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Chapter 1MAGNETIC CIRCUIT

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It is the path which is followed by magnetic flux.

It is basically ferromagnetic with coil wound around them

MAGNETIC CIRCUIT

Why MAGNETIC CIRCUIT?

It is an important component

in the design of electrical machines.

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Examples of Magnetic Circuits

Simple magnetic circuit

Magnetic circuit with air gap

Simple machine

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It is required to understand the concepts of magnetic circuits

The object of today lecture

By making Analogy between Electric circuit and magnetic circuit

Analogy between Electric circuit and magnetic circuit

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Definitions Related to Electromagnetic Field(Unit is Weber (Wb)) = Magnetic Flux

is the number of flux lines crossing a surface area.

B (Unit is Tesla (T)) = Magnetic Flux Density

Is the number of flux lines per unit area = /A

H (Unit is Amp/m) = Magnetic Field Intensity =

B

Permeability

It is the degree of magnetization of a material to allow magnetic flux to pass through it.

It is analogous to conductivity in an electrical circuit

relative permeability.

µ permeability of a material

For ferromagnetic materials

For non-ferromagnetic materials

0 r

o = Permeability of air = 4*10-7 H/m

Magnetic Reluctance•It is the property of a material which

opposes the creation of magnetic flux in it

• It is analogous to •resistance in an electrical circuit•The reluctance of a material is given

by

Magneto Motive Force (mmf)FIt is the external force required to set

up the magnetic flux lines within the magnetic material.

The magneto motive force F is equal to the product of the number of turns around the core and the current through the turns of wire.

Magnetic Field Intensity (H)It is The magneto motive force per unit length

magnetic field intensity (H) produce a magnetic flux density B (Tesla).

a magnetic flux density is given by:

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Magnetization Curves

•In magnetic circuit calculations,

Magnetic Circuit Calculations

• it is required to determine

• the excitation mmf (F) needed • to

establish• a desired flux or• flux density at a given

point.

The magnetic circuit for the toroidal coil can be analyzed to obtain an expression for flux.

Magneto motive force F is

Where the reluctance is

`

and the magnetic flux is

Magnetic Circuit Calculations

Magnetic Circuit Calculationsobtain an expression for flux for the shown magnetic circuit

Effect of air gap on a magnetic circuitobtain an expression for flux for the shown magnetic circuit

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•Increase the reluctance. •Greater values of ampere-turn •are required to obtain the same• value of B for circuit without air gap•linearize magnetic circuits•i.e. no saturation

Summary of Effect of air gap on a magnetic circuit

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Air gap is practically an unavoidable part of any magnetic circuitThe B-H loop of a magnetic circuit is affected by the presence of air gap.so greater values of H are required to obtain the same value of B as compared with magnetically materials.

Effect of air gap on Magnetization Curves

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As a result the B-H loop gets  slanted,

Effects of air gaps on Magnetization Curves

Example 1

Find magneto motive force (mmf) F in a coil, if

the number of turns is 100, and I=2 A.

Find the reluctance if the flux

produced is 100mWb.

Find the permeability if l=50cm and A=0.5 m2

Find the flux density B

Find the magnetic force H

Example 2:Given : i=1 A, N=100, lc=40 cm, A= 100 cm2

r =5000 Calculate : F, H, B, and

100. iNF

2504.0

100

cl

FH

0157.001.057.1. AB

385.636601.05000104

4.07

Alc

In the shown Magnetic circuit relative permeability of the core material is 6000, its rectangular cross section is 2 cm by 3 cm. The coil has 500 turns. Find the current needed to establish a flux density in the gap of Bgap=0.25 T.

Magnetic Circuits (Example 3)

The current needed to establish a flux density in the gap of Bgap can be calculated as follow:

Magnetic Circuits (Solution Example 3)

where

Medium length of the magnetic path in the core is lcore=4*6-0.5=23.5cm, and the cross section area is Acore= 2cm*3cm = 6*10-4 m2

the core permeability is

Magnetic Circuits (Solution Example 3)

Am

Wbrcore

370 1054.71046000

The core reluctance is

the gap area is computed by adding the gap length to each dimension of cross-section:

thus the gap reluctance is:

Continue Solution Example 3

Wb

A

A

l

corecore

corecore

443

2

10195.51061054.7

105.23R

241075.85.035.02 mcmcmcmcmAgap

Wb

A

A

l

gap

gapgap

647

2

0

10547.41075.8104

105.0R

Total reluctance is

based on the given flux density B in the gap, the flux is

thus magneto motive force is

thus the coil current must be

Continue Solution Example 3.

Wb

Acoregap

6106.4RRR

WbAB gapgap44 10188.21075.825.0

AF 100610188.2106.4R 46

AN

Fi 012.2

500

1006

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•AC Excitation will increase core losses•It is important for the engineer to understand •Why the core losses increase ?•Core losses are important in• determining heating, •temperature rise, •rating and efficiency.

Magnetic Circuits with AC Excitation

1-Hysteresis Losses: hysteresis loss is proportional to the loop area (shaded).

CORE LOSSES (iron losses) are

To minimize hysteresis loss use materials with thin hysteresis(Silicon steel)

2-Eddy Current Losses:Eddy currents are created

when a conductor experiences changes in the magnetic field.

CORE LOSSES (iron losses) are

These induced currents cause Eddy Current Losses. These losses can be reduced by using thin sheets of laminations of the magnetic material.

CORE LOSSES (iron losses) are

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Thus, Iron Losses in Magnetic Circuit are:

a)Hysteresis losses

b)Eddy Current Losses

The iron loss is the sum of these two losses