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Overview
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25-Series DC Motors
Text Chapter 6.1-6.5
Introduction
DC Motor Operation
Starting DC Motors
Series Motor Model
Torque vs Speed
Speed Regulation
ECEGR 450
Electromechanical Energy Conversion
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Introduction
Introduction
• Motors: convert electrical energy into mechanical
energy
• Physical construction of DC motors are the same
as DC generators
• DC motors are powered by a DC electrical system
• AC electrical systems are prevalent
 Separately-excited DC motors are rare
motor
load
electrical
power
 AC/DC converters are available, but add cost
 DC motors are used only when a specific
application dictates their use
mechanical
power
shaft
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Introduction
• Magnetic flux is established by permanent
magnets or field windings (electromagnets)
• DC current is applied to the armature through
brushes
• Interaction of the current in the armature and
magnetic flux causes rotation
 High starting torque
 High speed operation
 Easy to control the position of the shaft
• Applications:
Automobiles
Cranes
Subways
Computer printers
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Operation of DC Motors
• Reasons to use DC motors
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Operation of DC Motors
Operation of DC Motors
Which way does the
rotor rotate?
Which way does the
rotor rotate?
N
F
x
x
ia
b
x
x
N
ia
b
+
-
vs
+
-
a
a
S
S
vs
F
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Operation of DC Motors
Operation of DC Motors
Regardless of motor configuration, for a given
power output:
• Recall developed torque is:
flux
N
F
ia
b
+
-
armature
current
(machine constant)
Ka
P
This is the same equation as
the torque in a dc generator
m
Ra
vs
S
9
ia
+
+
-
-
Ea
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Starting DC Motors
• Circuit equations:
Ea
PCNc
a
Ea
vs
Operation of DC Motors
vs
Ka
F
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ia
K a Pia
a
torque speed
vs Ea
Ra
Td
• Recall back emf:
x
x
torque speed
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• Induced emf when motor is starting is zero
Ea K a P m (ω is 0)
m
vs Ea
• Large armature current will flow ia
Ra
iaR
Ra is generally small, so vs is slightly greater than
Ea
Ra
vs
 NEVER start a DC motor at its rated voltage!
ia
+
+
-
-
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• Overheating and may damage the motor and/or
dc source may occur
Ea
How can we start a PM DC motor?
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Starting DC Motors
Armature Reaction
• Insert a variable resistance in the armature
circuit
• Armature reaction for DC motors is nearly the
same for DC generators
 Start at a high resistance and lower it as speed
(and emf) increase
 Important difference: current in the armature is in
the opposite direction for given rotation direction
• Adjust vs
 Start at low value, and increase as speed increases
starting
Ra resistance
vs
+
+
-
-
Ra
Ea
vs
ia
+
+
-
-
Ea
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DC Motor Types
Series DC Motor
• There are several types of DC motors
 Series
 Shunt
 Compound
• Different methods of connecting the field winding
and armature winding
• Armature and field windings are connected in
series to the same external source
• Flux is therefore related to the armature current
• An external variable resistance may be present to
start or control the speed of the motor
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Series Motor Model
Field and armature windings are connected in series
Rax: variable starting/speed control resistance (Ohm)
Ra: armature resistance (Ohm)
Rs: field winding resistance (Ohm)
Xs: series winding reactance (Ohm)
vs: voltage source (volts)
Ea: armature back emf (volts)
Xs
Rs
Ra
is
ia
-
Same current through the field winding and armature
•
Armature current and flux increase and decrease together
is
ia
vs
-
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Rax
+
-
+
Ea
Xs
Rs
Ra
+
•
 ia = is
Rax
+
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Series Motor Model
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
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vs
Ea
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Series Motor Model
Series Motor Model
• Analyzing the circuit
Ea
vs
ia(R a
Rs
• Pole flux and armature current relationship:
R ax )
P
• Letting R be the total series resistance
Ea
vs
k fia
• From the dc motor equations:
iaR
Ea
Ka
Td
Ka Pia
P
m
• back emf:
Rs
Ra
Xs
•
Rax
+
ia
+
-
vs
Ea
Kak fia
Td
Kak fia2
torque:
m
Back emf is proportional to armature current
Ea
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Question
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Question
Assume the power delivered by the motor is held
constant. Qualitatively explain why increasing the
armature current increases the torque and
decreases the speed of the motor.
Assume the power delivered by the motor is held
constant. Qualitatively explain why increasing the
armature current increases the torque and
decreases the speed of the motor.
Increasing the armature current increases force on
the armature conductors (Lorentz force), but it also
increases the B field, so the force further increases.
(Hence, the torque increase is proportional to the
square of the current.) Since power is held
constant, but torque is increased, the speed must
decrease.
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Series Motor Torque
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Series Motor Speed
Torque developed is proportional to the square of
the armature current (assuming operation in linear
permeability region) Td Kak fia2
Speed decreases as armature current increases:
Ea
torque (Nm)
m
Kak fia
Ea
Kak fia
m
Vs iaR
K ak fia
Note: it is possible for a
series motor to rotate so fast
that it self destructs if
operating without a load
speed (rpm)
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armature current (A)
armature current (A)
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Series Motor Power
Series Motor Power
Power developed by the motor is:
m
Td
Pd
Ea
Kak fia
Power consumed by back emf voltage source =
power developed by the motor
Vs iaR
Kak fia
Pd
m
Td
Eaia
Kak fia2
m
Td
Vs iaR
K k i2
Kak fia a f a
(Vs
iaR)ia
Eaia
Rs
Ra
Xs
Rax
+
ia
+
-
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vs
Ea
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Series Motor Power
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Series Motor Power
• What is the maximum power of the motor?
armature current (A)
PD
Eaia
(vs
dPd
dia
0
vs
2R
ia,max
• So the theoretical maximum power occurs when
armature current (A)
speed (rpm)
iaR)ia
• Let the applied voltage be constant
• The maximum occurs when
power (W)
torque (Nm)
unique point of maximum
developed power
Pd,max
vs2
4R
Generally motors are operated below
their maximum power point
armature current (A)
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Series Motor Torque vs Speed
• We can rewrite
m
vs iaR
K ak fia
as ia
Series Motor
vs
K ak f
m
Td
R
ia
• Write an expression that relates the torque
developed as a function of the speed of the rotor
and applied voltage vs
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Td
K ak fia2
Vs
K ak f
m
R
K ak f vs2
[K ak f m R]2
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Series Motor
High torque at
low speeds
Series Motors
• Series motors are appropriate for loads with large
starting torque
torque
 Hoists, cranes, trains, etc
torque (Nm), power (w)
torque (Nm), power (w)
torque
Nearly constant
power operation
region
speed (rpm)
power
Low torque at
high speeds
speed (rpm)
power
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Speed Regulation
Speed Regulation
T
torque (Nm)
• What happens as the load torque on the motor
increases?
• Is there a large change in speed, or is it nearly
constant?
TL1
TL2
speed
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consider a change in
load torque from TL1 to TL2
speed (rpm)
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Speed Regulation
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Speed Regulation
• Speed regulation is computed as:
SR
100
mnL
mfL
mfL
torque (Nm)
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



TL1
T
100
NmnL NmfL
NmfL
SR: speed regulation (%)
ωmnL: speed under no load (rad/s)
ωmfL: speed under full load (rad/s)
NmnL: speed under no load (rpm)
NmfL: speed under full load (rpm)
TL2
speed (rpm)
speed
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Speed Regulation
Example
• Series DC motors are variable speed (large speed
regulation)
• Shunt DC motors are nearly constant speed
(small speed regulation)
• Compound DC motors: in between series and
shunt motors
A compound DC motor operates at 600 rpm under
no load. At rated load the motor operates at 570
rpm. Compute the speed regulation.
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Example
Series Motor Control
A DC motor operates at 600 rpm under no load. At
rated load the motor operates at 570 rpm. Compute
the speed regulation.
• What are ways of controlling the speed of a series
DC motor?
SR
100
NmnL NmfL
NmfL
100
600 570
570
5.26%
 Adjust vs
 Adjust Rax
Rs
Ra
Xs
+
-
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vs
Ea
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Series Motor Control
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Series Motor Control
• We can control the torque by adjusting the
source voltage in accordance with:
Td
Rax
+
ia
• We can control the torque by adjusting the
source voltage in accordance with:
Kak f Vs2
[Kak f m R]2
Td
• For a given speed, what happens to the torque if
we double the applied voltage?
Kak f Vs2
[Kak f m R]2
• For a given speed, what happens to the torque if
we double the applied voltage?
 Torque quadruples
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Series Motor Control
Series Motor Control
Vs1
torque (Nm)
torque (Nm), power (w)
Vs2
increasing
voltage
speed (rpm)
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speed
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Series Motor Control
torque (Nm)
TL1 = TL2
speed (rpm)
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Summary
• Flux and armature current are directly related in
series DC motors
• Series DC motors have high starting torque, but
torque decreases with speed (near-constant
power operation)
• DC motors should not be operated under no load,
and should not be started at rated voltage
decreasing
Rax
speed (rpm)
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