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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 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**

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 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 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 1-5 ( Urut 1 - 20 ) 6-10 ( Urut 21 – 40) 11-15 ( Urut 41 – 60)**

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**Electrical Motor Development**

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

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