Unit-IV-Induction Motors

7/28/2019 Unit-IV-Induction Motors

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IFETCE/EEE/M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0


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Output equation of Induction motor Main dimensions

Length of air gap- Rules for selecting rotor slots of

squirrel cage machines Design of rotor bars & slots

Design of end rings Design of wound rotor - Magnetic

leakage calculations Leakage reactance of polyphase

machines- Magnetizing current - Short circuit current

Circle diagram - Operating characteristics.

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INTRODUCTION

Popularly used in the industry and are usedworldwide in many residential, commercial,industrial, and utility applications.

MAIN FEATURES: cheap and low maintenance(absence of brushes)

MAIN DISADVANTAGES: speed control

is noteasy

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Construction : similar to 3 induction motor A single-phase motor is a rotating machine that has

both main and auxiliary windings and a squirrel-cagerotor.

Supplying of both main and auxiliary windings enablesthe single-phase machine to be driven as a two-phasemachine.

OVERVIEW OF SINGLE PHASE IM

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APPLICATIONS

Home air conditioners

Kitchen fans

Washing machines

Industrial machines Compressors

Refrigerators

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OVERVIEW OF SINGLE PHASE IM

Types of 1 induction Motor

Split Phase Motor

Capacitor Start Motors

Capacitor Start, Capacitor Run

Shaded Pole Induction Motor

Universal Motor (ac series motors)

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OVERVIEW OF 3 PHASE IM

Simple and rugged construction

Lowcostand minimummaintenance

High reliability and sufficiently

high efficiency The speed is frequency dependent.

noteasy to control the speed

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OVERVIEW OF 3 PHASE IM

can be part of a pump or fan, or connected to someother form of mechanical equipment such as a winder,conveyor, or mixer.

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CONSTRUCTION

Basic parts of an AC motor : rotor, stator, enclosure.

The stator and the rotor are electrical circuits thatperform as electromagnets.

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The stator - stationarystationary partpartofof thethe motormotor.. Stator laminations are stacked togetherstacked together forming a hollowhollow

cylindercylinder.

Coils of insulated wire are inserted into slots of the statorCoils of insulated wire are inserted into slots of the statorcore.core.

Each grouping of coilsEach grouping of coils, together with the steel core itsurrounds, form an electromagnet.

CONSTRUCTION (STATOR)

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The rotor is the rotating partof the motor

It can be found in two types:

Squirrel cage (most common)

Wound rotor

CONSTRUCTION (ROTOR)

/rotor winding/rotor winding

Short circuits allShort circuits all

rotor bars.rotor bars.

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SQUIRREL CAGE TYPE:Rotor winding is composed of copper bars

embedded in the rotor slots and shorted at bothend by end rings

Simple, low cost, robust, low maintenance


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WOUND ROTOR TYPE:

Rotor winding is wound by wires. The windingterminals can be connected to external circuitsthrough slip rings and brushes.

(similar to DC motor, with the coils connectedtogether that make contact with brushes)

Easy to control speed, more expensive.


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The enclosure consists of a frame (or yoke) andtwo end brackets (or bearing housings). The statoris mounted inside the frame. The rotor fits insidethe stator with a slight air gap separating it fromthe stator (NO direct physical connection)

Stator

Rotor

Air gap

CONSTRUCTION (ENCLOSURE)

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The enclosure protects the electrical and operatingparts of the motor from harmful effects of theenvironment in which the motoroperates.

Bearings, mounted on the shaft, support the rotorand allow it to turn. A fan, also mounted on the shaft,is used on the motor shown below for cooling.

CONSTRUCTION (ENCLOSURE)

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OUTPUT EQUATION:

The output kVA, Q = Co D2L ns x 10

-3and

The output coefficient, Co = 11 Bavac Kw x 10-3Q is calculated as ,( hp x 0.746 )/( cos)

EFFICIENCY AND POWER FACTOR:

For squirrel cage motors,

The efficiency varies from 0.72 to 0.91 and The power factor varies from 0.66 to 0.9 .

For slip ring motors, The efficiency varies from 0.84 to 0.91 and The power factor varies from 0.7 to 0.92 .

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OUTPUT EQUATIONS OF I.M

KVA rating of the machine

Q= no. of phases X output voltage per phase X current perphase X 10-3

Q =

Output voltage per phase = induced emf = Eph = 4.44 fTph Kw

No of phases=m

3

3

4.44 10

.

2

4.44 10 (1)2

ph w ph

s

sph w ph

Q m f T K I

pnSub f

pnQ m T K I

310ph ph

mE I


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Now current in each conductor

Total no. of conductors Z= no. of phase X 2 X Turns per phase

Z= 2mTph

Rewrite Equ.1

z phI I

3

3

1.11 ( )(2 ) 10

1.11 ( )( ) 10

w ph ph s

w z s

Q K p mT I n

Q K p ZI n

31.11 ( . . ) ( . . ) ( . ) 10wQ K total magnetic loading total electric loading sync speed


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3

3 2

2

0

3

0

1.11 ( )( ) 10

(11 10 )

. . .11 10 .

av

z c

w av c s

av c w s

s

av c w

P DLB

I Z Da

therefore

Q K DLB Da n

Q B a K D Ln

Q C D Ln output equation of IM C B a K output coefficient


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CHOICE OF SPECIFIC LOADINGS

TYPES:

Choice of specific electric loading

Choice of specific magnetic loading

CHOICE OF SPECIFIC MAGNETIC LOADING:

The factors to be considered are:

Power factor.

Iron loss.

Overload capacity.

CHOICE OF SPECIFIC ELECTRIC LOADING:

Copper loss and temperature rise.

Voltage.

Over load capacity.

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CHOICE OF Bav:

i) Low Bav large size machine for a given hpii) high Bav large magnetizing current low power factor

iii) high Bav high iron loss

iv) high Bav high m less Tph low leakage reactance

larger diameter for the circle diagram larger overload capacity

For 50 Hz motors Bav : 0.3 to 0.6 Wb/m2

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Choice ac (ampere conductor /m):

Low ac large size machine for a given hp

High ac higher copper loss and temp rise

High ac large Tph large leakage reactance lower

diameter for the circle diagram lower over load

capacity

For 50 Hz motors ac : 10,000 to 45,000 amp.cond/m The value ac chosen depends on the ventilation and

cooling

It should be remembered that the Power factor (PF) andefficiency () of the motor at full load increases with the

rating of the machine. Again and Pf are higher for high

speed motors compared to low speed motors.

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Main Dimensions

The ratio of core length to pole pitch for various

design features

Minimum Cost 1.5 2 Good power factor 1- 1.25

Good efficiency 1.5 Good overall design 1

Best power factor

In general the ratio lies between 0.6 and 2 dependingupon he size of machine and characteristics desired

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/ratio L

0.18L



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Peripheral speed

For Standard constructions 60m/s Higher peripheral speed up to 75 m/s

For normal design the peripheral speed can not beexceed 30m/s

Ventilating ducts

Radial ventilating ducts

Core length = 100-125mm

Width of each duct = 8 to 10mm

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LENGTH OF AIR GAP

The length of air gap in Induction motor is decided by the

following factors:

Power factor

Pulsation loss

Cooling

Over load capacity

Unbalanced magnetic pull

Noise

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Relations for calculation of length of air gap

For small induction motor

Alternate formula for small induction motor

Alternate formula to use

For machines with journal bearings

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0.125 0.35 0.015g al D L V

0.2 2g

l DLmm

0.2gl Dmm

1.6 0.25gl D mm



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CHOICE OF ROTOR SLOTS:

With certain combinations of stator and rotor slots, thefollowing problems may develop in the I.M:

The motor may refuse to start.

The motor may crawl at some sub-synchronous speed.

Severe vibrations are developed and so the noise will be

excessive.

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Rules for selecting rotor slots

Number of rotor slots never equal to number of stator slots

Number of rotor slots is 15 -30% greater than number of stator slots

Difference between the stator and rotor slots never equal to p, 2p or

5p to avoid synchronous cusps

Difference between the stator and rotor slots never equal to 3p to

avoid magnetic locking

Difference between the stator and rotor slots never equal to 1,2 ,

+(p+1), +(p+2) to avoid noise and vibrations

Summarizing (Ss Sr ) should not equal to p, 2p,3p, 5p , 1,2 , +(p+1), +(p+2)

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DESIGN OF SQUIRREL CAGE ROTOR

It involves:Selection of no.of rotor slots.

Design of rotor bars and slots.

rotor bar current

area of rotor bars shape and size of rotor slots

rotor slot insulation

Design of end rings.

end ring current area of end rings

Full load slip.

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EFFECTS OF HARMONICS

Harmonic induction torques Harmonic synchronous torques

Vibration and noise

Voltage ripples

REDUCTION OF HARMONIC TORQUES:

Chording

Integral slot winding

Skewing Increasing air-gap length

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DESIGN OF ROTOR BARS AND SLOTS

For a 3 phase machine , the rotor bar current is given bythe equation

Is = stator current in phase

Ts= stator turns per phase

Sr= number of rotor slots The performance of induction motor is greatly influenced

by resistance of rotor

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6s s

b ws

r

I TI K Cos

S

60.85 s sbr

I TIS



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DESIGN OF ROTOR BARS AND SLOTS

Higher rotor resistance = High starting torque & less % Rotor resistance = resistance of bars + resistance of end

rings

The current density in rotor bar= 4 to 7 A/mm2

Area of each rotor bars

Rotor slots for squirrel cage rotor may be either closed

and semi closed types Semi closed slots provide better overload capacity

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2bb

b

Iarea a mm



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ADVANTAGES OF CLOSED SLOTS:

Low reluctance Less magnetizing current

Quieter operation

Large leakage reactance, starting current is

limited.

DISADVANTAGES OF CLOSED SLOTS:

Reduced overload capacity

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DESIGN OF END RINGS

If the flux distribution is sinusoidal then the bar end ringcurrent will also be sinusoidal

Maximum value of end ring current

Current is not maximum in all bars under one pole atsame time but varies according to sine law, hence the

maximum value of the current in end ring is averagecurrent of half the bars under one pole.

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(max)2

(max) (max)2

e

re b

BaseperpoleI Currentperbar

SI Ip



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DESIGN OF END RINGS

Maximum value of end ring

The end ring current varies sinusoidally

Rms value of end ring current

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2(max)

2( ) (max)

(max) 2

r b

b b

b b

S IIe

p

I avg I

I I

r be

S II

p



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DESIGN OF END RINGS

Let the current density in end ring be 4 to 7 A/mm2

Area of cross section of end ring

The depth of end ring can be assumed depending on the

inner and outer diameter of rotor

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2

( ) ( )

ee

e

e e e

Ia mm

rea endring Depth thickness endring

a d t



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DESIGN OF WOUND ROTOR

It involves:

Rotor windings

Number of rotor turns.

Number of rotor Slots

Rotor Teeth.

Rotor core.

Slip rings and brushes

Rotor windings

Small motors- mush windings employed

Large motor double layer bar type wave winding is used

Motor output more than 750kw, we have to use more number of barsper slot to reduce the current handled by slip rings. This type ofwindings called barrel winding and wave wound

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Number of rotor turns

Rotor voltage on open circuit between slip ring not

exceed 500V for small machineFor large machine the voltage between slip ring upto 2000V

Rotor turns per phase

Rotor ampere turn

Rotor current

Area of rotor conductor38

w s s r

rw r s

K T ET

K E

0.85 s sr

r

I T

I T

0.85r r s sI T I T

rr

r

Ia



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Number of rotor Slots

Windings always 3 phase winding and star connected at

one end and other three end are terminated on three sliprings mounted on the shaft

When fractional slot windings are used , it is preferable tohave the number of slots as multiples of phases and pairof poles

Rotor Core

Depth of rotor core

Bcr= flux density in rotor coreInner diameter of rotor lamination

39

2

mcr

cr i

dB L

2( )i r sr cr

D D d d



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Rotor teeth

Maximum teeth area per pole

Total teeth area per pole = no of rotor slot per pole X

net iron length X width of rotor

Minimum width of rotor

Actual minimum width of rotor

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1.7

mMinimumteeth

ri tr

SL w

p

(min)

1.7

mtr

ri

WS

Lp

( 2 )r srsr

r

D dW

S



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Slip rings Rings made up of either brass or phosphor bronze

The current density of 4 to 7A/mm2

The length & breadth of rectangle are decided based onmechanical stability constraints

Brushes It is made up of metal graphite

Metal graphite is an alloy of copper and carbon

Current density of 0.1 to 0.2A/mm2

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LOSSES IN THE INDUCTION MOTOR

i) stator copper loss

ii) rotor copper loss

iii) iron loss in the stator teeth and core

iv) friction and windage loss (1- 1.5 % of output)

The rotor resistance in stator terms can be obtained as

rotor copper loss/ I2 ; where I2 = 0.85 I1

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MAGNETIC LEAKAGE CALCULATIONS

It is classified in to Slot leakage reactance (xss)

Rotor Slot leakage reactance (xsr)

Zigzag leakage reactance(xz) Overhang leakage reactance(xe)

Skew leakage reactance(xsk)

Magnetizing reactance(xm) Total leakage reactance

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LEAKAGE REACTANCE OF POLYPHASE MACHINES

Slot leakage reactance (xss)

Rotor Slot leakage reactance (xsr)

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216 ( )ss m wm ss xL

x f T K CS

2

2

' 16 ( )

16 ( ) ( )

sr m wm sr

r

ss m wm x ss sr

s r

Lx f T K

S

totalslotleakagereactacne

SLx f T K C

S S



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Zigzag leakage reactance(xz)

Overhang leakage reactance(xe)

Skew leakage reactance(xsk)

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216 ( )z m wm z

z

Lx f T K

S

2 016 ( ) [ ( ) . ]6.4

e m wm ss

s

Lx f T K D d Avg coilspan

S p

2

12

ssk m l

x X K



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Magnetizing reactance(xm)

Total leakage reactance

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2 016 ( )10

m m wm

g g s

Lx f T K

l k p F

'

2

lm ss sr z o sk

lm

lm m

x x x x x x

X

x X



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NO LOAD CURRENT

Magnetizing current Mmf for Air gap

Mmf for stator teeth

Mmf for rotor teeth

Mmf for stator core Mmf for rotor core

Loss component of current Ii Iron loss

Friction and windage loss

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MAGNETIZING CURRENT

Mmf for Air gap

Mmf for stator teeth

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60

60

1.36

800,000

g av

g g g g

B B

T B K l

13

13 ( / ) )

( )

ts

m

tss i

g ts ss

BS p L W

Statorteeth AT at d



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MAGNETIZING CURRENT

Mmf for rotor teeth

Mmf for stator core

Mmf for rotor core

50

13

13 ( / ) )

( )

tr

m

trr i

g sr lr

BS p L W

rotorteeth AT at d

( 2 )

3

ss cscs

D d dl

p

( 2 )

3

r sr cscr

D d dl

p



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Magnetizing current per phase

Iron loss

Hysteresis and eddy current loss in teeth and coresdue to variation of air gap density,

tooth pulsation loss due to non uniform flux distributionand loss in end plates

Frict ion & windage loss

Loss component at no load current per phase

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600.427

m

ws s

pATI

K T

.

3l

total noloadlossI

voltageperphase



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SHORT CIRCUIT CURRENT

Stator resistance

Stator resistance per phase

Value of resistivity for copper 0.021/m

Rotor ResistanceRotor resistance per phase

Rotor resistance per phase referred to stator

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mts

s

s

Lr

a

mtrr

n

Lr

a

2

' ws sr rwr r

K Tr r

K T



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CIRCLE DIAGRAM

The locus of extremity of the current phasor, obtained

for various values of a variable element is called alocus diagram.

The locus diagram of such a current phasor is circularin nature and hence called CIRCLE DIAGRAM of

three phase induction motor.

CIRCLE DIAGRAM FOR R-L SERIES CIRCUIT:

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CIRCLE DIAGRAM OF 3-PHASE INDUCTION MOTOR:

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CIRCLE DIAGRAM OF 3-PHASE INDUCTION MOTOR:

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OBTAINING DATA TO PLOT CIRCLE DIAGRAM:

The data required to draw the circle diagram is obtained byconducting 2 tests namely,

1. No-load test or Open circuit test

2. Blocked rotor test or Short circuit test.

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IFETCE/EEE/M SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1 0

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Unit-IV-Induction Motors

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