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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
CONSTRUCTION (ROTOR)
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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.
CONSTRUCTION (ROTOR)
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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
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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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LEAKAGE REACTANCE OF POLYPHASE MACHINES
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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LEAKAGE REACTANCE OF POLYPHASE MACHINES
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
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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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