Title: DC Motors
1DC Motors
The construction of a DC motor is essentially the
same as the construction of a DC generator. In
general, the same machine can be used as either a
motor or as a generator. If power is supplied to
the armature terminals, causing the machine to
turn, then its a motor. If mechanical power is
supplied to the machine by turning it, and it
supplies electrical power to an electrical load,
then its a generator. Like DC generators, there
are several variants of the basic DC motor.
These are shunt motors, series motors, and
compound motors.
2DC Motors
Consider a DC machine, with its armature
connected to a DC source. Well ignore (for now)
the field connections and assume that excitation
current is somehow supplied to the field
windings. When the connection to the DC source is
made (by closing a switch), current flows in the
armature windings. This current is equal to the
source voltage Es divided by the armature
resistance R. R is simply the resistance of the
armature windings, which is usually very small
this means the armature current is quite large.
The armature coils are
immersed in a magnetic field, so the Lorentz
force appears as soon as armature current begins
to flow. The large current thus causes a large
torque, and the armature begins to rotate.
R
S
N
f
Es

3DC Motors
What happens when an armature rotates in a field?
An armature voltage is induced across the
brushes. This occurs in a generator, and the
only difference between that and our motor is the
generators armature is made to turn by an
external mechanical torque. The fact that the
motors armature is made to turn by an internal
electromagnetic torque makes no difference. A
voltage Eo, porportional to the speed of
rotation, is induced across the brushes
R
The polarity of the induced voltage is always
opposite the voltage supplied to the armature,
Eo. Because of this, its called the
counterelectromotive force (cemf) or back emf.
S
N
Eo
f
Es



4DC Motors
Now, because of the counter emf, the voltage
across the armature resistance R is the
difference between the source voltage Es and the
back emf, Eo. This means that when the armature
starts to turn and the cemf increases, the
armature current starts to decrease
As the motors speed increases, the counter emf
increases and the armature current decreases.
This continues until the counter emf nearly
equals the source voltage. At this speed, the
armature current is quite low just enough that
the armature power is sufficient to maintain the
motors speed.
R
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Eo
f
Es



5DC Motors
The only purpose of a motor is to supply power
and torque to a load. From our study of DC
generators, we know that the counter emf
developed by a lapwound armature is
R
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Eo
f
Es



6DC Motors
Weve already seen that the armature current is
And its obvious that the power supplied to the
armature is
But with a little manipulation we see that
R
R is the armature resistance, so the second term
is the power dissipated as heat by the armature.
The first term represents the power delivered to
the mechanical load.
S
N
Eo
f
Es



7DC Motors
The electrical power converted to mechanical
power is
But we have an expression which relates torque
and mechanical power
Where n is the motor speed in rpm, and T is the
torque. Combining the last two expressions,
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Eo
f
And with a little more manipulation,
Es



8Speed Control
When a motor is driven at less than full load,
the armature voltage drop is always much smaller
than the source voltage Es. This means that the
second term in
Is negligible, so
We know that the counter emf is given by
so
R
The speed of the motor can be controlled by
varying the voltage supplied to the armature, or
by varying the field flux.
S
N
Eo
f
Es



9WardLeonard Speed Control
Controlling the motor speed via the armature
voltage is an attractive idea. Nowadays this can
be done by means of a variableoutput DC supply,
but it was formerly done by an interesting
electromechanical arrangement called a
WardLeonard system. In this system, we have a
fixedspeed motor (probably a 3phase,
synchronous AC motor) driving a
separatelyexcited DC generator with variable
field current. The output voltage of the DC
generator can be controlled by varying
the excitation current, providing a means to vary
the
Ix
R
armature voltage and control the speed of the DC
motor.
Ix
Es
Eo
DC motor
3f motor
DC Generator

10WardLeonard Speed Control
In the WardLeonard system, as long as the DC
motor is supplying mechanical power to a
mechanical load, it absorbs electrical power from
the generator. Suppose we decide to reduce the
motor speed, by reducing Es. For some period of
time, Eo is greater than Es, so current flows
from the motor to the generator. For this period
of time, the motor actually operates as a
generator, and viceversa. This briefly causes
the AC motor to act as a generator and deliver
power back to its supply.
The kinetic energy given up by the slowing
mechanical
Ix
R
Load is converted to electrical power which
drives the DC generator (operating as a motor),
and finally is delivered to
Ix
Es
Eo
DC motor
3f motor
DC Generator

the 3phase power supply, temporarily reducing or
reversing the systems energy consumption.
11Armature Speed Control
Of course, its also possible to control the
motor speed by means of a rheostat in series with
the armature. This is simple, but inefficient
due to the power dissipated by the rheostat.
Furthermore, it results in poor speed regulation.
If the mechanical load increases, the armature
current increases. This increases the voltage
drop across the rheostat, which effectively
reduces the armature voltage, further reducing
the motor speed.
R
Ix
Es
Eo
DC motor

12Flux Speed Control
Another way to control the motor speed is by
varying the field flux. The relationship between
speed, armature voltage, and flux is
This says that increasing the flux reduces the
speed, and vice versa. If the motor is running
at its rated speed and the excitation current is
reduced, the counter emf is also reduced. This
causes an increase in armature current, which
causes the speed to increase until the counter
emf is again nearly equal to the supply voltage.
Rf
R
Ix
Es
Eo
DC motor

13Series Motor
Heres a series DC motor, where the field winding
is connected in series with the armature. This
means that the excitation current and the
armature current are the same. If an increasing
load causes the armature current to increase, the
increasing excitation current increases the field
flux, which reduces the motor speed but increases
the torque
R
Es
At low speeds under heavy loads, the series motor
can produce a very large torque. This is good
for applications such as railroad locomotives.
Under light load, when the field current is low,
it may tend to run at a dangerously high speed.
This is called runaway.
Eo
DC motor
Series Field Winding

14Compound Motor
A compound motor has both a shunt field winding,
and a series field winding. If the two field
windings are connected so their mmfs have the
same direction, then the two mmfs add to produce
the total field. This is called a cumulative
compound motor. When the motor is lightly
loaded, the armature current is very small, so
the series field winding produces a very small
mmf. A series motor would run at an excessive
speed, and possibly run away. In the cumulative
compound motor, excitation
Current still flows in the shunt field winding,
producing an mmf which does not vary with load.
This protects the motor from running away. As
the load increases, the series field mmf
increases, which increases the total mmf and
reduces the speed of the motor. Thus, the speed
of a cumulative compound motor drops by 10  30
as the motors load is increases from noload to
fullload.
Series Field
Armature
Es
Eo
Shunt Field

15Differential Compound Motor
It is also possible to connect the series and
shunt field windings so their mmfs have opposite
directions. In this case, the series field mmf
subtracts from the shunt field mmf. This is
called a differential compound motor. When the
motor is lightly loaded, the armature current is
very small, so the series field winding produces
a very small mmf. When the load increases, the
series field current increases, but this causes a
reduction in total mmf and a resulting increase
in speed.
As the load increases, the motors speed
increases, which can cause instability. For this
reason, there are few applications for the
differential compound motor.
Series Field
Armature
Es
Eo
Shunt Field

16Reversing a motor
To reverse the direction of rotation (e.g., a
reversible drill), we must reverse the direction
of the Lorentz force on the armature coils. How
to do this? There are two ways. Either reverse
the direction of the current flowing in the
armature coils by reversing the polarity of the
voltage supplied to the armature, or reverse the
direction of the field mmf by reversing the
polarity of the field connections.If the motor is
A compound motor, both the shunt and series field
connections must be reversed.
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Eo
f
Es



17Starting a motor
Weve previously observed that, for a separately
excited motor (or a shunt motor), the armature
current is given by
If Es is suddenly connected to a motor whose
armature is at rest, the counter emf Eo is zero,
so the armature current is only limited by R, the
resistance of the armature windings. R is
usually very small, so the
armature current is very high. This would
produce a very high starting torque, which may be
desirable, but it also causes excessive heating
(and possibly burnout) of the armature, heavy
sparking of the commutator and brushes, tripped
circuit breakers in the power supply, and
mechanical shock.
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Eo
f
Es



18Starting a motor
Obviously, some means of controlling the armature
current during startup is desirable. Wed
usually like to limit the armature current during
startup to no more than 1.5 2 times the full
load current. This can be done by connecting a
variable resistance (a rheostat) in series with
the armature to control the armature current. As
the speed of the motor increases, causing the
counter emf to increase, the resistance of the
rheostat is reduced until the motor is running at
full speed.
A faceplate starter, described in detail by
Wildi, is a similar arrangement. The rheostat is
replaced by a set of current limiting resistor,
which are switched in or out of the armature
circuit by a movable contact arm. This provides
acceleration of the motor in steps, with limited
current and torque.
R
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Eo
f
Es



19Dynamic Braking
One way of stopping the motor electrically is
called dynamic braking. Consider the shunt motor
below. When the switch is in the position shown,
power is applied to the armature and the motor
runs normally, driving whatever mechanical load
it is coupled to. The counter emf is Eo. When
the switch is thrown, the armature is
disconnected from the power supply and connected
to a load resistor R. Initially, the armature is
still turning at full speed, so the counter emf
is still Eo. Now the motor acts as a generator,
causing current to flow through the load
resistor. This current flows through the
armature, but
The armature current is reversed in direction
when the switch is thrown. This reverses the
resulting torque on the armature, and the torque
now acts in the direction opposing the rotation
of the armature. This torque will bring he motor
promptly to a stop.
Armature
Es
Eo
R
Shunt Field

20Dynamic Braking
The resistor R is usually chosen so the braking
current is initially (when the switch is thrown)
about 2 times the rated motor current. This
makes the braking torque twice the normal motor
torque. Of course, as the motor slows down the
counter emf is reduced. This reduces the braking
current, and therefore the braking torque. The
motors speed decays exponentially, like the
voltage across a discharging capacitor. While
the initial deceleration is quite rapid, it
tapers off. If wed like to stop the motor even
faster, we can use a technique called plugging.
Armature
Es
Eo
R
Shunt Field

21Plugging
Plugging means abruptly reversing the armature
current. Shown below is a simplified arrangement
for doing this Throwing the switch reverses the
polarity of the armature connection, reversing
the direction of the armature current. Before
throwing the switch, the counter emf across the
armature is Eo, and the armature current is
Where Ro is the series resistance of the
armature. The polarity of the counter emf is
opposite that of the armature supply, so the two
subtract. After throwing the switch, the
polarity of the armature supply is reversed, so
the two emfs add
Armature
Es
Eo
Shunt Field

22Plugging
Throwing the switch causes a VERY large reverse
current to flow in the armature, which would
cause a correspondingly huge braking torque if
the armature or brushes and commutators were not
destroyed in the process. Or if the shaft or
motor mounts didnt shatter. These undesirable
consequences can be avoided by adding a series
resistor R, as shown below. R should be chosen
to limit the initial braking current to about
twice the normal, fullload motor current. With
this arrangement, when the motor comes to a stop
the
reverse torque will still be the torque developed
by an armature current of
Armature
Es
Eo
R
Shunt Field
In dynamic braking, the braking torque approaches
zero as the speed approaches zero. In plugging,
the braking torque never approaches zero.

23Plugging
Plugging will obviously stop the motor faster
than dynamic braking, but when the armature stops
the reverse torque is still applied. If the
armature supply is not disconnected, the motor
will immediately start to rotate in the opposite
direction. In a practical plugging system, a
means must be provided to disconnect the armature
the moment it stops turning. Plugging has the
advantage of speed, but dynamic braking is
simpler and more common.
Armature
Es
Eo
R
Shunt Field

24Mechanical Time Constant
As weve observed, with dynamic braking the
motors speed decays exponentially, like the
voltage across a discharging capacitor. As a
discharging RC circuit has a time constant, we
can define a mechanical time constant T for a
motor under dynamic braking. T would be the
amount of time required for the motor to slow to
36.8 of its initial speed. Well define another
constant, To, as the ammount of time required for
the motor to slow to 50 of its initial speed.
The two constants are related by
Armature
Es
Eo
R
Shunt Field

25Mechanical Time Constant
The mechanical time constant is related to the
initial speed, moment of inertia, and the power
delivered to the braking resistor R by
Where J is the moment of inertia for all rotating
parts (armature, shaft, load, etc.) in kgm2, n1
is the initial speed of the motor (when braking
is first applied) in rpm, and P1 is the power
initially dissipated by the braking resistor.
As a practical matter, the motor will be brought
to a stop by a combination of dynamic braking and
mechanical friction (imperfect bearings) in
approximately 5T0. If plugging is used, the
motor will stop in 2T0.
Armature
Es
Eo
R
Shunt Field

26Armature Reaction
As we saw with DC generators, a current flowing
in the armature makes the armature a source of
MMF. This MMF interacts with the pole flux in a
way which weakens and distorts the shape of the
pole flux. This is called armature reaction.
This does not happen when the motor runs under
noload conditions, but does occur when a load
causes the armature to draw current. The
consequences are the same as for the DC
Generator Poor commutation, sparking, and loss
of power and efficiency. A small series field
winding may be added to compensate for some of
the loss in field flux, this is called a
stabilizedshunt winding.
R
Commutating poles may also be used, as in DC
Generators, to compensate for the neutral zone
shift.
R
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Eo
f



27Armature Reaction
Some large motors, which must be started, stopped
and reversed rapidly, incorporate compensating
windings. These are stationary windings,
distributed in slots cut into the faces of the
pole pieces, connected in series with the
armature but so their mmf is equal and opposite
to the armature mmf. Because theyre distributed
across the poles, they almost completely cancel
the field distortion due to armature reaction.
This results in several advantages A shorter
air gap can be used, because the armature no
longer causes demagnetization. This means the
shunt field strength can be reduced.
Second, the inductance of the armature coils is
reduced by a factor of up to 5. This obviously
improves commutation, it also improves the
response of the motor to control input. Finally,
such a motor can briefly develop up to 4 times
its rated torque.
R
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Eo
f



28Variable Speed Control
One of the most attractive features of the DC
motor is that it offers the ability to control
speed. This is an advantage in many industrial
applications, and also in vehicular applications
such as electric cars, locomotives, and
submarines. We should take a closer look at
controlling the speed of a DC motor. Well
consider a separatelyexcited motor, with
perunit values for the armature current Ia,
armature voltage Ea, torque T, and field flux ff.
This means the rated values of Ea has a value of
1 p.u., the rated armature current has a value of
1 p.u., etc. This makes it easy to apply the
results of this discussion to any
motor of the same type. The torque and the
armature voltage are given by
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Eo
f



29Variable Speed Control
Notice that speed is proportional to Ea, but
torque is only related to flux and armature
current. This means that we can vary the speed
from zero to rated speed (n 1 p.u.) by
increasing Ea from zero to rated voltage (Ea 1
p.u.). At the same time, if we keep Ia and ff at
their rated values, the torque remains
constant at 1 p.u. However, we cannot increase
the speed above the rated speed this way, because
that would require exceeding the rated armature
voltage. If we need to increase the speed
further, we must do so by reducing the flux.
This causes a reduction in torque. The plot here
illustrates the relationship between flux and
speed.
30Variable Speed Control
Because torque is proportional to flux, the
speedtorque curve looks identical to the
previous plot. It shows that torque is constant
from zero to rated speed, so when the motor is
operated on this portion of the curve, it is
operating in constanttorque mode. If we
increase the speed above rated speed by
reducing the flux, we can keep the armature
current constant at 1 p.u., and also keep the
armature voltage at 1 p.u. (rated value)
31Variable Speed Control
When operating above rated speed, we keep Ea and
Ia constant at 1 p.u. Since the product of Ea
and Ia is the power supplied to the motor, the
power remains constant. Weve assumed that the
motor is ideal, so the mechanical power delivered
to the load is also constant. Thus, when
operated above
Rated speed, the motor is said to be operating in
constanthorsepower mode. If we operate a motor
below rated speed, its ventilation is reduced
and it may overheat. This requires reducing the
armature current, which reduces torque. Thus, as
a practical matter the torque may not really be
constant below rated speed.
32Permanent Magnet Motors
Weve talked about motors that have field
windings to produce the flux that results in the
Lorentz force on the armature. These field
windings may be connected in shunt, in series, or
both. Of course, its also possible to use
permanent magnets as field poles. This
eliminates the heat due to the field current, and
reduces the space required for the poles,
resulting in a smaller and more efficient motor.
A larger air gap may also be used, reducing
armature reaction and reducing the inductance of
the armature. Permanent magnets are often used
as field poles in motors smaller than 5 hp.
R
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Eo
f


