Chapter 06 Magnetic Circuits

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Chapter 6

Magnetic Circuits

SUJIT K. PATEL

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Saturday, September 18, 2010 Ch. 6 Magnetic Circuits 2

Topics to be Discussed

Magnetomotive Force (MMF). Magnetic Field Strength (H).

Magnetic Permeability.

Reluctance (R). Analogy between Electric and Magnetic

Circuits.

Composite Magnetic Circuit. Magnetic Leakage and Fringing.

Air Gaps in Magnetic Circuits.

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Introduction

Unlike electric field lines, the lines of magneticflux form closed loops.

A magnetic circuitis a closed path followed bylines of magnetic flux.

A copper wire, because of its high conductivity,confines the electric current within itself.

Similarly, a ferromagnetic material (such as ironor steel), due to its high permeability, confinesmagnetic flux within itself.

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Magnetomotive Force (MMF)

The electric current is due to the existence of anelectromotive force (emf).

By analogy, we may say that in a magnetic circuit, themagnetic flux is due to the existence of amagnetomotive force(mmf).

mmf is caused by a current flowing through one or moreturns.

The value of the mmf is proportional to the current andthe number of turns.

It is expressed in ampere turns(At).

But for the purpose of dimensional analysis, it isexpressed in amperes.

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Magnetic Field Strength (H) The mmf per metre length of the magnetic circuit

is termed as the magnetic field strength,magnetic field intensity, or magnetizing force.

Its units are ampere-turns per metre (At/m) .

Its value is independent of the medium .

l

IN

lH

F

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Magnetic Permeability ()

If the core of the toroid is vacuum or air, themagnetic flux density Bin the core bears adefinite ratio to the magnetic field strength H.

This ratio is called permeability of free space.

Thus, for vacuum or air,

Tm/A104 70H

B

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The flux produced by the given mmf is greatlyincreased, if iron replaces the air in the core.

As a result, the flux density Balso increasesmany times.

In general, we can write B= H.

is called the permeabilityof the material.

Normally, we write = r0.

ris called relative permeability(just a number).

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Reluctance (R) and Permeance (G) The current in an electric circuit is limited by the

presence of resistance of the electric circuit.

Similarly, the flux in a magnetic circuit islimited by the presence of the reluctanceof the

magnetic circuit,

A

l

A

l

r0

11R

The reciprocal of reluctance is known aspermeance(G).

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Magnetic Circuit Theory

For a toroid, mmf, F= NI ampere-turns.

Because of this mmf, a magnetic field of strength

H is set up throughout the length l.

Therefore, F = Hl

If, B is the flux density, total flux is given as

= B A

Dividing, we get

l

A

l

A

l

A

H

B

Hl

BA

r 0F )/( 0Al

r

F

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Comparing this with R

E

I

We getA

l

r 0

1R

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Analogy between Electric and Magnetic Circuits

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Example 1

Calculate the magnetomotive force (mmf)required to produce a flux of 0.015 Wb acrossan air gap of 2.5 mm long, having an effectivearea of 200 cm2.

Solution :

T0.7510200

015.04

A

B

A/m00059710475.0 7-

0

BH

At14923

105.2000597HlF

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Composite Magnetic Circuit

11

1

1

A

lR

22

2

2A

lR

22

2

11

1

21,ReluctanceTotalA

l

A

lRRR

Case 1 :

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22

2

11

1

reluctancetotalcoilofmmfflux,Total

A

l

A

l

NI

R

F

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Case 2 : (with air gap)

Total reluctance,

A

l

A

l

0

2

1

1R

2

01

1

0 )/(

1l

l

A

21

0

1l

l

Ar

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Since the relative permeability r

(= 1/0) of

steel is very large (of the order of thousand), themajor contribution in the total reluctance Ris by

the air-gap, though its length l2 may be quite

small (say, a few millimetres).

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Magnetic Leakage and Fringing

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The flux lines, such as a, b and c, leak

through the core. This is called leakage flux, since it does not

contribute to the useful fluxpassing throughthe metallic ring.

We define leakage factoras the ratio of totalflux through the exciting winding to the usefulflux.

The value of the leakage factor for electricalmachines is about 1.15 to 1.25.

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There is another effect called fringing.

The useful flux passing across the air-gaptends to bulge outward.

This happens because the magnetic flux lines

tend to repel each other in

Its effect is to cause a slight increase (say,about 10 %) in the cross-sectional area at the

air gap.

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Kirchhoffs Laws

Kirchhoffs Flux Law(KFL) : The totalmagnetic flux towards a junction is equal to the

total magnetic flux away from that junction.

Kirchhoffs Magnetomotive Force Law(KML) In a closed magnetic circuit, the

algebraic sum of the product of the magnetic

field strength and the length of each part of the

circuit is equal to the resultant magnetomotive

force.

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Steps to solve a problem on magnetic circuit

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Air Gaps in Magnetic Circuits

Two purposes :1. To permit part of a magnetic circuit to

move, for example, in relays and in

electrical machines.2. To make the magnetization characteristic

of the circuit more linear.

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Saturday September 18 2010 Ch 6 Magnetic Circuits 23

Review

Magnetomotive Force (MMF).

Magnetic Field Strength (H).

Magnetic Permeability.

Reluctance (R).

Analogy between Electric and MagneticCircuits.

Composite Magnetic Circuit.

Magnetic Leakage and Fringing.

Air Gaps in Magnetic Circuits.

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Chapter 06 Magnetic Circuits