
inverse
variation
of
speed
to
maintain
counter
e.m.f.
approximately equal
to the impressed terminal voltage. A maximum speed
range of about 4
or
5
to
I
can
be
obtained
by
this
method.
The
limitation
again
being
commutating
conditions.
By
variation
of
the
impressed
armature
voltage,
very
speed
ranges
can
be
obtained.
In
the
series
motor,
increase
in
load
is
accompanied
by
increase
in
the
armature
current and m.m.f.
and the stator field flux (provided the iron is
not completely saturated).
Because flux
increase with load, speed must drop in order to
maintain the balance between
impressed
voltage and counter e.m.f. Moreover, the increased
in armature current caused
by
increased
torque
is
varying-speed
motor
with
a
markedly
drooping
speed-load
characteristic.
For
applications
requiring
heavy
torque
overloads,
this
characteristic
is
particularly
advantageous
because
the
corresponding
power
overloads
are
held
to
more
reasonable
values
by
the
associated
speed
drops.
Very
favorable
starting
characteristics
also result
from the increase flux with increased armature
current.
In the compound motor the
series field may be connected either cumulatively,
so that
its m.m.f. adds to that of the
shunt field, or differentially, so that it
opposes. The differential
connection
is
very
rarely
used.
A
cumulatively
compounded
motor
has
speed-
load
characteristic intermediate
between those of a shunt and a series motor, the
drop of speed
with load depending on
the relative number of ampere-turns in the shunt
and series fields.
It does not have
disadvantage of very high light-load speed
associated with a series motor,
but it
retains to a considerable degree the advantages of
series excitation.
The
application
advantages
of
D.C.
machines
lie
in
the
variety
of
performance
characteristics
offered by the possibilities of shunt, series and
compound excitation. Some
of
these
characteristics
have
been
touched
upon
briefly
in
this
article.
Still
greater
possibilities
exist
if
additional
sets
of
brushes
are
added
so
that
other
voltages
can
be
obtained
from
the
commutator.
Thus
the
versatility
of
D.C.
machine
system
and
their
adaptability to control, both manual
and automatic, are their outstanding features.
A D.C machines is made up of two basic
components:
－
The
stator
which
is
the
stationary
part
of
the
machine.
It
consists
of
the
following
elements:
a
yoke
inside
a
frame;
excitation
poles
and
winding;
commutating
poles
(composes)
and
winding;
end
shield
with
ball
or
sliding
bearings;
brushes
and
brush
holders; the terminal box.
－
The rotor which is the
moving part of the machine. It is made up of a
core mounted on
the machine shaft. This
core has uniformly spaced slots into which the
armature winding is
fitted. A
commutator, and often a fan, is also located on
the machine shaft.
The
frame
is
fixed
to
the
floor
by
means
of
a
bedplate
and
bolts.
On
low
power
machines
the
frame
and
yoke
are
one
and
the
same
components,
through
which
the
magnetic flux produced by the
excitation poles closes. The frame and yoke are
built of cast
iron or cast steel or
sometimes from welded steel plates.
In
low-power and controlled rectifier-supplied
machines the yoke is built up of thin
(0.5
～
1mm)
laminated
iron
sheets.
The
yoke
is
usually
mounted
inside
a
non-ferromagnetic frame (usually made
of aluminum alloys, to keep down the weight). To
either side of the frame there are
bolted two end shields, which contain the ball or
sliding
bearings.
The
(main)excitation
poles
are
built
from
0.5
～
1mm
iron
sheets
held
together
by
riveted
bolts.
The
poles
are
fixed
into
the
frame
by
means
of
bolts.
They
support
the
windings carrying the excitation
current.
On the rotor side, at the end
of the pole core is the so-called pole-shoe that
is meant to
facilitate
a
given
distribution
of
the
magnetic
flux
through
the
air
gap.
The
winding
is
placed
inside an insulated frame mounted on the core, and
secured by the pole-shoe.
The
excitation windings are made of insulated round or
rectangular conductors, and
are
connected either in series or in parallel. The
windings are liked in such a way that the
magnetic flux of one pole crossing the
air gap is directed from the pole-shoe towards the
armature (North Pole), which the flux
of the next pole is directed from the armature to
the
pole-shoe (South Pole).
The commutating poles, like the main
poles, consist of a core ending in the pole-shoe
and
a
winding
wound
round
the
core.
They
are
located
on
the
symmetry
(neutral)
axis
between
two
main
poles,
and
bolted
on
the
yoke.
Commutating
poles
are
built
either
of
cast-
iron or iron sheets.
The
windings
of
the
commutating
poles
are
also
made
from
insulated
round
or
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