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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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Electrical Motor Development

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

Type of Electric Motors

Classification of MotorsElectric Motors

Alternating Current (AC) Motors

Direct Current (DC) Motors

Synchronous Induction

Three-PhaseSingle-Phase

Self ExcitedSeparately Excited

Series ShuntCompound

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Introduction

Three types of Motor LoadMotor loads Description Examples

Constant torque loads

Output power varies but torque is constant

Conveyors, rotary kilns, constant-displacement pumps

Variable torque loads

Torque varies with square of operation speed

Centrifugal pumps, fans

Constant power loads

Torque changes inversely with speed

Machine tools

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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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Type of DC Electric Motors

• Separately excited DC motor: field current supplied from a separate force

• Self-excited DC motor: shunt motorSpeed constant independent of load up to certain torque

Speed control: insert resistance in armature or field current

DC motors

(Rodwell Int. Corporation, 1999)

• Field winding parallel with armature winding

• Current = field current + armature current

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Type of DC Electric Motors

Self-excited DC motor: series motorDC motors

(Rodwell Int. Corporation, 1999)

• Field winding in series with armature winding

• Field current = armature current

• Speed restricted to 5000 RPM

• Avoid running with no load: speed uncontrolled

Suited for high starting torque: cranes, hoists

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Type of DC Electric Motors

DC compound motorDC motors

Field winding in series and parallel with armature winding

Good torque and stable speed

Higher % compound in series = high starting torque

Suited for high starting torque if high % compounding: cranes, hoists

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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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050

100150

200250

Ia

0-200

200400600800

1000

n

0 0.2 0.4 0.6 0.8 1Time (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

• 9.3-9.5• 9.13-9.14• 9.19-9.21