Unit-IV-Induction Motors

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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 used worldwide in many residential, commercial, industrial, and utility applications.  MAIN FEATURES: cheap and low maintenance (absence of brushes)  MAIN DISADVANTAGES: speed control  is not easy

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OVERVIEW OF SINGLE PHASE IM • Construction : similar to 3 induction motor • A single-phase motor is a rotating machine that has both main and auxiliary windings and a squirrel-cage rotor. • Supplying of both main and auxiliary windings enables the single-phase machine to be driven as a two-phase machine.

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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 Low cost and minimum maintenance High reliability and sufficiently high efficiency The speed is frequency dependent.  not easy to control the speed

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OVERVIEW OF 3 PHASE IM •

can be part of a pump or fan, or connected to some other 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 that perform as electromagnets.

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CONSTRUCTION (STATOR) • The stator - stationary part of the motor motor.. • Stator laminations are stacked together forming a hollow cylinder. cylinder • Coils of insulated wire are inserted into slots of the stator core. • Each grouping of coils, coils together with the steel core it surrounds, form an electromagnet.

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CONSTRUCTION (ROTOR) • The rotor is the rotating part of the motor • It can be found in two types: – Squirrel cage (most common) – Wound rotor

Short circuits all rotor bars.

/rotor winding

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CONSTRUCTION (ROTOR) SQUIRREL CAGE TYPE: Rotor winding is composed of copper bars embedded in the rotor slots and shorted at both end by end rings Simple, low cost, robust, low maintenance

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CONSTRUCTION (ROTOR) WOUND ROTOR TYPE: Rotor winding is wound by wires. The winding terminals can be connected to external circuits through slip rings and brushes. (similar to DC motor, with the coils connected together that make contact with brushes) Easy to control speed, more expensive.

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CONSTRUCTION (ENCLOSURE) • The enclosure consists of a frame (or yoke) and two end brackets (or bearing housings). The stator is mounted inside the frame. The rotor fits inside the stator with a slight air gap separating it from the stator (NO direct physical connection)

Stator Rotor Air gap

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CONSTRUCTION (ENCLOSURE) • The enclosure protects the electrical and operating parts of the motor from harmful effects of the environment in which the motor operates. • Bearings, mounted on the shaft, support the rotor and allow it to turn. A fan, also mounted on the shaft, is used on the motor shown below for cooling.

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OUTPUT EQUATION: The output kVA, Q = Co D2L ns x 10-3 and The output coefficient, Co = 11 Bav ac Kw x 10-3 Q is calculated as ,( hp x 0.746 )/(η cosΦ) 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 per phase X 10-3 3 mE I  10 Q= ph ph Output voltage per phase = induced emf = Eph = 4.44 fФTph Kw No of phases=m Q  m  4.44 f Tph K w  I ph 103 pns Sub. f  2  pn  Q  m  4.44  s  Tph K w  I ph  103    (1)  2 

• Now current in each conductor

I z  I ph

• Total no. of conductors Z= no. of phase X 2 X Turns per phase Z= 2mTph • Rewrite Equ.1

Q  1.11K w ( p )(2mTph I ph )ns 10 Q  1.11K w ( p )( ZI z )ns 10

3

3

Q  1.11K w (total.magnetic.loading )  (total.electric.loading )  ( sync.speed ) 10 3

P   DLBav I z Z   Dac therefore Q  1.11K w ( DLBav )( Dac )ns 10 3

3

2

Q  (11Bav ac K w  10 ) D Lns 2

Q  C0 D Lns    output.equation.of .IM 3

C0  11Bav ac K w 10    output.coefficient

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

CHOICE OF Bav: i) Low Bav → large size machine for a given hp ii) high Bav → large magnetizing current → low power factor iii) high Bav → high iron loss iv) high Bav → high Φm→ less Tph→ low leakage reactance → larger diameter for the circle diagram→ larger over load 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) and efficiency (η) of the motor at full load increases with the rating of the machine. Again η 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

ratio  L /  • • • •

Minimum Cost Good power factor Good efficiency Good overall design

– 1.5 – 2 – 1- 1.25 – 1.5 –1

•

Best power factor

•

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

  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 be exceed 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 lg  0.2  2 DLmm

 Alternate formula for small induction motor lg  0.125  0.35D  L  0.015Va

 Alternate formula to use

lg  0.2 Dmm  For machines with journal bearings

lg  1.6 D  0.25mm 26 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

CHOICE OF ROTOR SLOTS: With certain combinations of stator and rotor slots, the following 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) 28 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

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

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

DESIGN OF ROTOR BARS AND SLOTS • For a 3 phase machine , the rotor bar current is given by the equation

6 I sTs Ib  K ws Cos Sr 6 I sTs I b  0.85 Sr

• • • •

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

DESIGN OF ROTOR BARS AND SLOTS • Higher rotor resistance = High starting torque & less η% • Rotor resistance = resistance of bars + resistance of end rings • The current density in rotor bar δ= 4 to 7 A/mm2 • Area of each rotor bars Ib area  ab  mm 2 b • 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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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 ring current will also be sinusoidal • Maximum value of end ring current Baseperpole I e (max)   Currentperbar 2 S I e (max)  r I b (max) 2p

• Current is not maximum in all bars under one pole at same time but varies according to sine law, hence the maximum value of the current in end ring is average current of half the bars under one pole.

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DESIGN OF END RINGS • Maximum value of end ring

2Sr Ib Ie(max)  p 2 I b (avg )  I b (max)  I b (max)  2 I b • The end ring current varies sinusoidally • Rms value of end ring current

Sr I b Ie  p 35 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

DESIGN OF END RINGS • Let the current density in end ring be 4 to 7 A/mm2 • Area of cross section of end ring

Ie ae  mm 2 e Area (endring )  Depth  thickness(endring ) ae  de  te • The depth of end ring can be assumed depending on the inner and outer diameter of rotor

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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 bars per slot to reduce the current handled by slip rings. This type of windings 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 machine For large machine the voltage between slip ring up to 2000V K T E w s s Rotor turns per phase T r   r K wr Es Rotor ampere turn I rTr  0.85I sTs Rotor current

0.85I sTs Ir  Tr

Area of rotor conductor

ar 

Ir

r 38

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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 slip rings mounted on the shaft When fractional slot windings are used , it is preferable to have the number of slots as multiples of phases and pair of poles

Rotor Core Depth of rotor core

m d cr  2 Bcr Li

Bcr= flux density in rotor core Inner diameter of rotor lamination

Di  Dr  2(d sr  d cr ) 39 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

Rotor teeth Maximum teeth area per pole

m Minimumteeth  1.7

Total teeth area per pole = no of rotor slot per pole X net iron length X width of rotor

Sr   Li  wtr p

Minimum width of rotor

Wtr (min)

m  Sr 1.7   Li p

Actual minimum width of rotor  ( D  2d ) r sr 

Sr

 Wsr

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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 on mechanical 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 43 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

LEAKAGE REACTANCE OF POLYPHASE MACHINES

• Slot leakage reactance (xss)

L xss  16 f (Tm K wm ) ss Cx S 2

• Rotor Slot leakage reactance (xsr’) L xsr '  16 f (Tm K wm ) sr Sr 2

totalslotleakagereactacne Ss L xs  16 f (Tm K wm ) (Cx ss  sr ) Ss Sr 2

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LEAKAGE REACTANCE OF POLYPHASE MACHINES

• Zigzag leakage reactance(xz) L xz  16 f (Tm K wm ) z Sz 2

• Overhang leakage reactance(xe) L 0 xe  16 f (Tm K wm ) [ ( D  d ss )  Avg .coilspan] 6.4 S s p 2

• Skew leakage reactance(xsk) s2 xsk  X m Kl 12 45 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

LEAKAGE REACTANCE OF POLYPHASE MACHINES

• Magnetizing reactance(xm) L0 xm  16 f (Tm K wm ) 10lg k g pFs 2

• Total leakage reactance

xlm  xss  xsr ' xz  xo  xsk X lm xlm  X m  2 46 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

OPERATING CHARACTERISTICS • No load Current

 Magnetizing current  Loss component of current Ii • Short Circuit Current

 

Stator resistance Rotor resistance 47 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

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

Bg 60  1.36 Bav ATg  800, 000 Bg 60 K g lg  Mmf for stator teeth

Bts 1

3

m  ( S s / p)  Li  W 1 ) ts

3

Statorteeth( ATg )  atts  d ss

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MAGNETIZING CURRENT  Mmf for rotor teeth

Btr 1

3

m  ( S r / p)  Li  W 1 ) tr 3

rotorteeth( ATg )  atsr  dlr  Mmf for stator core

 ( D  2d ss  d cs ) lcs  3p  Mmf for rotor core

 ( Dr  2d sr  d cs ) lcr  3p 50 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

Magnetizing current per phase

Iron loss

0.427 pAT60 Im  K wsTs

 Hysteresis and eddy current loss in teeth and cores due to variation of air gap density,  tooth pulsation loss due to non uniform flux distribution and loss in end plates

Friction & windage loss Loss component at no load current per phase total.noloadloss Il  3  voltageperphase 51 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

SHORT CIRCUIT CURRENT

Stator resistance Stator resistance per phase

 Lmts rs  as • Value of resistivity for copper 0.021 Ώ/m Rotor Resistance  Lmtr Rotor resistance per phase rr  an Rotor resistance per phase referred to stator 2

 K wsTs  rr '     rr  K wrTr  52 IFETCE/EEE/ M.SUJITH / III YR/VI SEM/EE2355/DEM/ VER 1.0

CIRCLE DIAGRAM •

•

The locus of extremity of the current phasor, obtained for various values of a variable element is called a locus diagram. The locus diagram of such a current phasor is circular in 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 by conducting 2 tests namely, 1. No-load test or Open circuit test 2.

Blocked rotor test or Short circuit test.

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