DC Machine
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Content
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Introduction
Elementary DC machine
Voltage and Torque Equations
Basic Type DC Machines
Dynamics characteristics of Magnet
Permanent and Shunt DC Motor
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Introduction
• DC machines application not widely used
• DC generator is replaced by rectifier
• DC Motor is still used in lower power :
– Shunt DC Motor
– Permanent Magnet DC Motor
• Brushless DC motor becomes popular and
widely used in electric vehicle.
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Elementary of DC Machine
• Stator coil as field winding  source of flux
• Rotor coil as armature
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Voltage Equation
Voltage equation for field winding and rotor coil
Flux linkage :
Mutual inductance winding between field winding and armature as a function of Θr :
Θr = 0, π, 2 π, ........
L= Constant
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Open circuit voltage
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DC Machine with paralel winding
in
out
A and a rotor coil
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Comutation of DC Machine with permanent magnet
• Constant flux is established by magnet permanent
• Small dc motor with low power control application
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Voltage Equation
• Voltage field and coil winding
is rotor speed
is referred as back emf
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Torque Equation
• Electromagnetic torque
• Torque and rotor speed equation :
J
= inertia of the rotor (kg m2 or Js2 )
TL = mechanical load
Bm = mechanical damping ratio (Nms)
Te is positive in direction of θr and direction of TL opposes of Te
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Basic Type of DC Machine (1)
• Separate Winding
• Shunt DC Machine
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Shunt Characteristic
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Basic Type of DC Machine (2)
• Series Winding
• Application : traction motor for train or bus, hoists and crane
• High starting torque with mechanical load at normal operation
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Series Characteristic
Torque and speed characteristics
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Dynamic characteristics of permanent
magnet and Shunt DC Machine
• Two modes of dynamic operation are of
interesting :
– Starting from stall
– Changing in mechanical load
Constant voltage source
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Starting characteristics of
permanent magnet DC motor
Direct on line starting for small power,
Current starting limitation in large hp motor
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Dynamic performance during
sudden changes in load torque.
DC motor 5 hp , 240 V, 127,7 rpm load 1 kg m2
DC motor 200 hp, 250 V, 600 rpm
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Time Block Diagram and State Equation
• Shunt DC motor
Solving field voltage equation and armature voltage equation:
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Solving for dωr /dt :
State equation in matrix (vector matrix) :
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• Permanent Magnet DC Motor
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System Equation :
x = state vector
u = input vector
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• Example For control Design  to express transfer functions between state
and input variables.
• To derive transfer function between state variables (ia and ωr) and input
variables (ia and TL).
Inertia time constant
Second order differential equation in term of ωr:
Coefficient of dumping ratio
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Finally ,
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DC shunt Motor Constant Torque
Parameter :
Vt (rated)= 120 V ; Ia (rated) = 10 A ; n = 1200 rpm ; If = 1,6 A
Ra = 0.5 Ω La = 0.01H
Typical loads include belt conveyors with a
Rf = 75 Ω Lf = 0.02 H
fixed loading, extruders, hoists, and mine lifts.
Mechanical Load = 50 N
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Ia
250
200
150
100
50
0
n
1000
800
600
400
200
0
-200
Tem_DC4
200
150
100
50
0
0
0.2
0.4
0.6
0.8
1
Time (s)
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Laplace Transform
Parameter dc permanent magnet : 6 V, ra = 7 Ω, LAA = 120 mH
kT = 2 oz.in/A, J = 150 µoz.in.s2 . No load rpm = 3350 rpm
I no load = 0,15 A
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For step voltage
Inverse Laplace
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Using euler equation :
Substituting parameter :
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PR
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1-5
6-10
11-15
16-19
( Urut 1 - 20 )
( Urut 21 – 40)
( Urut 41 – 60)
(Urut 61 – 80)
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Electrical Motor Development
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Basic Priciples of Electrical Machine Analysis
DC Machine
Reference Frame Theory
Induction Machine
Synchronous Machine
BLDC Machine
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