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DC Machine 1

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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 2

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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. 3

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Elementary of DC Machine Stator coil as field winding source of flux Rotor coil as armature 4

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Voltage Equation Flux linkage : 5 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 6

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A and a rotor coil DC Machine with paralel winding 7 in out

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Constant flux is established by magnet permanent Small dc motor with low power control application 8 Comutation of DC Machine with permanent magnet

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Voltage Equation Voltage field and coil winding 9 is rotor speed is referred as back emf

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Torque Equation Electromagnetic torque 10 Torque and rotor speed equation : J = inertia of the rotor (kg m 2 or Js 2 ) T L = mechanical load B m = mechanical damping ratio (Nms) T e is positive in direction of θ r and direction of T L opposes of T e

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Basic Type of DC Machine (1) 11 Separate Winding Shunt DC Machine

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Shunt Characteristic 12

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Basic Type of DC Machine (2) 13 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 14 Torque and speed characteristics

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Dynamic characteristics of permanent magnet and Shunt DC Machine 15 Two modes of dynamic operation are of interesting : – Starting from stall – Changing in mechanical load Constant voltage source

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16 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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17 Dynamic performance during sudden changes in load torque. DC motor 5 hp, 240 V, 127,7 rpm load 1 kg m 2 DC motor 200 hp, 250 V, 600 rpm

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Time Block Diagram and State Equation Shunt DC motor 18 Solving field voltage equation and armature voltage equation:

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19 Solving for dω r /dt : State equation in matrix (vector matrix) :

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Permanent Magnet DC Motor 20

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21 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 (i a and ω r ) and input variables (i a and T L ). 22 Inertia time constant Second order differential equation in term of ωr: Coefficient of dumping ratio

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23 Finally,

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DC shunt Motor Constant Torque 24 Parameter : Vt (rated)= 120 V ; Ia (rated) = 10 A ; n = 1200 rpm ; If = 1,6 A Ra = 0.5 Ω La = 0.01H Rf = 75 Ω Lf = 0.02 H Mechanical Load = 50 N Typical loads include belt conveyors with a fixed loading, extruders, hoists, and mine lifts.

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Laplace Transform 26 Parameter dc permanent magnet : 6 V, ra = 7 Ω, LAA = 120 mH kT = 2 oz.in/A, J = 150 µoz.in.s 2. No load rpm = 3350 rpm I no load = 0,15 A

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28 Inverse Laplace For step voltage

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29 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) 30

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Electrical Motor Development Basic Priciples of Electrical Machine Analysis DC Machine Reference Frame Theory Induction Machine Synchronous Machine BLDC Machine 31

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