MAGNETIC AND ELECTRIC CIRCUITS IN MACHINES

1Dr.R.RAMESH

Dr. R. RAMESHAssociate Professor

Dept of Electrical and Electronics EnggAnna University , Chennai

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MAGNETIC CIRCUIT OF TRANSFORMER

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MAGNETIC CIRCUIT OF DC MACHINES

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MAGNETIC CIRCUIT OF INDUCTION MOTOR

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Electric circuit Magnetic circuitThe emf circulates current in a closed path

The mmf creates flux in a closed path.

Flow of current is opposed by resistance of the circuit.

The creation of flux is opposed by reluctance of the circuit.

The path of current is The path of flux is called The path of current is called electric circuit.

The path of flux is called magnetic circuit.

Resistance, R Reluctance,S=Current=emf/Resistance Flux=mmf/ReluctanceCurrent density,=Current/(area of cross-section)

flux density,B=Flux/(Area of cross-section)

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Electric circuit Magnetic circuit

Current actually flows in the electric circuit.

Flux does not flow, but it is only assumed to flow.

When current flows, the energy is spent

Energy is needed only to create the flux but not to energy is spent

continuously.create the flux but not to maintain it.

Resistance of the electric circuit is independent of current strength.

Reluctance of the magnetic circuit depends on total flux or flux density in the material.( this is due to saturation).

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ESTIMATION OF MMF OF A SECTION

Determine the flux in the concerned section

Calculate the cross-section of the section Calculate the flux density Calculate the flux density From calculated B , detemine H (mmf per

unit length) from B-H curve mmf for concerned section

= length of section * mmf per unit length

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ESTIMATION OF MMF OF A MACHINE

mmf = flux * relucatnce Reluctance will not be uniform Reluctance calculation

Reluctance of air-gap in machines with smooth armature

Reluctance of air-gap in machines with open armature slots

Reluctance of air gap neglecting fringing effect

Reluctance of air gap including fringing effect

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Reluctance of air-gap in machines with smooth

armature

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Reluctance of air-gap in machines with open

armature slots

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Reluctance of air gap fringing effect

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Reluctance of air-gap in machines with smooth armature (sg )

lg / o L y s

Reluctance of air gap neglecting fringing effect

lg / o L (y s - w s)Reluctance of air gap including fringing effect

lg / o L (y s - K cs w s)Effect of ventilating ducts L = L - K n wEffect of ventilating ducts on reluctance of air gap

L = L - K cd nd wdK cs = Carters gap coefficients for slots depends on the ratio of slot opening /airgap length orthe empirical relation is 1/ {1+ (5lg /Ws )}

K cd = Carters gap coefficients for ducts the empirical relation is 1/ {1+ (5lg /Wd )}

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Kgs : Gap contraction factor for slotsReluctance of air gap in machine with open armature

slots / Reluctance of air gap in machine with smooth armature = ys/ys

Kgd : Gap contraction factor for ductsReluctance of air gap in machine with open armature

radial ducts / Reluctance of air gap in machine without armature radial ducts = L/L armature radial ducts = L/L

Kg : Total Gap contraction factor Reluctance of air gap in machine with slotted

armature & ducts / Reluctance of air gap in machine with smooth armature without ducts

Kg = Kgs * KgdKgs = Kgss * Kgsr (for induction motor)

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MMF

mmf required for air gap in machine= 8,00,000 Bav kg lg

if armature is smooth kg =1slot , no ducts kg = Kgssmooth and with ducts kg = Kgd

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MMF CALCULATION FOR TEETH:The calculation of MMF for producing flux in the teeth

of the machine is difficult because :i) The teeth are tapered when parallel sided slots are

used and this results in variation in the flux densityover the depth of the tooth.over the depth of the tooth.

ii) The slots provide another parallel path for the fluxflow, the teeth are normally worked in saturationand hence r becomes low.

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Following METHODS are usually employed for the calculation of MMF required for the tapered teeth:-

i) GRAPHICAL METHOD :ATt = at mean x lt

ii) SIMPSONS RULE :ii) SIMPSONS RULE :at mean = (at1 +4 at2 + at3)/6 A/miii) BT1/3 METHOD : ATt = at1/3 x lt , where at1/3 = MMF for corresponding to B at 1/3 rd

height from the narrow end.

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Graphical Method

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B app= total flux in a slot pitch / Tooth area

B real = Actual flux in a tooth/Tooth B real = Actual flux in a tooth/Tooth area

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Magnetic leakage The flux which passes through unwanted

path is called the leakage flux. Leakage coefficient

= Total flux/ useful flux= (useful flux+ leakage flux) / useful flux

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Types of leakage flux Slot leakage flux Tooth top leakage flux Zigzag leakage flux Zigzag leakage flux Overhang leakage flux Harmonic leakage flux Skew leakage flux Peripheral leakage flux

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Slot leakage flux

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Tooth top leakage flux

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Zigzag leakage flux

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