Chap 5 DC Motor

EBB2133 Electrical Machine 1Chapter 5: DC Machines

Lecturer:

Dr Zuhairi Baharudin

Room: 22‐03‐09 Ext: 7810

email: [email protected]: [email protected]

DC Motor

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ObjectivesObjectives• Students should be able to :a) describe the equivalent circuit for different types ofa) describe the equivalent circuit for different types of

DC motors b) describe the terminal characteristics (torque vs. ) ( q

speed) for a DC motorc) determine speed and torque generated by a DC

t i it t i l h t i ti dmotor given its terminal characteristics and magnetization curve

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Separately Excited DC MotorSeparately Excited DC Motor• A separately excited DC motor is a motor whose field circuit

receives power from a separate constant‐voltage supply.

FF

VI =adjF

F RRI

+Lumped together

AAAT RIEV +=as RF

AL II =

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Shunt DC MotorShunt DC Motor• A shunt DC motor is a motor whose field circuit gets its

power directly across the armature terminals.

TVI =Lumped together

as RFAAAT

FF

RIEV

RI

+=

=

FAL III +=

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Separately Excited and Shunt DC MotorsMotors

• When the supply voltage is assumed constant, there is no practical difference between a separately excited DC motor and a shunt DC motor.difference between a separately excited DC motor and a shunt DC motor.

Lumped together

Lumped together

as Ras RF

as RF

(a) Equivalent circuit of a separately excited DC motor.

(b) Equivalent circuit of a shunt DC motor.

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excited DC motor. motor.

Shunt DC Motorl hShunt DC Motor• Terminal Characteristics– A plot of machine’s output quantities versus each other.

– Terminal characteristics of a motor is torque versus speed and we canTerminal characteristics of a motor is torque versus speed and we can derive the plot from the KVL equation of a shunt DC motor, VT = EA + IARA.

Since E = Kφω RIKV +φω– Since EA = Kφω,

– Meanwhile, the armature current can be expressed as

AAT RIKV += φω

φτK

I indA =

therefore

φK

Aind

T RK

KVφ

τφω +=

AT RV

K

τω

φ

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indAT

KKτ

φφω

2)(−=

Shunt DC MotorShunt DC Motor• The terminal characteristics of

a shunt DC motor

Let’s check !

• When load on a motor is increased :

– τload will exceed τind, motor slowsdown

– Internally induced voltage (EA = Kφω↓) drops, armature current, IA = (VT – EA↓)/RA increases

– As the IA increases, induced torque in the machine, τind = KφIA↑A , q , ind φ A

increases until it is equal to the τload at a lower mechanical speed.

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Shunt DC MotorShunt DC Motor• The torque‐speed characteristics is linear when the terminal voltage, VT

and other variables are kept constant.

• Armature reaction can also affect the shape of the plot• Armature reaction can also affect the shape of the plot.

– As load increases, the flux‐weakening effects reduces the total flux in the machine.

As amo nt of fl decreases the speed of the motor increases– As amount of flux decreases, the speed of the motor increases.

indT

KRA

KV

τφφ

ω2)(

−=

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Shunt DC MotorShunt DC Motor• Nonlinear Analysis

– Flux φ is nonlinear function of magnetomotive force F– Flux, φ is nonlinear function of magnetomotive force, F.

][ φωKEA =

⎥⎦

⎤⎢⎣

⎡=

F

FF R

VI

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Shunt DC MotorShunt DC Motor• Nonlinear Analysis

– In a machine with armature reaction present, total flux is reduced when load increaseswhen load increases.

– Therefore, the resultant/net mmf in a shunt DC motor is

Fnet = NFIF - FAR

– To find the resulting EA, we locate the equivalent field current, IF* on the magnetization curve, given by

ARFF N

II F−=*

– With changing values of EA, the speed of the machine changes too. Since the magnetization curve is plotted for a particular speed, the

FN

g p p p ,relationship between EA and speed is given by

nn

EEA =

where EA0 and n0 are reference values from the magnetization curve.

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00 nE A

Shunt DC MotorShunt DC Motor• Speed Control

– Three methods are available to control the speed of a shunt DC motor :

• Adjusting the field resistance, RF (and thus the field flux)

d h l l l d h• Adjusting the terminal voltage applied to the armature

• Adding a resistor in series with the armature circuit (less common method)common method)

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Shunt DC Motor Speed ControlShunt DC Motor Speed Control• Adjusting Field Resistance, RF

– Increasing RF causes field current,I (= V /R ↑) to decreaseIF ( VT/RF↑) to decrease.

– Decreasing IF decreases flux, φ.– Decreasing φ reduces armature

voltage E (E = Kφ ω)

Lumped together

as RF

voltage, EA. (EA = Kφ ω)– Decreasing EA increases armature

current, IA (= (VT - EA↓)/RA).

i I i i d d ( Kφ I ⇑)– Increasing IA increases induced torque, (τind = Kφ IA⇑), with the change in IA dominant over change of flux.

– Increasing τind makes τind > τload , and the speed of the F

TF R

VI =

machine, ω increases.

– Increasing ω increases EA (= Kφ ω↑) again.– Increasing EA decreases IA.

FAL

AAAT

III

RIEV

+=

+=

g A A

– Decreasing IA decreases τind until τind = τload at a higher speed.

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Shunt DC Motor Speed ControlShunt DC Motor Speed ControlTorque –speed characteristic

IIf1 f1 < < IIf2f2 < < IIf3f3

τm

f2f2 f3f3

ΦΦ11 < < ΦΦ22 < < ΦΦ33

τ

nnNL3NL3 nnn11nn22 nn33 nnNL2NL2nnNL1NL1

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Shunt DC Motor Speed ControlShunt DC Motor Speed Control• Adjusting Terminal Voltage, VT applied to the armature

– Voltage applied to the armature is adjusted without changing the voltage applied to the field.pp f

– Increasing armature voltage, VA increases armature current, IA [= (VA ↑– EA) /RA ].

– Increasing IA increases induced torque τi dIncreasing IA increases induced torque, τind.

– Increasing τind makes τind > τload , increasing ω.– Increasing ω increases EA (= Kφ ω↑) again.– Increasing EA decreases IA [= (VA – EA ↑) /RA ].– Decreasing IA decreases τind until τind = τload at a higher speed.

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τm

VV33 < < VV22 < < VV11

ττ

nnNL1NL1nnn11nn22nn33 nnNL2NL2nnNL3NL3

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Shunt DC Motor Speed ControlShunt DC Motor Speed ControlArmature resistance speed controlArmature resistance speed control

‐ Speed may be controlled by changing Ra‐ The total resistance of armature may be varied by means of a

rheostat in series with the armature

‐ The armature speed control rheostat also serves as a starting resistor.

‐ From τ‐n characteristic,

⎞⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛==

a

ffstart R

IVKc

πτ

222 Will b h d⎟⎟⎠

⎞⎜⎜⎝

⎛−=

a

ff

RnIK

slopeπ2

22 Will be changed

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RRa1a1

τm

RRa1 a1 < < RRa2a2 < < RRa3a3RRa2a2

RRa3a3

RRa1 a1 < < RRa2a2 < < RRa3a3

τ

nNLnnn11nn22nn33

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ELECTRICAL MACHINES 1EBB 2133

Series and Compounded pDC Motors

ObjectivesObjectives• Students should be able to :a) describe the equivalent circuit for series anda) describe the equivalent circuit for series and

compounded DC motors b) describe the terminal characteristics (torque vs. ) ( q

speed) for both DC motorsc) determine speed and torque generated given its

t i l h t i ti d ti titerminal characteristics and magnetization curve

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Series DC MotorSeries DC Motor• A DC motor whose field windings consist of a relatively few

turns, connected in series with the armature circuit.

B i i i l b hi d i DC t i th t fl i di tl• Basic principle behind a series DC motor is that flux is directly proportional to the armature current, IA, at least until saturation is reached.

)( SAAAT

LSA

RRIEV

III

++=

==

)( SAAAT

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Series DC MotorI d d T Series DC Motor• Induced Torque– As load is increased, IL and IA increase and so does flux.

– An increase in flux causes a decrease in the speed of the motor.p

– For a series DC motor, induced torque is given by τind = KφIA and flux is proportional to its armature current (at least prior to saturation), φ=cIA.A

– Therefore, the induced torque is proportional to the square of its armature current, τind = KcIA

2 .

– This makes the series DC motor suitable for high‐torque applicationsThis makes the series DC motor suitable for high torque applications such as starter motors in cars, elevator and cranes.

)(

LSA III ==

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)( SAAAT RRIEV ++=

Series DC MotorSeries DC Motor• Terminal Characteristics

– The torque‐speed relationship can be derived using KVL

VT = EA + IS (RA +RS) and proportionality of flux and armatureVT EA + IS (RA +RS) and proportionality of flux and armature current, φ =cIA..

RRV SAT +−=ω 1 For detailed derivation, refer to Chapman,

pg. 564

– A disadvantage of a series DC motor is that its speed goes to infinity h th t i

KcKc indτω

when the torque is zero.

– In practice, this will not be so as the motor needs to overcome mechanical, stray and core losses.

– However, it is essential to remember not to completely unload a series DC motor as the motor will turn too fast and damage itself.

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Series DC MotorSeries DC Motor• Terminal Characteristics

The torque-speed characteristic of a series DC motor.

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Series DC MotorSeries DC Motor• Speed Control

– The only method to control the speed of a series DC motor is by changing its terminal voltagechanging its terminal voltage.

KcRR

KcV SA

ind

T +−=

τω 1

– The first term of the torque‐speed relationship shows increased speed for any given torque.

ind

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Compounded DC MotorCompounded DC Motor• A DC motor with both a shunt and series field circuits.

• To differentiate between a cumulatively and differentially compounded DC motors we will use the dot convention : Current flowing into a dotDC motors, we will use the dot convention : Current flowing into a dot produces positive magnetomotive force.

• If current flows into the dots on both field coils, the resulting mmfs add to produce a larger total mmf⇒ cumulative compoundingto produce a larger total mmf⇒ cumulative compounding.

• If current flows into the dot on one field coil and out of the dot on the other field coil, the resulting mmfs subtract ⇒ differential compounding.

• Cumulatively compounded

■ Differentially compounded

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Compounded DC MotorCompounded DC Motor• Cumulatively

compounded


(a) Compounded DC motor with long-shunt connection

(b) Compounded DC motor

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( ) pwith short-shunt connection

Compounded DC MotorCompounded DC Motor• The Kirchhoff’s voltage law equation for a compounded DC motor :

VT = EA + IA (RA + RS)• The current relationship for this motor isThe current relationship for this motor is

F

TFFAL R

VIIII =+=



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Compounded DC MotorCompounded DC Motor• The resultant magnetomotive force and the effective shunt field current :

ARSEFnet FFFF −±=

F

ARA

F

SEFF N

INN

II F−±=*

where the positive sign is for cumulatively compounded motor and negative sign for differentially compounded motor.



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Compounded DC MotorCompounded DC Motor• Terminal Characteristics of a Cumulatively Compounded DC

MotorThere are is a component of flux which is constant plus another– There are is a component of flux which is constant plus another component which is proportional with the armature current.

– In total, the cumulatively compounded DC motor has a higher starting torque than a shunt motor but lower than that of a seriesstarting torque than a shunt motor but lower than that of a series motor so it does not overspeed at no load.



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Motor– At small loads most of the load current goes through the shuntAt small loads, most of the load current goes through the shunt

circuitry so the motor behaves like a shunt motor.

– At heavy loads, the series flux becomes quite important and the motor behaves more like a series motormotor behaves more like a series motor.



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Motor

(a) Torque-speed relationship of a cumulatively compounded motor compared to shunt and series motors with the same full-

(b) Torque-speed relationship of a cumulatively compounded motor compared to a shunt motors with the same no-load

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load rating speed.

Compounded DC MotorCompounded DC Motor• Terminal Characteristics of a Differentially Compounded DC

Motor– The shunt mmf and the series mmf subtract from each otherThe shunt mmf and the series mmf subtract from each other.

– As load increases, IA increases but flux in the motor decreases.

– As flux decreases, speed of the machine increases.

H i i d i h l d hi h f h d– However, increase in speed increases the load which further reduces the flux, thus speed will be further increased



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Compounded DC MotorCompounded DC Motor• Terminal Characteristics of a Differentially Compounded DC

Motor– The differentially compounded DC motor is unstable and it tends to

run away with its increased speed.

– This makes the motor unsuitable for any useful application.

Torque-speed relationship of a differentially compounded DC motor.

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DC Motor EfficiencyP L DC Motor Efficiency• Power Losses

Pconv

mappoutP ωτ=LTin IVP = IELTin

S

mindAAIE ωτ=

Stray lossesMechanical

lossesCore lossesI2R &

brush drop l

Power flow diagram of a DC motor.

losses

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Permanent Magnet DC MotorPermanent Magnet DC Motor• A DC motor whose poles are made of permanent magnets.

• Advantages :No external field circuit means no field circuit copper losses– No external field circuit means no field circuit copper losses.

– No field windings means it is smaller than shunt DC motor.

• Disadvantages :– Permanent magnets cannot produce high flux density.

– Low induced torque, τind per ampere of armature current, IA.

– A large armature current may produce enough armature mmf toA large armature current may produce enough armature mmf to demagnetize the permanent magnets.

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Permanent Magnet DC MotorPermanent Magnet DC Motor• For a PMDC machine, the pole flux is just the residual flux in permanent

magnets.

• A good material for the poles should have as large a residual flux density• A good material for the poles should have as large a residual flux density, Bres as possible and at the same time, have as large a coercive magnetizing intensity, HC as possible.

(a) The magnetization curve of a (b) The magnetization curve of a

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typical ferromagnetic material ferromagnetic material suitable for a PMDC machine

Permanent Magnet DC MotorPermanent Magnet DC Motor• Major types of materials used as permanent magnets are ferrite

magnetic materials and rare‐earth magnetic materials.

(c) Magnetization curves of a typical magnetic materials. (Alnico 5 is a

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ferromagnetic alloy)

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Chap 5 DC Motor