48571_EM_DCM_v1_1

DC MachinesDC Machines

Prof. J.G. ZhuProf. J.G. Zhu

School of Electrical, Mechanical and School of Electrical, Mechanical and MechatronicMechatronic SystemsSystemsFaculty of Engineering and Information TechnologyFaculty of Engineering and Information Technology

University of Technology, SydneyUniversity of Technology, Sydney

48571 Electrical Machines48571 Electrical Machines ContentsContents

Introduction Principle Elemental DC Machines Structure Name Plate Magnetic Fields EMF and Torque Steady State Equivalent Circuit DC Generator Performance

Establishment of terminal voltage External characteristics and voltage regulation Efficiency

DC Motor Performance Torque/speed curve Efficiency Speed control

IntroductionIntroduction

The DC machine is an electromechanical device that converts mechanical energy into DC electrical energy (generator) or the other way around as in the case of a motor.

The DC machine is the first type of electrical machine employed for practical applications. DC generators are commonly used for battery charging, electrolysis, synchronous machine excitation and welding, etc.

DC motors have excellent drive performance for wide speed range with convenient, smooth, and accurate speed control, and high starting, braking, and over load capability, and therefore,are suitable for electrical drive systems with requirements for wide speed range and high precision and dynamic performance, such as steel rolling, electrical propulsion, crane, textile andcold machining, etc.

With the fast development of power electronics and control, DC generators are being replaced by rectifiers, and motors by AC motor drive systems, but still there are a number of applications.

PrinciplePrinciple Elementary DC machineElementary DC machine

The fundamental principle is based on the Faradays law, and the electromagnetic force/torque produced by current carrying conductors in a magnetic field.

Diagram on the right shows the structure of an elementary DC machine, which consists of a pair of electromagnets on the stator, and a rotor also known as armature with slots to hold coils.

MohammadHighlight

PrinciplePrinciple Elementary DC generatorElementary DC generator

Consider a coil placed in a uniform magnetic field inclined at an angle . The magnetic flux linkage of the coil varies with its angular position by

where N is the number of turns, A the cross sectional area, B the flux density, and =AB the flux linking the coil.

When the coil is rotated at an angular speed r, an electromotive force (emf) is induced. By Faradays law, this emfcan be expressed as

where

dtd

r = and 0)( += tt r

( ) sinsin == NNABt

( ) ( )0cos)( +== tNdttdte rr

PrinciplePrinciple Elementary DC generatorElementary DC generator

In order to generate a DC emf, a device known as commutator(rectifier by mechanical means) can be used. The average value of the DC emf can be calculated as

When there are a great number of coils embedded in the slots around the rotor or armature surface, a stable DC emf can be obtained.

( )[ ]( ) =+=

+= NtN

tdtNE

rrr

rrrav

2sin1

cos1

2

230

23

2 0

PrinciplePrinciple Elementary DC motorElementary DC motor

When the elementary DC generator is operated inversely, i.e. supplied by a DC current, a unidirectional torque can be produced with the help of the commutator.

If the DC current is ia, the average torque can be calculated by dividing the electromagnetic power by the speed, i.e.

ar

aavav iN

iET == 2

DC Machine StructureDC Machine Structure Large DC machineLarge DC machine

Stator Poles

Inter PolesArmature Slots and Winding

Shaft

Bearing

Stator Case

Commutator

Brushes

DC Machine StructureDC Machine Structure Small DC machineSmall DC machine

DC Machine StructureDC Machine Structure Permanent Magnet DC machinePermanent Magnet DC machine

DC Machine StructureDC Machine Structure Cross sectional illustrationCross sectional illustration

DC Machine StructureDC Machine Structure StatorStator

The DC machine housing supports the stator, brushes, and bearings.

The stator contains main poles excited by DC current to produce the magnetic fields. These poles are mounted on an iron core that provides a closed magnetic circuit.

On the surface of main poles, there are slots to hold the compensation windings, which are connect in series with the armature winding to reduce the effect of armature reaction.

In the middle between main poles or the neutral zone, commutating/inter poles, which are connected in series with the armature winding, are placed to reduce sparks on the commutator.

MohammadHighlight

DC Machine StructureDC Machine Structure Rotor or armatureRotor or armature

The rotor has a ring-shaped laminated iron core with slots.

Coils with multiple turns are placed in the slots. The distance between the coil sides is about 180o electrical.

The coils are connected in series through the commutator segments.

DC Machine StructureDC Machine Structure CommutatorCommutator and brushesand brushes

The commutator consists of insulated copper segments mounted on an insulated tube. The ends of each coil are connected to two commutatorsegments.

Brushes of positive and negative polarities are pressed to the commutator to permit current flow.

These brushes are placed in the neutral zone, where the magnetic field and hence the induce emf are close to zero, to reduce arcing.

The commutator and brushes switch the current from one rotor coil to the adjacent coil.

|

Shaft

Brush

Coppersegment

InsulationRotor

Winding

N S

Ir_dcIr_dc/2Rotation

Ir_dc/2

Ir_dc

12

3

45

6

7

8

Polewinding

DC Machine StructureDC Machine Structure Armature windingsArmature windings

According to the pattern how the coils are connected, the armature windings can be classified as (a) Lap windingLap winding and (b) Wave windingWave winding.

These two different connections result in different numbers of the parallel paths of the armature winding between the positive and negative brushes, aa.


Lap winding: a = pLap winding: a = p, where p is the number of poles.

MohammadHighlight

MohammadHighlight

MohammadHighlight


Wave winding: a = 2Wave winding: a = 2

DC Machine Name PlateDC Machine Name Plate Rated quantities Rated quantities

Rated Power Prated (W or kW) The output power under the rated operating conditions. For a generator, it is the electrical power output at the terminals, whereas for a motor, the mechanical power output at the shaft.

Rated voltage Vrated (V) The voltage at the electrical terminals when the machine is operated under the rated conditions.

Rated current Irated (A) The current at the electrical terminals when the machine is run with rated voltage and output power.

Rated speed rrated (rev/min) The rotor speed when the machine is operated with rated voltage and output power.

Rated excitation current Ifrated (A) The field winding current when the machine is run with rated voltage, current and speed.

Rated efficiency rated (%) The percentage ratio between the output and input power when the machine is in rated conditions.

Magnetic FieldsMagnetic Fields Stator, rotor and combined field distribution Stator, rotor and combined field distribution

Stator field Armature field Resultant field

The stator and armature fields in a DC machine are perpendicular to each other, because of the effect of commutator.

The resultant field is distorted by the armature field with the neutral zone shifts towards the rotating direction in the case neutral zone shifts towards the rotating direction in the case of a generator, or away from the rotating direction in a motorof a generator, or away from the rotating direction in a motor.

Magnetic FieldsMagnetic Fields Armature field in Armature field in airgapairgap

Cut and unroll of a 2 pole DCM Armature mmf

MohammadHighlight

Magnetic FieldsMagnetic Fields Resultant Resultant airgapairgap field and armature reaction field and armature reaction

Stator airgap field and mmf Resultant field

Armature reactionArmature reaction: Shift the neutral zone for an

angle Reduce the total flux

because of the magnetic saturation

Magnetic FieldsMagnetic Fields Armature field compensation and commutationArmature field compensation and commutation

The armature reaction can cause serious commutation difficulty heavy sparks.

Three methods to improve commutation: (a) Interpoles, (b) Compensation coils, and (c) Shift brushes.

EMF & TorqueEMF & Torque Assume a real DC machine has p poles, Ca conductors in the

armature, and a parallel paths between the positive and negative brushes. The total number of coils, which has N turns each, is Ca/(2N), and the number of coils in each path is Ca/(2Na).

Previously, it was calculated that the induced emf and electromagnetic torque in an elementary single coil two pole elementary single coil two pole DC machineDC machine are

= NE rav 2

ar

aavav iN

iET == 2and

The real machine however has p poles. Once the coil rotates for a complete cycle of NSN poles, or 2 electrical radians, mechanically it only rotates for 4/p mechanical radians, or =(p/2)m, and r=dm/dt, where m is the angular position in mechanical radians. Therefore, we obtain

)(2

)( 0mrtpt += and rpdt

d 2

=

EMF & TorqueEMF & Torque The induced emf and electromagnetic torque of a single coil in single coil in

the real DC machine of p polesthe real DC machine of p poles are

where

ra

ra

coila

a apCNp

NaCE

NaCE === 222

raa KE =a

pCK aa 2=constant.

= NpE rcoil araav

coil iNpiET == and

The total armature emf and electromagnetic torque can then be calculated by multiplying the emf and torque of a single coil by the number of coils in a parallel path and the total number of coils respectively as

aa

aa

coila I

apCiNp

NCT

NCT === 222and

or and aa IKT =aa aiI = , and is known as the emf or torque

MohammadHighlight

MohammadHighlight

MohammadHighlight

MohammadSticky Notecheat sheet

MohammadHighlight

MohammadHighlight


MohammadHighlight

MohammadPencil


MohammadText BoxC=# of coils in rotorZ=# of conductors on rotorN=# of turns per coila=# of current paths in the rotor

MohammadHighlight

MohammadHighlight

MohammadHighlight

MohammadHighlight

MohammadHighlight

MohammadHighlight

Steady State Equivalent CircuitSteady State Equivalent Circuit SymbolSymbol

The DC machine symbol shown below on the right hand side resembles its cross section on the left hand side. The field winding produces a flux when excited by a DC current, and across the brushes, an emf is produced when the armature or rotor rotates.

Steady State Equivalent CircuitSteady State Equivalent Circuit Excitation connectionsExcitation connections

There are four types of connections: (a) Separate excitation, (b) Series excitation, (c) Shunt excitation, and (d) Compound excitation.

Steady State Equivalent CircuitSteady State Equivalent Circuit Separately excited DC generatorSeparately excited DC generator

Complete dynamic equivalent circuit of a separately excited DC generator

Model

dtdiLiRevv aaaaaat ==

dtdi

LiRv fffff +=

dtdJTTT rlossshaft=

Steady State Equivalent CircuitSteady State Equivalent Circuit Separately excited DC generatorSeparately excited DC generator

aaaa IREV = fff IRV = lossshaft TTT =

Corresponding to the steady state equivalent circuit of a separately excited DC generator shown below, the circuit and torque equations are:

and

Steady State Equivalent CircuitSteady State Equivalent Circuit Separately excited DC motorSeparately excited DC motor

dtdiLiRevv aaaaaat ++==

dtdi

LiRv fffff +=

dtdJTTT rshaftloss=

Complete dynamic equivalent circuit of a separately excited DC motor

Modelaaaa IREV += fff IRV = lossload TTT +=

Steady State Equivalent CircuitSteady State Equivalent Circuit Separately excited DC motorSeparately excited DC motor

Corresponding to the steady state equivalent circuit of a separately excited DC motor shown below, the circuit and torque equations are:

and

aft VVV ==

For shunt DC generator

fat III += fta III +=

For shunt DC motor

Steady State Equivalent CircuitSteady State Equivalent Circuit Shunt DC machinesShunt DC machines

aaaa IREV += fff IRV =

lossshaft TTT =and

aaaa IREV = fff IRV =

lossload TTT += andaft VVV ==

Steady State Equivalent CircuitSteady State Equivalent Circuit Series DC machinesSeries DC machines

ast VVV +=

For series DC generator

sat III == sat III ==

For series DC motor

aaaa IREV += sss IRV =

lossshaft TTT =and

aaaa IREV = sss IRV =

lossload TTT += andsat VVV =

RsRa

Vt

It

Ea Va

Is

T+Tloss

Tshaftr

Ia

Vs

Steady State Equivalent CircuitSteady State Equivalent Circuit Compound DC machinesCompound DC machines

fast VVVV =+=

For compound DC generator

fst III +=

For compound DC motor

aaaa IREV += fff IRV =

lossshaft TTT =and lossload TTT += and

sss IRV =as II =

fsat VVVV ==fst III =

aaaa IREV = fff IRV =sss IRV =

as II =

Steady State Equivalent CircuitSteady State Equivalent Circuit Parameter determinationParameter determination

The DC machine steady state equivalent circuit parameters to be determined are the field winding resistance, armature circuit resistance (winding resistance plus brush-commutator contact resistance), and emf or torque constant.

The resistances can be measured by V/A method. It should be noted that the shunt field winding has a large resistance while the armature circuit and series field winding have small resistances. Therefore, the Ammeter should be connect in series with the shunt field winding first and then in parallel with the Voltmeter, where for the latter test, the Voltmeter should be connected in parallel with the armature circuit or series field winding and then in series with the Ammeter.

Steady State Equivalent CircuitSteady State Equivalent Circuit Parameter determinationParameter determination

The emf or torque constant can be determined by the no load test in the following steps: Set up and connect the DC

machine as a separately excited generator with the armature open circuited;

Drive it at the rated speed; Adjust If from zero to the rated

value, and measure the terminal voltage or emf;

Ka = Ea/r Ea(If) is known as the

magnetisation curve When magnetic saturation is

considered, Ka is not a constant.

DC Generator PerformanceDC Generator Performance Shunt generator self excitationShunt generator self excitation

The conditions for voltagebuild-up: There must be residual

magnetism If not, use a battery to given an initial excitation;

The connection of the field circuit to the armature circuit must be correct such that the excitation field aids the residual magnetism If not, swap the terminals;

The Re + Rf line must be lower than the airgap line such that the rated voltage can be established.

aaaat IREVV == Theoretical

DC Generator PerformanceDC Generator Performance External characteristicExternal characteristic

The relationship between the terminal voltage and current, Vt vs. It, of a DC generator excited by the rated field current and driven at the rated speed is defined as the external characteristic.

It can be determined experimentally by measuring the terminal voltage at different load currents when the generator is operated at the defined condition.

It can also be calculated by the equivalent circuit model. For example, for a separately excited generator, it can be calculated by

The discrepancy between the experimental and theoretical results is due to the armature reaction.

rratedr =fratedf II =

whenand

DC Generator PerformanceDC Generator Performance External characteristicExternal characteristic

DC Generator PerformanceDC Generator Performance Voltage regulationVoltage regulation

The voltage regulation of a DC generator is defined as the percentage variation of the terminal voltage from no load to full load, i.e.

For a separately excited DC generator, for example, the voltage regulation can be calculated as

ratedt

ratedta

ratedt

FLtNLt

VVE

VVV

VR,

,

,

,, ==

ratedL

a

ratedt

ratedaa

RR

VIR

VR,,

, == For a shunt DC generator, the voltage

regulation can be calculated as( )

++=

+==

efratedLa

ratedt

fratedta

ratedt

ratedaa

RRRR

VIIR

VIR

VR

11 ,

,

,

,

,

DC Generator PerformanceDC Generator Performance EfficiencyEfficiency

The efficiency of a DC generator is defined as the percent ratiobetween the output power and input power, and can be expressed as

where Tloss is the retarding torque corresponding to the total of core and mechanical power losses, which is approximately equal to the no load power.

rlossttssaaff

tt

in

out

TIVIVRIIVIV

PP

++++== 2

rlossaaaaff

aa

rlossff

aa

rshaftff

tt

TIVRIIVIV

TTIVIV

TIVIV

+++=++=+= 2)(

For the separately excited DC generator, for example, one has

DC Motor PerformanceDC Motor Performance EfficiencyEfficiency

The efficiency of a DC motor is defined as the percent ratio between the output power and input power, and can be expressed as

ffaa

rloss

ffaa

rout

in

out

IVIVTT

IVIVT

PP

+=+==

)(

where Tloss is the retarding torque corresponding to the total of core and mechanical power losses, which is approximately equal to the no load power, and Tout = TL.

DC Motor PerformanceDC Motor Performance Torque/Speed curvesTorque/Speed curves

The external characteristic of a DC motor is the torque/speed curve.

For a separately excitedseparately excited DC motor, one has

== a

aaa

a

ar K

IRVKE

( ) TKR

KV

a

a

a

ar 2=or

Because of the armature reaction, at heavy load the speed increases.


For a shuntshunt DC motor, the torque/speed curve can be expressed same as the separately excited motor, i.e.

( ) TKR

KV

a

a

a

tr 2=

or

The operating point of seriesseries DC motors are generally designed in the linear region, i.e. = KsIs, where Is = Ia, and thus

2asaaa IKKIKT ==

saa KK

TI =

asa

asat

a

asat

a

ar IKK

IRRVK

IRRVKE )()( +=

+==Therefore, we have

orsa

sa

sa

tr KK

RRTKK

V +=


( )2

2

sa

tsa

RRVKKT +=

sa

sar KK

RR +=

The torque/speed curve of a typical seriesseries DC motor is plotted on the right hand side. Because the torque of a series DC motor is proportional to the square of armature current, for the same value of armature current, the series motor can produce much higher torque, and as the load torque increase, the speed drops very fast. Therefore, the series DC motors are suitable for electrical vehicle drive. It should be noted that series DC motors must not be operated at no load.

As the armature current changes its direction, the magnetic field alters its direction accordingly, and hence series motors can also be operated by AC current universal motorsuniversal motors.


In a compound DC motor, the series excitation is employed to compensate the field weakening effect of armature reaction such that the total flux remains constant. The torque/speed curve can be derived as

RsRa

Vt

It

Ea Va

Is

TL+Tloss

Tr

Ia

VsVf

If

Rf

( ) ( )( )( ) TK

RRKV

KIRRV

KE

a

sa

a

t

sfa

asat

sfa

ar

+=

++=+=

DC Motor PerformanceDC Motor Performance Speed controlSpeed control

There are two methods to control the speed of a separately excited separately excited DC motorDC motor: (a) Varying armature terminal voltage, and (b) Flux weakening.

( ) TKR

KV

a

a

a

ar 2=

When the armature voltage varies, the no load speed varies accordingly, but the gradient is kept constant. Therefore, the torque/speed curves are in parallel. Note that Va must < Va,rated.

When Vf is reduced while Va = Va,rated, both the no load speed and gradient increase. For a normal load torque, the operating speed increases.


There are also two methods to control the speed of a shunt DC motorshunt DC motor: (a) Varying armature circuit resistance, and (b) Flux weakening, while the terminal voltage is kept constant.

( ) TKRR

KV

a

eaa

a

ar 2

+=

When the armature resistance increases, the no load speed does not vary, but the gradient increases. Therefore, for a given load, the speed reduces.

When the field circuit resistance increases, both the no load speed and gradient increase. For a normal load torque, the operating speed increases.


There are also two method to control the speed of a series DC motorseries DC motor: (a) Varying the terminal voltage, and (b) Varying the armature circuit resistance.

sa

easa

sa

tr KK

RRRTKK

V ++=

T

r

0

( )2

2

sa

tsa

RRVKKT +=

sa

sar KK

RR +=

TL

sa

easar KK

RRR ++=

( )2

2

easa

tsa

RRRVKKT ++=

PP1

When reducing the terminal voltage below the rated value, the intersection of the torque/speed curve and the T axis moves towards the origin and the operating speed is reduced.

When the armature circuit resistance is increased while the terminal voltage is kept constant, the lower bound of the torque/speed curve moves down, and the operating speed is reduced.

T

r

0

sa

sar KK

RR +=

TL

P1P

( )221

sa

tsa

RRVKKT +=

( )2

22

sa

tsa

RRVKKT +=

Vt1 > Vt2


Since the seriesseries excitation is used to compensate the field weakening effect of the armature reaction, the torque/speed curves of acompound DC motorcompound DC motor arethe same as those of a shuntmotor, and therefore the speedcontrol methods are the same asthose for a shunt DC motor.

The speed control methods areoften employed to limit thestarting current of DC motors. The diagram on the right hand sideillustrates the three step starting of a shunt DC motor to limit the armature current below I2=T2/(Ka). T

r

0

ro

Rea = 0

Rea = R1+R2+R3

P

T1 T2

Rea = R1Rea = R1+R2

DC Motor PerformanceDC Motor Performance Speed control systemsSpeed control systems

Multi stage starting (DCM_MultiStage_Starting.mdl). One quadrant chopper 5HP DC motor drive system

(power_dcdrive.mdl, power_dcdrive_disc.mdl, dc5_example.mdl). Two quadrant three phase rectifier 200HP DC motor drive system

(dc3_example.mdl) Note that Ka = LafIf, where Laf is the mutual inductance between

field and armature windings (a parameter used in the Simulink DC machine model).

More examples can be found in Matlab/Simulink help Contents and Demo.

DC Motor PerformanceDC Motor Performance Speed control systemsSpeed control systems

Example: One quadrant chopper 5HP DC motor drive system (power_dcdrive.mdl).

Specified speed r = 120 rad/s; TL = 5 Nm; In the PI controller, Ia is capped at 30 A to avoid overheating.

If = Vf/Rf = 1 A, and in steady state, Ia = (TL+Tloss)/(Ka) = (5+0.02x120)/1.23 = 6.016(A), and Va= Kar + RaIa = 1.23x120 + 0.5x6.016 = 150.608 (V)

ReadingReadingTextbook:

Chapter 4. Introduction to Rotating Machines Chapter 7. DC Machines Exercises: Textbook Section 7.12, Problems 7.1 7.27

Lecture notes at UTSOnline

Date post:	25-Nov-2015
Category:	Documents
Upload:	d00md00m
View:	9 times
Download:	1 times

48571_EM_DCM_v1_1

Documents