DC Machines.pptx

Electrical Engineering: Principles and Applications, 6e
Allan R. Hambley
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
TOPIC 4 - DC MACHINES
• Overview of motors
• Principles of DC Machines
• Rotating DC Machines
• Shunt-connected and Separately Excited
DC Motors
• Series-Connected DC Motors
• Speed Control of DC Motors
• DC Generators

Allan R. Hambley
CHAPTER 16
DC MACHINES

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At the end of this topic, you should be able to:
1. Select the proper motor type for various
applications.
2. State how torque varies with speed for
various motors.
3. Use the equivalent circuit for dc motors to
compute electrical and mechanical
quantities.

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4. Use motor nameplate data.
5. Understand the operation and characteristics
of shunt-connected dc motors, series-connected
dc motors, and universal motors.

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Allan R. Hambley
An electrical motor consists of a stationary part,
or stator, and a rotor, which is the rotating part
connected to a shaft that couples the machines to
its mechanical load. The shaft and rotor are
supported by bearings so that they can rotate
freely. This is illustrated in Figure 16.1.

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Figure 16.1 An electrical motor consists of a cylindrical rotor that spins inside a stator.

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Depending on the type of machine, either the
stator or the rotor (or both) contain current-
carrying conductors configured into coils. Slots
are cut into the stator and rotor to contain the
windings and their insulation. Currents in the
windings set up magnetic fields and interact with
fields to produce torque.

Allan R. Hambley
Usually, the stator and the rotor are made of iron
to intensify the magnetic field. As in
transformers, if the magnetic field alternates in
direction through the iron with time, the iron
must be laminated to avoid large power losses
due to eddy currents. (In certain parts of some
machines, the field is steady and lamination is
not necessary.)

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Table 16.1 Characteristics of Electrical Motors

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Table 16.1 (continued) Characteristics of Electrical
Motors

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Armature and Field Windings
The primary purpose of a field winding is to set up
the magnetic field in the machine. The current in the
field winding is independent of the mechanical load
imposed on the motor (except in series-connected
motors). On the other hand, the armature winding
carries a current that depends on the mechanical
power produced. Typically, the armature current
amplitude is small when the load is light and larger
for heavier loads. If the machine acts as a generator,
the electrical output is taken from the armature. In
some machines, the field is produced by permanent
magnets (PM), and a field winding is not needed.

Allan R. Hambley
Table 16.1 shows the location (stator or rotor) of
the field and armature windings for some
common machine types. For example, in three-
phase synchronous ac machines, the field
winding is on the rotor, and the armature is on
the stator. In other machines, such as the wound-
field dc machine, the locations are reversed.

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DC Motors
DC motors are those that are powered from dc
sources. One of the difficulties with dc motors is
that nearly all electrical energy is distributed as
ac. If only ac power is available and we need to
use a dc motor, a rectifier or some other
converter must be used to convert ac to dc. This
adds to the expense of the system. Thus, ac
machines are usually preferable if they meet the
needs of the application.

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Exceptions are automotive applications in which
dc is readily available from the battery. DC
motors are employed for starting, windshield
wipers, fans, and power windows.

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In the most common types of dc motors, the
direction of the current in the armature
conductors on the rotor is reversed periodically
during rotation. This is accomplished with a
mechanical switch composed of brushes
mounted on the stator and a commutator
mounted on the shaft.

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The commutator consists of conducting
segments insulated from one another. Each
commutator segment is connected to some of the
armature conductors (on the rotor). The brushes
are in sliding contact with the commutator. As
the commutator rotates, switching action caused
by the brushes moving from one segment to
another changes the direction of current in the
armature conductors.

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The brushes and commutator are subject to wear,
and a significant disadvantage of dc motors is
their relatively frequent need for maintenance.

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Until recently, an important advantage of dc
motors was that their speed and direction could
be controlled more readily than those of ac
motors. However, this advantage is rapidly
disappearing because electronic systems that can
vary the frequency of an ac source have become
economically advantageous. These variable-
frequency sources can be used with simple
rugged ac induction motors to achieve speed
control.

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Figure 16.2 Power flows left to right from a three-phase electrical source into an induction motor and then to a
mechanical load. Some of the power is lost along the way due to various causes.

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Losses, Power Ratings and Efficiency
Pin = √3 Vrms Irms cos (θ)
Mechanical output power is
Pout = Tout ωm
in which Pout is the output power in watts, Tout is
the output torque in newton-meters, and ωm is
the angular speed of the load in radians per
second.

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The power rating of a motor is the output power
that the motor can safely produce on a
continuous basis. For example, we can safely
operate a 5-hp motor with a load that absorbs 5
hp of mechanical power. If the power required
by the load is reduced, the motor draws less
input power from the electrical source, and in the
case of an induction motor, speeds up slightly.

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It is important to realize that most motors can
supply output power varying from zero to
several times their rated power, depending on the
mechanical load. It is up to the system designer
to ensure that the motor is not overloaded.
The chief output power limitation of motors is
their temperature rise due to losses.

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Thus, a brief overload that does not cause
significant rise in temperature is often
acceptable.
It is up to the system designer to ensure that the
motor is not overloaded .
The power efficiency of a motor is given by

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Well-designed electrical motors operating close
to their rated capacity have efficiencies in the
range of 85 to 95 percent. On the other hand, if
the motor is called upon to produce only a small
fraction of its rated power, its efficiency is
generally much lower.

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Speed Regulation
Depending on the torque-speed characteristics, a
motor may slow down as the torque demanded
by the load increases. Speed regulation is defined
as the difference between the no-load speed and
the full-load speed, expressed as a percentage of
the full-load speed:

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Principles of DC Machines
Idealized linear machine shown in Figure 16.6 .
In Figure 16.6, a dc voltage source VT is
connected through a resistance RA and a switch
that closes at t = 0 to a pair of conducting rails. A
conducting bar slides without friction on the
rails. We assume that the rails and the bar have
zero resistance.

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Figure 16.6 A simple dc machine consisting of a conducting bar sliding on conducting rails.

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A magnetic field is directed into the page,
perpendicular to the plane of the rails and the
bar.
Suppose that the bar is stationary when the
switch is closed at t = 0. Then, just after the
switch is closed, an initial current given by iA
(0+) = VT /RA flows clockwise around the circuit.
A force given by f = iA l x B is exerted on the
bar.

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The direction of the current (and l) is toward the
bottom of the page. Thus, the force is directed to
the right. Because the current and the field are
mutually perpendicular, the force magnitude is
given by
f = iAlB

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This force causes the bar to be accelerated
toward the right. As the bar gains velocity u and
cuts through the magnetic field lines, a voltage is
induced across the bar. The voltage is positive at
the top end of the bar and is given by Equation
15.9 (with a change in notation, see Hambley’s
page 739):

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Figure 16.7 Equivalent circuit for the linear machine operating as a motor.

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An equivalent circuit for the system is shown in
Figure 16.7. Notice that the induced voltage eA
opposes the source VT. The current is

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As the velocity of the bar builds up, energy is
absorbed by the induced voltage eA, and this
energy shows up as the kinetic energy of the bar.
Eventually, the bar speed becomes high enough
that eA = VT. Then, the current and the force
become zero, and the bar coasts at constant
velocity.

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Operation as a Motor
Now, suppose that a mechanical load exerting a
force to the left is connected to the moving bar.
Then, the bar slows down slightly, resulting in a
reduction in the induced voltage eA. Current
flows clockwise in the circuit, resulting in a
magnetically induced force directed to the right.
Eventually, the bar slows just enough so that the
force created by the magnetic field
(f = iAlB) equals the load force. Then, the system
moves at constant velocity.

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In this situation, power delivered by the source
VT is converted partly to heat in the resistance RA
and partly to mechanical power. It is the power p
= eAiA delivered to the induced voltage that
shows up as mechanical power p = fu.

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Operation as a generator
Again suppose that the bar is moving at constant
velocity such that eA = VT and the current is zero.
Then, if a force is applied pulling the bar even
faster toward the right, the bar speeds up, the
induced voltage eA exceeds the source voltage
VT, and current circulates counterclockwise as
illustrated in Figure 16.8. Because the current
has reversed direction, the force induced in the
bar by the field also reverses and points to the
left.

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Figure 16.8 Equivalent circuit for the linear machine operating as a generator.

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Eventually, the bar speed stabilizes with the
pulling force equal to the induced force. Then,
the induced voltage delivers power p = eAiA,
partly to the resistance (pR = RAiA
2) and partly to
the battery (pt = VTiA)· Thus, mechanical energy
is converted into electrical energy that eventually
shows up as loss (i.e., heat) in the resistance or
as stored chemical energy in the battery.

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ROTATING DC MACHINES
The basic principles of rotating dc machines are
the same as those of the linear dc machine.
The most common type of dc machine contains a
cylindrical stator with an even number P of
magnetic poles that are established by field
windings or by permanent magnets. The poles
alternate between north and south around the
periphery of the stator.

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Inside the stator is a rotor consisting of a
laminated iron cylinder mounted on a shaft that
is supported by bearings so that it can rotate.
Slots cut lengthwise into the surface of the rotor
contain the armature windings. A rotor with
armature conductors is illustrated in Figure 16.9.

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Figure 16.9 Rotor assembly of a dc machine.

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The cross section of a two-pole machine showing
the flux lines in the air gap is illustrated in Figure
16.10. Magnetic flux tends to take the path of least
reluctance. Because the reluctance of air is much
higher than that of iron, the flux takes the shortest
path from the stator into the rotor. Thus, the flux
in the air gap is perpendicular to the surface of the
rotor and to the armature conductors. Furthermore,
the flux density is nearly constant in magnitude
over the surface of each pole face. Between poles,
the gap flux density is small in magnitude.

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Figure 16.10 Cross section of a two-pole dc machine.

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In a motor, external electrical sources
provide the currents in the field windings and
in the armature conductors. The current
directions shown in Figure 16.10 result in a
counterclockwise torque. This can be
verified by applying the equation f= il x B
that gives the force on a current-carrying
conductor.

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The cross section of a four-pole machine is
shown in Figure 16.11. Notice that the
directions of the currents in the armature
must be reversed under south poles relative
to the direction under the north poles to
achieve aiding contributions to total torque.

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Figure 16.11 Cross section of a four-pole dc machine.

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Induced EMF and Commutation
As the rotor turns, the conductors move through
the magnetic field produced by the stator. Under
the pole faces, the conductors, the field, and the
direction of motion are mutually perpendicular,
just as in the linear machine discussed in slides
of principles of dc machines.
Thus, a nearly constant voltage is induced in
each conductor as it moves under a pole.
However, as the conductors move between poles,
the field direction reverses.

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Therefore, the induced voltages fall to zero and
build up with the opposite polarity. A
mechanical switch known as a commutator
reverses the connections to the conductors as
they move between poles so that the polarity of
the induced voltage seen from the external
machine terminals is constant.

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Let us illustrate these points with a two-pole
machine containing one armature coil, as shown
in Figure 16.12. In this case, the ends of the coil
are attached to a two-segment commutator
mounted on the shaft. The segments are insulated
from one another and from the shaft. Brushes
mounted to the stator make electrical contact
with the commutator segments.

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Figure 16.12 Commutation for a single armature winding.

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Notice that as the rotor turns in Figure 16.12, the
left-hand brush is connected to the conductor
under the south stator pole, and the right-hand
brush is connected to the conductor under the
north stator pole.
The voltage vad induced across the terminals of
the coil is an ac voltage, as shown in the figure.
This voltage passes through zero when the
conductors are between poles where the flux
density goes to zero.

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While the conductors are under the pole faces
where the flux density is constant, the induced
voltage has nearly constant magnitude. Because
the commutator reverses the external
connections to the coil as it rotates, the voltage
vT seen at the external terminals is of constant
polarity.

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Notice that the brushes short the armature
winding briefly during the switching process.
This occurs because the brushes are wider than
the insulation between commutator segments.
This shorting is not a problem, provided that the
voltage is small when it occurs. (Actual
machines have various provisions to ensure that
the coil voltage is close to zero during
commutation for all operating conditions.)

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Commutators in typical machines contain 20 to
50 segments. Because only part of the coils are
commutated at a time, the terminal voltage of a
real machine shows relatively little fluctuation
compared to the two-segment example that we
used for the illustration of concepts. The terminal
voltage of an actual dc machine is shown in
Figure 16.13.

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Figure 16.13 Voltage produced by a practical dc machine. Because only a few (out of many) conductors are
commutated (switched) at a time, the voltage fluctuations are less pronounced than in the single-loop case
illustrated in Figure 16.12.

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Generally, the commutator segments are copper
bars insulated from one another and from the
shaft. The brushes contain graphite that
lubricates the sliding contact. Even so, a
significant disadvantage of dc machines is the
need to replace brushes and redress the
commutator surface because of mechanical wear.

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Actual armatures consist of a large number of
conductors placed around the circumference of
the rotor. To attain high terminal voltages, many
conductors are placed in series, forming coils.
Furthermore, there are usually several parallel
current paths through the armature. The armature
conductors and their connections to the
commutator are configured so that the currents
flow in the opposite direction under south stator
poles than they do under north stator poles.

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As mentioned earlier, this is necessary so that the
forces on the conductors produce aiding torques.
The construction details needed to produce these
conditions are beyond the scope of our
discussion. As a user of electrical motors, you
will find the external behavior of machines more
helpful than the details of their internal design.

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Equivalent Circuit of the DC Motor
The equivalent circuit of the dc motor is shown
in Figure 16.14. The field circuit is represented
by a resistance RF and an inductance LF in series.
We consider steady-state operation in which the
currents are constant, and we can neglect the
inductance because it behaves as a short circuit
for dc currents. Thus, for dc field currents, we
have

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Figure 16.14 Equivalent circuit for the rotating dc machine.

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The voltage EA shown in the equivalent circuit
represents the average voltage induced in the armature
due to the motion of the conductors relative to the
magnetic field. In a motor, EA is sometimes called a
back emf (electromotive force) because it opposes the
applied external electrical source. The resistance RA is
the resistance of the armature windings plus the brush
resistance. (Sometimes, the drop across the brushes is
estimated as a constant voltage of about 2 V rather than
as a resistance. However, in this Hambley’s book, we
lump the brush drop with the armature resistance.)

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The induced armature voltage is given by
in which K is a machine constant that depends on
the design parameters of the machine, ϕ is the
magnetic flux produced by each stator pole, and
ωm is the angular velocity of the rotor.

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The torque developed in the machine is given by
in which IA is the armature current. (We will see that the
output torque of a de motor is less than the developed
torque because of friction and other rotational losses.)
The developed power is the power converted to
mechanical form, which is given by the product of
developed torque and angular velocity:
This is the power delivered to the induced armature
voltage, and therefore, is also given by

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Magnetization Curve
The magnetization curve of a dc machine is a
plot of EA versus the field current lF with the
machine being driven at a constant speed. (EA
can be found by measuring the open-circuit
voltage at the armature terminals.) A typical
magnetization curve is shown in Figure 16.15.

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Figure 16.15 Magnetization curve for a 200-V 10-hp dc motor.

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Because EA is proportional to the flux ϕ, the
magnetization curve has the same shape as a ϕ versus IF
plot, which depends on the parameters of the magnetic
circuit for the field. The magnetization curve flattens
out for high field currents due to magnetic saturation of
the iron. Of course, different machines usually have
differently shaped magnetization curves.
The induced armature voltage EA is directly propor-
tional to speed. If EA1 represents the voltage at speed n1,
and EA2 is the voltage at a second speed n2, we have
(Look at Example 16.3)

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Shunt-Connected DC Motor
In a shunt-connected dc machine, the field circuit is in
parallel with the armature, as shown in Figure 16.16.
The field circuit consists of a rheostat having a variable
resistance, denoted as Radj , in series with the field coil.
Later, we will see that the rheostat can be used to adjust
the torque-speed characteristic of the machine.
We assume that the machine is supplied by a constant
voltage source VT. The resistance of the armature circuit
is RA, and the induced voltage is EA. We denote the
mechanical shaft speed as ωm and the developed torque
as Tdev·

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Figure 16.16 Equivalent circuit of a shunt-connected dc motor. Radj is a rheostat that can be used to adjust
motor speed.

Allan R. Hambley
Power Flow
Figure 16.17 shows the flow of power in the shunt-
connected dc machine. The electrical source supplies an
input power given by the product of the supply voltage
and the line current IL :
Some of this power is used to establish the field. The
power absorbed by the field circuit is converted to heat.
The field loss is given by

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Furthermore, armature loss occurs due to heating of the
armature resistance:
Sometimes, the sum of the field loss and armature loss
is called copper loss.
The power delivered to the induced armature voltage is
converted to mechanical form and is called the
developed power, given by
in which Tdev is the developed torque.
The output power Pout and output torque Tout are less
than the developed values because of rotational losses,
which include friction, windage, eddy-current loss, and
hysteresis loss. Rotational power loss is approximately
proportional to speed.

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Figure 16.17 Power flow in a shunt-connected dc motor.

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Torque-Speed Characteristic
Applying Kirchhoff's voltage law to the equivalent
circuit shown in Figure 16.16, we obtain VT =RAIA + EA
Rearranging, from
And using
Solving for the developed torque,

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Notice that this torque-speed relationship plots as a
straight line, as illustrated in Figure 16.18. The speed
for no load (i.e., Tdev = 0) and the stall torque are
labelled in the figure. The normal operating range for
most motors is on the lower portion of the torque- speed
characteristic, as illustrated in the figure. [The starting
or stall torque of a shunt-connected machine is usually
many times higher than the rated full-load torque].
[Look at Example 16.4]

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Figure 16.18 Torque–speed characteristic of the shunt dc motor.

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Figure 16.19 Magnetization curve for the motor of Example 16.4.

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Figure 16.20 Equivalent circuit for Example 16.4.

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Figure 16.21 Equivalent circuit for a separately excited dc motor. Speed can be controlled by varying either
source voltage (VF or VT).

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Series-Connected DC Motor
The equivalent circuit of a series-connected dc motor is
shown in Figure 16.22. Notice that the field winding is
in series with the armature. In this section, we will see
that the series connection leads to a torque-speed
characteristic that is useful in many applications.
In series dc motors, the field windings are made of
larger diameter wire and the field resistances are much
smaller than those of shunt machines of comparable
size. This is necessary to avoid dropping too much of
the source voltage across the field winding.

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Figure 16.22 Equivalent circuit of the series-connected dc motor.

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Torque-Speed Characteristic
We use a linear equation to approximate the relationship
between magnetic flux and field current. In equation
form , we have
in which KF is a constant that depends on the number of
field windings, the geometry of the magnetic circuit,
and the B-H characteristics of the iron. Of course, the
actual relationship between ϕ and IF is nonlinear, due to
magnetic saturation of the iron. (A plot of ϕ versus IF
has exactly the same shape as the magnetization curve
of the machine.)

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Because IA = IF in the series machine, we have
ϕ = KF IA
Substitute for ϕ in &
If we apply Kirchhoff's voltage law to the equivalent
circuit shown in Figure 16.22, we get
VT = RFIA + RAIA + EA

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Solving for IA, Equation 16.33
Finally,
Equation 16.34
Equa

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A plot of torque versus speed for the series dc motor is
shown in Figure 16.23. The figure shows a plot of
Equation 16.34 as well as an actual curve of torque
versus speed, illustrating the effects of rotational loss
and magnetic saturation. Equation 16.34 predicts
infinite no-load speed. (In other words, for Tdev = 0, the
speed must be infinite.) Yet, at high speeds, rotational
losses due to windage and eddy currents become large,
and the motor speed is limited.
However, in some cases, the no-load speed can become
large enough to be dangerous. It is important to have
protection devices that remove electrical power to a
series machine when the load becomes disconnected.

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At very low speeds, Equation 16.33 shows that the
current IF= IA becomes large. Then, magnetic saturation
occurs. Therefore, the starting torque is not as large as
predicted by Equation 16.34.

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Figure 16.23 Torque–speed characteristic of the series-connected dc motor.

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Speed Control of DC Motors
Several methods can be used to control the speed of de
motors:
1. Vary the voltage supplied to the armature circuit
while holding the field constant.
2. Vary the field current while holding the armature
supply voltage constant.
3. Insert resistance in series with the armature circuit.
In this section, we discuss briefly each of these
approaches to speed control.

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Variation of the Supply Voltage
This method is applicable to separately excited motors
and PM motors. For the shunt motor, varying the supply
voltage is not an appropriate method of speed control,
because the field current and flux vary with VT. The
effects of increasing both armature supply voltage and
the field current tend to offset one another, resulting in
little change in speed.
In normal operation, the drop across the armature
resistance is small compared to EA, and we have
EA ≅VT. Since we also have
we can write

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Thus, the speed of a separately excited motor with
constant field current or of a PM motor is approximately
proportional to the source voltage.
Variation of the supply voltage is also appropriate for
control of a series-connected dc motor; however, the
flux does not remain constant in this case. Equation
16.34 shows that the torque of a series machine is
proportional to the square of the source voltage at any
given speed. Thus, depending on the torque-speed
characteristic of the load, the speed varies with applied
voltage. Generally, higher voltage produces higher
speed.

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Speed Control by Varying the Field Current
The speed of either a shunt-connected or a separately
excited motor can be controlled by varying the field
current. The circuit for the shunt-connected machine
was shown in Figure 16.16, in which the rheostat Radj
provides the means to control field current.
On the other hand, PM motors have constant flux. In
series-connected motors, the field current is the same as
the armature current and cannot be independently
controlled. Thus, using field current to control speed is
not appropriate for either of these types of motors.

Allan R. Hambley
Speed Control by Inserting Resistance in Series
with the Armature
This approach can be applied to all types of dc motors:
shunt, separately excited, series, or Permanent Magnet.
For example, a shunt-connected motor with added
armature resistance is illustrated in Figure 16.26(a). We
denote the total resistance as RA, which consists of the
control resistance plus the resistance of the armature
winding. The torque-speed relationship for a shunt-
connected motor is

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Plots of the torque-speed characteristic for various resistances are
shown in Figure 16.26(b). Similar results apply to separately
excited and PM motors.
Starting controls for shunt or separately excited dc motors usually
place resistance in series with the armature to limit armature
current to reasonable values while the machine comes up to
speed.
A disadvantage of inserting resistance in series with the armature
to control speed is that it is wasteful of energy. When running at
low speeds, much of the energy taken from the source is
converted directly into heat in the series resistance.

Allan R. Hambley
Figure 16.26 Speed can be adjusted by varying a rheostat that is in series with the armature.

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For series-connected dc motor,
Notice that if RA is made larger by adding resistance in
series with the armature, the torque is reduced for any
given speed.

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DC Generators
Generators convert kinetic energy from a prime mover,
such as a steam turbine or a diesel engine, into electrical
energy. When dc power is needed, we can use a dc
generator or an ac source combined with a rectifier. The
trend is toward ac sources and rectifiers; however, many
dc generators are in use, and for some applications they
are still a good choice.
Several connections, illustrated in Figure 16.29, are
useful for dc generators. We will discuss each type of
connection briefly and conclude with an example
illustrating performance calculations for the separately
excited generator.

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Figure 16.29 DC generator equivalent circuits.

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Separately Excited DC Generators
The equivalent circuit for a separately excited dc
generator is shown in Figure 16.29(a). A prime mover
drives the armature shaft at an angular speed ωm, and
the external dc source VF supplies current IF to the field
coils. The induced armature voltage causes current to
flow through the load. Because of the drop across the
armature resistance, the load voltage VL decreases as the
load current IL increases, assuming constant speed and
field current. This is illustrated in Figure 16.30(a).

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Figure 16.30 Load voltage versus load current for various dc generators.

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For some applications, it is desirable for the load voltage to be
nearly independent of the load current. A measure of the amount
of decrease in load voltage with current is the percentage load
voltage regulation given by
in which VNL is the no-load voltage (i.e., IL = 0) and VFL is the
full-load voltage (i.e., with full-rated load current).
One of the advantages of the separately excited dc generator is
that the load voltage can be adjusted over a wide range by
varying the field current either by changing VF or by changing
Radj . Also, the load voltage is proportional to speed.

Allan R. Hambley
Performance Calculations
for separately excited generator
As for dc motors, the following equations apply to dc
generators:
Referring to Figure 16.29(a), we can write:

Allan R. Hambley
Figure 16.31 illustrates the power flow of a dc
generator. The efficiency is given by

Allan R. Hambley
Figure 16.31 Power flow in dc generators.

DC Machines.pptx

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