# DC Machine.

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DC Machine

Content Introduction Elementary DC machine
Voltage and Torque Equations Basic Type DC Machines Dynamics characteristics of Magnet Permanent and Shunt DC Motor

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.

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

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

Open circuit voltage

DC Machine with paralel winding
out A and a rotor coil

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

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

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

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

Shunt Characteristic

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

Series Characteristic
Torque and speed characteristics

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

Starting characteristics of permanent magnet DC motor
Direct on line starting for small power, Current starting limitation in large hp motor

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 Solving field voltage equation and armature voltage equation:

Solving for dωr /dt : State equation in matrix (vector matrix) :

Permanent Magnet DC Motor

System Equation : x = state vector u = input vector

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

Finally ,

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.

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

For step voltage Inverse Laplace

Using euler equation : Substituting parameter :

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

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

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