DC Machine 1. Content Introduction Elementary DC machine Voltage and Torque Equations Basic Type DC...

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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

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