Ch9 DC Motors

8/8/2019 Ch9 DC Motors

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Electric Machines & Power Electronics

ENEE4301

Chapter 9: DC Motors (only)

DC motors are driven from a dc power supply. Unless otherwise specified, the input voltage to a dc

motor is assumed constant, because it help simplifies

the analysis and the comparison between different types of

motors.

There are five major types of dc motors in general use:

1) The separately excited dc motor

2) The shunt dc motor

3) The permanent-magnet dc motor

4) The series dc motor

5) The compounded dc motor


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The equivalent circuit of a dc motor

Below is the equivalent circuit of a dc motor.

The armature (rotor) circuit is represented by:

an ideal voltage source EA

a resistorRA

(including rotor coils, interpoles and compensating

windings, if present)

a Thevenin equivalent of

the entire rotor structure


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The brush voltage drop is represented by asmall battery Vbrush opposing the direction of

current flow in the machine.

The field coils (producing the magnetic flux in the

motor) are represented by:- an inductorLF

- a resistorRF

Note: resistorRadj is an external variableresistorused to control the amount of current

in the field circuit.


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Some variation and simplifications can be made:

Vbrush may be left out (Vbrush


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The internal generated voltage is given by:EA = KJ[

and the torque induced is

Xind = KJIA

The tools necessary to analyse the behaviourand performance of a dc motorare:

1) Equations for EA and Xind

2) Kirchoffs voltage law (KVL) equation of thearmature circuit

3) The machines magnetisation curve


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The magnetisation curve of a dc machine

EA is directly proportional to the flux in the machine andthe speed of rotation of the machine.

How is the internal generated voltage related to the field

current in the machine?

The field current IF

produces a field magnetomotive force

(mmf) given by F= NFIF.

This mmf produces a flux in the machine in

accordance with its magnetisation curve shown below.

The magnetisation curveofa ferromagnetic

material (Jvs. F)


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,Since, mmfwFI and JfluxwAE , it is c sto ary to presentthe magnetisation curve as a p ot o

EA vs IF for a given speed [0. ( ig re be ow

EA [= KJ[]

IF [=VF/RF]

Magnetisation curve ofa dc machine

expressed as a plot ofEA vs IF for a fixed

speed [0


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Separately excited and shunt dc motors

A separately exciteddc motoris a motorwhose field circuit is supplied from a separate

constant-voltage power supply.

adjF

F

F

RR

VI

!

The equivalent circuit ofa separately excited dc motor.


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Separately excited and shunt dc motors

While a shunt dc motoris a motor whose fieldcircuit gets its power directly across the armature

terminals of the motor

The equivalent circuit ofa shunt dc motor.


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When the supply voltage to a motor is assumedconstant, there is no practical difference in

behaviourbetween these two motors.

Hence, unless otherwise specified, whenever the

behaviour of a shunt motor is described, theseparately excited motor is included too.

The KVL equation for the armature circuit of

these motors is: VT = EA + IARA


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The terminal characteristic of a shunt dc motor

The terminal characteristic of a machine is aplot of the machines output quantities versus

each other.

The terminal characteristic ofa motoris A plot

of its output torque vs. Speed Howdoes a shuntdcmotor respondto a load?


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If the load on th shaft of a shunt motor is incr ased,

The output characteristic of a shunt dc motor can be derivedfrom the induced voltage and torque equations of the motor plus

the KVL.

Xload> XindMotorslows

down ([q)

EAq

= K [q

Armature current

IAo= ( VT-EAq) / RAXindo

(=KJIAo)

Finally,Xind= Xload

at a lower

mechanical

s eed [


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From KVL, AAAT RIV ! .

The induced voltage EA= KJ[, so

AATRIKV ! [

Since Xind= KJIA, current IA can be expressed as

J

X

KI

ind

A!

Combining equations (9.4) and (9.5) yields

A

ind

TRV

JJ[ !

(9.4)

(9.5)

(9.6)


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Finally, the motor speed is given by:

(9.7)

This equation is just a st aig t li e wit a egative slope.The resulting torque-speed characteristic of a shunt dc motor isshown below:

indAT

K

R

K

VX

JJ[

2!

Torque-speed

characteristic ofa shunt or

separately excited dcmotor with compensating

windings toeliminate

a matu e ea tion.


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It is important to realize that, in order for the speed of themotor to vary linearly with torque, the other terms in thisexpression must be constant as the load changes. Theterminal voltage supplied by the dc power source isassumed to be constant - if it is not constant, then thevoltage variations will affect the shape of the torque-speed

curve.

Another effect internal to the motor that can also affect theshape of the torque-speed curve is armature reaction. If amotor has armature reaction, then as its load increases,the flux-weakening effects reduce its flux. From the motorspeed equation above, the effect of reduction in flux is to

increase the motors speed at any given load over thespeed it would run at without armature reaction. Thetorque-speed characteristic of a shunt motor with armaturereaction is shown below:


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If a motor has compensating windings, there will be no fluxweakening problems and the flux in the motor will beconstant.

If a shunt dc motor has compensating windings so that flux

is constant regardless of load, and the motors speed andarmature current are known at any one value of load, thenit is possible to calculate its speed at any other value ofload, as long as the armature current at that load is knownor can be determined.

Torque-speed characteristic of

the motor with armature

reaction present.


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Therefore, if shunt otoris onnectedto load (condition

1), andthe otor s eedn1, IA1andEA1are known, hence

1

'

1nKE

AJ!

ssuming the fi ld curr nt is c nst nt and there are no

armature reaction effects, the flux will rem in c nst nt .Therefore, atan th r l ad c nditi n (condition 2):

2

'

2 nKEA J

Hence, themotor s dat condition 2can ecalculatedusing:

(9.8)

rovid dEA2is known or can b d t rmin dfrom .

nE

En

A

A!


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Example 9.1

A 50HP, 250V, 1200 r/min DC shunt motor with compensating

windings has an armature resistance (including the brushes,compensating windings, and interpoles) of 0.06 ;. Its field circuit hasa total resistance Radj + RF of 50 ;, which produces a no-load speed of1200r/min. There are 1200 turns per pole on the shunt field winding(Figure below)

(a) Find the speed of this motor when its input current is 100A.

(b) Find the speed of this motor when its input current is 200A.

(c) Find the speed of this motor when its input current is 300A.


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Speed control of shunt dc motors

Adjusting the fiel

dresistance RF

Adjusting the terminal voltage applied to the armature

Inserting a resistance in series with the armature

circuit - less common method.

iT

R

XJJ[ 2

!


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Changing the Field Resistance

1. In easing RF causes IF to de ease. oq! FTF RI

2.Decreasing IF,

de eases J-

3.Decreasing J lo e s EAinstantaneously.

[J qq KEA

4.Decreasing EA causes IA to

in ease.

AATAREVI qo!

5.Increasing IA,

in eases XindNote:IAop edominates overJq.

q!AindIJX

6.Increasing Xi dcauses Xind> Xload,hence moto speeds up ([o).

-

7. Since [o, EA in eases again. oo! J[KEA

8. IncreasingEA causes

IA tode ease . AATA REVI oq

9.

Decreasing IA causes Xi d tode ease until

Xind= Xloadat a highe speed[.qq!

AindIJX

Note: Decreasing RFreverses the whole process and [q.


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The effect of increasing the field resistance on theoutput characteristic of a shunt motor is shown

below.

(b) Over the entire range from no load to

stall conditions(a) Over the normal operating range

The effect of field resistance RF speed control on a shunt

motors torque-speed characteristics


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WARNING about field resistance speed control:

As the fluxd

ecreases, the motors:1) no-load speed increases

2) torque-speed curve slope becomes steeper

Figure on previous slide shows the terminal

characteristic of the motorover the whole full

range from no-load to stall conditions (speed = 0).

It is apparent that at very slow speed, an

increase in RFwill actuallyd

ecrease the speed

of the motor.


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This is because at very slow speeds, the increase in

IA

(due to decrease in EA) is not large enough to

compensate for decrease in Jin the Xindequation (see

step 5 in the previous table).

With Jdecrease larger than IA

increase,

Xinddecreases

and motor slows down.

Some small dc motors used for control purposes actually

operate at speeds close to stall conditions. For these

motors, an increase in field resistance might have no

effect, or it might even decrease the speed of the motor.Since the results are not predictable, field resistance

control should not be used in these types of dc motors.


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Changing the armature voltage

This method involves changing the voltageapplied to the armature circuit withoutchanging

the voltage appliedto the field.

In effect the motor must be separately excitedto

use armature voltage control.


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1. IncreasingVAcausesIAtoincrease. AAAA REVI oo!

2.IncreasingIA,

increasesXindAindIK q! JX

3.IncreasingXindcausesXind>Xload,he cemotors ee s ([o). -

4. ince[o, EAincreases. oo! JKEA

5.IncreasingEAcausesIAtodecrease .

AATA

REVI oq!

6.DecreasingIAcausesXindtodecrease until

Xind=Xloadata highers eed[.qq!

AiJX


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The effect of increasing

VA on the torque-speedcharacteristic of a separately excited motor is

shown below.

Notice that the no-load speed is shifted by this

method of speed control but the slope of thecurve remains constant.


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Insertinga resistorin series with the

armature circuit

If a resistor is inserted in series with the armature circuit (RAo), the

effect is to drastically increase the slope of the motors torque-

speed characteristic, making it operate more slowly if loaded.

The effect of armature resistance speed control on a shunt motors

torque-speed characteristics.

The insertion of a resistor is very wasteful since the losses in the

inserted resistor are very large.Hence, this method for speedcontrol is rarely used.

.

id

AT

K

R

K

VX

JJ[

2!


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Safe ranges of operation for the two common

methods of shunt motor speed control

Fieldresistancecontrol Armature voltagecontrol

the lo er the field curre t,

faster it turns

(IFq, [o)

thelo er thearmature voltage,

slo er it turns (VAq, [q)

thehigher the field curre t,slo er it turns

(IFo, [q)

the higher the armaturevoltage, faster it turns

(VAo, [o)


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There is a minimumachi vabl s eed

whe otorsfi l circuithas

maximumpermissiblecurrent lowing.

There is a maximumachievablespee

whe otors armature

voltagereachesitsmaximum

permissible level.

Controls otor s ee s above

basespee ( but not orbelow bases ee s)

If [ < [base, IF > IF,max a field

windings a be da age .

Controls otor s ee s below

basespee (but not forabove bases ee s)

If [ > [base, VA > VA,max a

ar ature windings a be

da age .


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Note: If a motor is operating at its rated terminalvoltage, power and field current, then it will be

running at rated speed orbase speed.

Hence, the two speed control techniques are

complementary. There is significant difference in torque and

power limits on the machine under these two

types of speed control.

In either case, the limiting factoris heating of

armature conductors (i.e. it places upper limit on

the magnitude of armature current IA)


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Fi ldresistance control

controls otor speeds above base

speed

Ar ature oltage controlcontrols otor speeds belo base

speed

y flu decreases ([ increase) y flu is constanty Xmaxmust decrease,

i.e.XmaxwJw 1/[(to ensure IA,max not exceeded)

y Xmax= constant(regardless of the speed)

y Pmax= constant y Pmaxw[


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Note:

and

The shuntd

c motor power and

torque limitations forsafe operation as a function of speed are shown below.

max,max AIKJX !

[X maxmax !P

RF control


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Electric Machines & Power ElectronicsENEE430

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The effect of an open field circuit

As RF is increased, the motor speed increases.

What happens if the field circuit were actually opened

while the motor is running?

y The flu in the machine would drop drasticall (i.e. allthe way down to Jres).

y Hence, EA (= KJ[)also drops.y This causes reall enormous increase inIA.y Since Xind wIA, the induced tor ue would be quite a bit

higher than load tor ue in the motor.y Therefore, motors speedrises and eeps going up.


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Therefore, in a shunt dc motor operating with lightfields, armature reaction can be severe such

that increase in loads can weaken its flux

enough to cause motors speed to rise.

However, most loads have torque-speed curveswhose torque increases with speed.


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Runaway!

This continues until motor overspeeds. This ondition isknownasrunaway.

Increased

speed[Increases

load

Increases

armature

reaction

More flux

weakening

urther

increasein

speed[


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The permanent magnet dc motor (PMDC)

PMDC is a dc motor whose poles are made of

permanent magnets.

Advantage (compared to shunt dc motor):

1) No external field circuit is required, no field circuit copper

losses

2) Smallerthan shunt dc motors because of no field circuit

Disadvantages:

1) Cannot produce high flux density as an externally

supplied shunt dc motor lower induced torque per

ampere of armature current compared to a shunt motor ofsame size.


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2) Runs the risk ofdemagnetisation due to armature

reaction or excessive heating during prolonged periods of

overload.

The PMDC is basically the same machine as a shunt dc

motorexcept the flux in the PMDC motor is fixed.

Speed control through varying the field current or

flux is not possible.

Hence, speed control methods forPMDC motors are:

1) Armature voltage control

2) Armature resistance control


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The series dc motor

A series dc motor contains field

wind

ings ofrelatively few turns connected in series with the

armature circuit.

The equivalent circuit:


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Inthe series dc otor,

IA = IS= IL

The KV e uationforthis otoris:

SAAAT

RRIEV !

armat re

c rrent

fie

c rrent

line

c rrent


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Induced torque in a series dc motor

The asic eha iourof a seriesdc otorisdue tothe factthatthe fl xis irectly roportional toIA, at eastuntilsaturation

is reachedi.e.

AScIcI !!J

where c constantof roportiona ity.

sloadincreases (IAincreases), fluxJincreasestoo.

This causesspeed[todecrease.

Hence, the series dc otor has a sharply droopin tor ue-

speedcharacteristic.


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The inducedtorque isgive by Aind IJX ! .

By substituting for, the induced torque in the series dc

machineis

2Aind KcI!X

Torque inaseries dcmotorisproportional to

the square ofitsarmature current.

Therefore, this motor is used in applications requiring veryhigh torques.

Exam le starter motors in cars, elevator motors a d tractor

motorsinlocomotives.

The terminal characteristic of a series dc


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The terminal characteristic of a series dc

motor

Assumption: The magnetisation curve is linear (nosaturation).

Hence, flux in the machine is given by equationA

cI!J .

erivationoftorque-speedcharacteristiccurve

1.KV for series dc motor, SAAAT

RRIE !

2.From torque equation, KcI indA X!


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1. lso, JKEA ! . ence,bysubstitutingforEAandIA intothe L equation

SA

i

cKV !

XJ[

2.If the flux canbe eliminated from this expression, it willdirectlyrelate the torqueofamotorto itsspeed. Notice that

cIA

J! , thus JX cKind ! . Therefore,

ind

K

cXJ!

3.Bysubstituting thisfluxexpression into theequationinpart 3andsolvingforspeed, theresultingtorque-

speed relationship fortheseries dcmotor is


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K

RR

TK

SA

i

T

!

1

[

Notice that for an unsaturated series motor,ind

X

[

1w

This ideal torque-speedcharacteristic is plotted below:


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Disadvantage ofseriesdc otor:

When the tor ue goes to zero, speedgoes to infinity ifno

load is connected to the motor, it can turn fast enough toseriously damage itself.

Warning!Never com letely unload a seriesmotorNever connectmotor to a load by a belt orothermechanismthat could brea . Use steel chains instead.


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Speed Control

There is onlyoneefficient ayto change the s eed of a seriesdc motor:Bychanging the terminal voltage

IfVTisincreased, the speed increasesfor any given torque


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Example 9.5

A series dc motor with VT=250V , totalRA+Rs=0.08 ohm , field circuit consists of 25 turns

per pole. Magnetizing curve is given in Fig. 9-22

a) Find the speed and induced torque of this motorfor when the armature current is 50A


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The compoundeddc motor

A compounded dc motor is a motor with both ashunt and a series field.The equivalent circuit of

the compounded motor is shown below:

Current flowing into adot produced positivemmf.


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Cumulative compound

ing current flows intodots on both field coils.Hence, resulting mmfs

add to give a larger total mmf.

Differential compounding current flows into

dot on one field coil and out of the dot on theother.Hence, resulting mmfs subtract


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Therearetwoco pon ntsofflu :y on isconstantandy anoth r whi h is proportional toIA (and hence to the

load)

Thus, CC otorhas:

y high rstartingtor uethanashunt otor(whosefluxisonstant)

y but a low r starting tor ue than a s ri s otor (whoseentirefluxisproportionaltoIA)

Co bin sb stfeaturesofboththeshuntandseries

otors.


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Advantages ofCC otor:y e tratorquefor starting(like series otor)y does notoverspeedatnoload(like shunt otor)

Atlightload

s:y series fieldhas ery s alleffecty motor eha es approximatelyli ea shuntdc motor

As loadgets verylarge:

y series flux ecomes uiteimportanty tor ue-speed ur e egins to look li e a series motors

haracteristic


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T

he torque-speed

characteristics ofad

ifferentiallycompoundeddcmotor

In a differentially co pounded dc otor, the shunt fand

series fsubtractfro each other.

Therefore, asthe loadincreases:

y IAincreases(Jse ieso IAo)y flu Jdecreases(Jnetq = Jshunt- Jse ieso)

Si e Jdecreases, speed[increases.

The i rease i s eed causesanotherincreasein load, whi h

furtheri reasesIA, further decreasi g the flux, and i reasi gthe s eed agai


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The result:differentially compounded motor is unstable and

tends toruna ay.

This instabilit is much orse than that of a shunt dc moto

with armature reaction. It is so bad that a differentiallcompoundedmotor is unsuitable forany application.


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It is also impossible to starta differentiall com ounde motor.

At startingconditions:

y The armature current and series field current are veryhigh.

y S

ince the series flux subtracts from the shunt flux, theseries field can actuall reverse themagnetic polarit othemachine s poles.

y Themotorwill t picall remain still or turn slowl in therong direction while burning up because of the

excessivearmaturecurrent.

ence, when starting this t pe ofmotor, theseries fieldmust

be short-circuited, so that it behaves as an ordinar shunt

motor during the starting period


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Speed control in the cumulativel compounded dcmotor

The techniques available for s eed control of a cumulativel

com ounded motor are the same as those availa le or a shunt

motor:

y Change the field resistance RFy Change the armature voltage VAy Change the armature resistance RA

Theoreticall , the differentiall com ounded dc motor could be

controlled in a similarmanner.

owever, since the differentiall com ounded motor is almost

never used, itss eed control method hardl matters.

The arguments des ribing

the effects of these

methods are ver similar

to the arguments given

earlier for the shunt motor

Documents

Ch9 DC Motors