L-8

MAGNETIC CIRCUITS

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 1

Objectives

To solve various kinds of problems involving series

magnetic circuits.

To understand losses involved in magnetic circuits.

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 2

Contents

• Series magnetic circuit• Fringing effect• Useful flux and leakage flux• Magnetic hysteresis• Losses in magnetic circuit

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 3

Series Magnetic Circuit

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 4

• Flux ɸ is the same in all sections if leakage flux is neglected.

• Flux density and reluctance in each section may vary, depending on its effective cross-sectional area and material. Rectangular shaped series

magnetic circuit with air gap.

Series Magnetic Circuit

Equivalent reluctance is the sum of reluctance of different parts/elements.

The resultant MMF is the sum of MMFs in each individual parts/elements

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 5

Series Magnetic CircuitELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 6

gg

rg

gg

rrrgg

lHlHlHl Hf Total mm

μμ

lB

μμ

lB

μμ

lB

μμ

lBSφSφSφSφmmf

332211

030

33

20

22

10

11332211

:

:

grg

gg

r

r

r

g

aμμ

l S

aμμ

l S

aμμ

l S

aμμ

l Where S

SSSSce SlucTotal

0

330

33

220

22

110

11

321tanRe

Ring shaped series magnetic circuit with air-gap

Fringing Effect

• Air gap is practically an unavoidable part of any magnetic circuit, in which there is a relative movement between different parts.

(e.g. in motors, generators, relays, etc.)• Due to increased reluctance of the air gap the flux

spreads into the surrounding medium causing flux fringing effect.

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 7

Fringing Effect

Effectively it increases the cross sectional area of air gap.

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 8

Useful Flux and Leakage Flux

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 9

Magnetic leakage : The passage of magnetic flux outside the path along which it can do useful work.

Total flux of coil = Useful flux + Leakage flux

fluxUseful

coiloffluxTotalλtCoefficienLeakage

Magnetic Hysteresis:

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 10

Lagging of magnetization or flux density behind the magnetizing force.

Residual magnetism : Magnetic flux remains in the ferromagnetic material even though the magnetizing force is made zero (Br)

Coercive force : The magnetizing force required to remove the residual magnetism from the material (Hc). Hysteresis loop

Losses in Magnetic Circuit

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 11

Hysteresis loss

• The energy dissipated as heat in the process of magnetization and demagnetization which is proportional to the area of hysteresis loop.

• ‘Soft' magnetic materials with low hysteresis loss , such as silicon steel, are usually used in cores of electric machines like motors, generators and transformers.

Losses in Magnetic Circuit

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 12

• The varying flux in the magnetic core induces emf and hence eddy current within the material.

• Flow in closed loops in planes perpendicular to the magnetic field

• Results in loss of power and heating of the material.

Eddy current loss

• Cores of electric machines are laminated to reduce eddy current loss

Exercise 1ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 13

A steel ring 25cm mean diameter and of circular section 3cm in diameter has an air-gap of 1.5mm length. It is wound uniformly with 700 turns of wire carrying a current of 2A. Calculate (i) magneto motive force (ii) flux density (iii) magnetic flux (iv) reluctance and (v) relative permeability of steel ring.

Neglect magnetic leakage and assume that iron path takes about 35% of the total magneto motive force.

(i) 1400 AT(ii) 0.762 Wb/m^2(iii) 0.538mWb(iv) 2.6×10^6 AT/Wb(v) 972

Summary

Only one flux path is available in series magnetic circuit and equivalent reluctance is the sum of reluctance of different parts.

Losses occurring in magnetic circuits are classified as hysteresis and eddy current losses.

ELE 1001: Basic Electrical Technology

Dept. of E & E, MIT, Manipal 14