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DC Machine
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Content
• 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
Flux linkage :
Voltage equation for field winding and rotor coil
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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A and a rotor coil
DC Machine with paralel winding
in
out
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• Constant flux is established by magnet permanent• Small dc motor with low power control application
Comutation of DC Machine with permanent magnet
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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 loadBm = 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
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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 vectoru = 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 ARa = 0.5 Ω La = 0.01HRf = 75 Ω Lf = 0.02 HMechanical Load = 50 N
Typical loads include belt conveyors with a fixed loading, extruders, hoists, and mine lifts.
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0
50
100
150
200
250
Ia
0-200
200
400600800
1000
n
0 0.2 0.4 0.6 0.8 1
Time (s)
0
50
100
150
200
Tem_DC4
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Laplace Transform
Parameter dc permanent magnet : 6 V, ra = 7 Ω, LAA = 120 mHkT = 2 oz.in/A, J = 150 µoz.in.s2 . No load rpm = 3350 rpm I no load = 0,15 A
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Inverse Laplace
For step voltage
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Using euler equation :
Substituting parameter :
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PR
• 1-5 ( Urut 1 - 20 )• 6-10 ( Urut 21 – 40)• 11-15 ( Urut 41 – 60)• 16-19 (Urut 61 – 80)
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Electrical Motor Development
• Basic Priciples of Electrical Machine Analysis• DC Machine• Reference Frame Theory• Induction Machine• Synchronous Machine• BLDC Machine