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Motors and Generators
►Electro-mechanical devices: convert electrical energy to mechanical motion/work and vice versa
►Operate on the coupling between current-carrying conductors and magnetic fields
►Governed by a set of fundamental principles
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Magnetism
►Magnets are composed of north and south pole pairs.
►B-field lines go from the north to the south poles.
N S
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Principle #1►Current in a conductor results in a magnetic
field around the conductor. Use the right-hand rule to determine the field direction.
Bi
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Principle #2►Moving a conductor in a magnetic field
induces a voltage across the conductor according to
S
B
N
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Motion of a Coil in a B-Field
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Commutation
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Motion of a Coil in a B-Field
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Motion of a Coil (cont.)
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Commutation
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Commutation (cont.)
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Commutation: Multiple Coils
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Principle #3►Passing a current through a conductor in a
magnetic field will result in a force acting on the conductor according to
S N
B
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SVapp
+-
F
i N
Step 1: Conductor initially at rest. Apply voltage; produces current; produces downward force; conductor accelerates downward; sees non-zero downward velocity.
v
B
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SVapp
+-
F
iN
Step 2: Conductor moving downward; produces voltage in conductor; superimposes with applied voltage; reduces effective voltage; reduces current; force reduced, still accelerating.
vVback
+-
B
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S
Vapp
+-
N
Step 3: Conductor downward velocity produces Vback equal to Vapp; zero current flowing in conductor; zero force; constant velocity.
vVback
+-
B
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How does a DC Motor work?
Wire length vector, dL
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Cross-section of DC motor
NN S
Soft Iron Core (Rotor)
Permanent Magnet (Stator)
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Cross-section of DC motor
Rotor supported on bearings (free to rotate)
NN SX
Generating ____ torque
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Cross-section of DC motor
NN SX
Still generating _____ torque
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Cross-section of DC motor
Rotation past 90 degrees:
NN SX
Now generating ___ torque!
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Cross-section of DC motor
NN S
X
_____________ of current flow after 90 degrees(the current switching process is called ___________ )
Now generating ____ torque!
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2 Commutator Bars
NN S
XDC
050
100
0 90 180 270 360
Angular Position
Torq
ue
Brushes; fixed
Two segment commutation on rotor
%Torque vs.Angular Position
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4 Commutator Bars
NN S
DC
0
50
100
0 90 180 270 360Angular Position
Torq
ue
Four segment commutation on rotor
%Torque vs.Angular Position
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24 Commutator Bars
NN S
DC
050
100
0 90 180 270 360
Angular Position
Torq
ue
Sixteen segment commutation on rotor
%Torque vs.Angular Position
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How does a DC Generator work?
Wire length vector, dL
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DC Motors & Generator
►Note that a DC motor always begins to act like a generator once the rotor wires start to move through the magnetic field
the induced “back EMF” is ___________ to angular velocity“back EMF” generates a current which _______ the applied current, reduces the force (torque) output of the motor
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Circuit Model for Permanent Magnet DC Motor
Va
+
-
ia
Vb
+Ra
-
Va= applied armature voltage Vb= back EMF
Ra= armature resistance ia= armature current
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PMDC Motor Steady-State Equations
from circuit
from dV= B v dL and v = rω
from df = ia dL X B and τ = rf
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PMDC Motor Steady-State Equations
►For a given motor, Ra, Ka, and Kb are constants
►Armature voltage Va, speed ω, and output torque τ are related by the 3 equations
►____________________________________
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PMDC Motor Equation Part #3
→stallτ
Torque, τ
Speed, ω
ωNL=“no-load” speed (ia=0)At any point on load curve,
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Number Assignments - Exercise #1
Student Group Speed (RPM)
Speed (rad/sec)
Student Group
Speed (RPM)
Speed (rad/sec)
#1 250 26 #5 1250 131
#2 500 52 #6 1500 157
#3 750 79 #7 1750 183
#4 1000 105 #8 2000 209
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In-Class Exercise #1Va = 48 voltsKa = 0.17 N-m/ampKb = 0.17 volt/rad/sRa = 0.9 ohms
A small DC motor has these parameter constants
Determine the output torque, τa, for the speed assigned to your group1) find back-EMF, Vb for your speed2) find current, ia for your speed3) find torque, τa for your speed
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Plot for In-Class Exercise #1
0
1
2
3
4
5
6
7
8
9
10To
rque
, N-m
0 500 1000 1500 2000 2500 3000Speed, RPM
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Manufacturer’s Data
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2nd In-Class Exercise
Va = ? voltsKa = 3.60 oz-in/ampKb = 2.67 volt/KRPMRa = 50 ohms
On a single graph, we will plot the torque vs. speed relationship for different input voltages -
24, 18, 12, 6 VDC
A small DC motor has these parameter constants
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Number Assignments - Exercise #2
Group Va, volts Group
#1 24 VDC #5
#2 18 VDC #6
#3 12 VDC #7
#4 6 VDC #8
Both1000and3000RPM
Both5000and7000RPM
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In-Class Exercise #2
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 1000 2000 3000 4000 5000 6000 7000 8000 9000Speed, RPM
Torq
ue, o
z-in
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In-Class Exercise - Solution
0.6
0.8
1.0
Torq
ue, o
z-in
6 volts12 volts18 volts24 volts
2.0
1.8
1.6
1.4
1.2
0.4
0.2
0.00 1000 2000 3000 4000 5000 6000 7000
Speed, RPM
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In-Class Exercise - Solution
0.6
0.8
1.0
Torq
ue, o
z-in
2.0
1.8
1.6
1.4
1.2
0.4
0.2
0.00 1000 2000 3000 4000 5000 6000 7000
Speed, RPM
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PMDC Motor Equation Part #2
baaa ViRV += ωbb kV = aaik=τ
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PMDC Motor Equation Part #2b
τω+= 2aaaa iRiV
Electrical Power = Power Dissipated + Mechanical Power (Input) (as heat) (useful output)
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Circuit Model for Permanent Magnet DC Generator
DC Motor/Generator
Vgen
+
-
ia
Vb
+Ra
Rexternal-
Vgen= generated armature voltage Vb= back EMF
Ra= armature resistance ia= armature current
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PMDC Generator Equations
baagen ViRV =+ ωbb kV = aaik=τ
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DC Motor CommutationDC Motor Commutation
►DC motors require periodic switching of currents to maintain rotation (“commutation”)
conventional DC motors use brushes to provide commutation, but"brushless" DC motors which use electronic commutation have been developed.
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DC Brushed Motor AdvantagesDC Brushed Motor Advantages
►Simplicity of operation, requiring only a voltage source, power op-amp, and analog control input for variable speed operation.
►Torque ripple can be easily minimizedthrough design variations
►Dynamic braking capability without additional power input
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DC Brushed Motor DisadvantagesDC Brushed Motor Disadvantages
► The brushes wear, the wear producing small particles which can affect the cleanliness of surrounding operations.
►High current through the brushes can cause them to burn out rapidly
►Heat is generated in the rotor windings which is primarily conducted away through the rotor shaft
► Small sparks are generated at the brush/rotor interface
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DC Brushless MotorDC Brushless Motor
►The magnetic field in the rotor is provided by permanent magnets on the _____
►Hall effect sensors (or resolver output) are used to signal a motor driver when to switch the current in the ______________
►Motor driver depends on the controller to set desired torque output
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DC Brushless Motor
Wound Wire Stator
Permanent Magnet Rotor
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DC Brushless Motor AdvantagesDC Brushless Motor Advantages
►No appreciable heat is generated in the rotor and hence the heat conducted to the shaft is minimized.
►Due to the lack of brushes, motors can be operated at high torque and zero rpm indefinitelyas long as the winding temperature does not exceed the limit.
►No brushes to wear out or contaminate the surroundings
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DC Brushless Motor Disadvantages
DC Brushless Motor Disadvantages
► Torque ripple is hard to minimize by design►Motor operation requires the purchase of an
electronic motor driver► Rotor magnets can become demagnetized in high
current or temperature environments►Most motor drivers brake DC brushless motors by
applying reverse current, in which almost as much power is expended to stop the motor as was required to start it moving
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Experimental Results #1
0
1
2
3
4
5
6
7
8
0 100 200 300 400 500Speed, rad/sec
Torq
ue, N
-m
Va = 40 voltsVa = 60 voltsVa = 80 voltsVa = 100 volts
Find the motor constants:kb, ka, Ra
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DC Tachometer Equations
Mechanical construction of a DC tachometer is essentially identical to DC motor
( )
0ik
VkV
0VVR1i
aa
abb
baa
a
==
==
=−=
τ
ω
High impedance load,No current
Output voltage proportional toangular velocity, ω
No current
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DC Motor - Magnetic Field Generation
►Magnetic field on the stator can be generated two ways
with a permanent magnet (PM)electro-magnetically with wound coils
►Wound DC motors►Series wound►Shunt wound►Compound wound ( series and shunt windings)
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Series Wound DC Motor
Vin
+
-
if = ia
Vb
+Rf Ra
-
Vin= input voltage Vb= back EMF
Ra= armature resistance ia= armature current
if = field currentRf = field resistance
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Series Wound DC Motor
►Large starting torque available►Rf is small
a few turns of large gage wire are used
Torque
Speed
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Shunt Wound DC Motor
if + ia
Vin
+
-
Rf
ia
Vb
+Ra
if-
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Shunt Wound DC Motor
►Used for both fixed & variable speeds►Rf is large
several turns of small gage wire are used
Torque
Speed
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Wound Motor Speed Control
►Change Vin
increase or reduce speed
►Increase field resistancereduces if → reduces Ka and Kb
►Increase armature resistancereduces Vb → reduce ω
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Compound Wound DC Motor
Vin
+
-Rf2
if1 ia
Vb
+Rf1 Ra
if2-
Has both a series and a shunt wound field
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Separately Excited DC Motor
Vb
+
-
Vin
+
-
ia
ifVf
-
+Ra
Acts like a permanent magnet DC motor(if a constant field excitation is used)