Magnetic inspection

8/10/2019 Magnetic inspection

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Magnetic Inspection


2/15

Magnetic Flux Leakage

Ferromagnetic Testpiece

Exc ter o

Sensor

Hall cell, etc.)

(small coil,

Advantages:

fast, inexpensivelarge, awkward shaped specimens (particle)

Disadvantages:

material sensitive

poor sensitivity

poor penetration depth


3/15

Elactromagnetics

Lorentz Force:

( )Q= + F E v B

Electrostatic force, Coulomb's law

1 224

e rQ Q

r=

F e

Magnetic force

Fm r

p p

r= 1 2

24e

Maxwell's Equations:

Ampre's law: = +H JD

t

Faraday's law:

t

=

BE

Gauss' law: q =D

nonexistence of magnetic monopole: =B 0

Constitutive relationships:

conductance = J E

permeability B H=

permittivity = D E


4/15

Magnetic Fields of Steady Currents

Biot-Savart Law

x2

x3

x1

Ie

d

r

er

dHP

24

rI ddr

=e eH

or24

rI d

r=

e eH

Infinitely long, straight, filamentary current:

rI

H

2 2 2 23/ 2 3/ 2

( )

4 ( ) 4 ( )

z r z I dzrI dz r z

dr z r z

= = + +

ee e eH

2 2 3/ 2 24 ( )I r Idz

rr z

= = +

H e e

Ampre's law:

=H J , d I =H


5/15

Magnetic Fields of Coils

single-turn circular coil,

2c

IH

a

=

solenoid of 1L a =/ solenoid of 3L a =/

( )cN I

HL

=


6/15

Infinitely Long Solenoid

dense coil:

1n a>>

where n denotes the number of turns over a unit length

current sheet of density sJ n I=

Js

+Js-

inside loop outside loopencircling

loop

2a

L

1 2( ) ( ) 0z zH d L H r L H r = =

( ) ( )z z sH d L H r a L H r a L J = > < =

z sH J N I L n I= = =/


7/15

Magnetism in Materials

0 0 ( )r= = = +B H H H M

1 1r = + = + M

H

0 permeability of vacuum, 74 10 H/ m

r relative permeability

magnetic susceptibility

[] = Vs/A = Henry

[B] = Vs/m2= Tesla

[H] = A/m

Diamagnetism:1r <

not remanentorbit distortion

mercury, gold, zinc

Paramagnetism:1r >

not remanent

orbit and spin alignment

aluminum, copper, platinum

Ferromagnetism:1r >>

remanent

self-amplifying paramagnetism

iron, nickel, cobalt


8/15

Ferromagnetism

(i) magnetic polarization is produced by collective action of similarly

oriented molecules within domains

(ii) magnetic hysteresis

(iii) very high permeability

(v) remnant magnetic polarization (remanence)

(vi) coercive magnetic field (coercivity)

(iv) depolarization above the (magnetic) Curie temperature

H

B

Br

Hc

first magnitazitionreversible boundary displacement

irreversible boundary displacement

magnetization rotation


9/15

Domain Movements During Reversible

Boundary Displacement

H


10/15

Magnetic Boundary Conditions

Ampre's law: = +H JD

t

nonexistence of magnetic monopole: =B 0

xt

xn

BII,n

B II,t

BI,t

B I,n

medium I

medium II

BI

BII

I

IIboundary

boundaryxt

xn

HII,n

HII,t

HI,t

HI,n

medium I

medium II

HI

HII

I

II

The normal component of the magnetic flux density is continuous:

I, II,n nB B=

The tangential component of the magnetic field intensity is continuous:

I, II,t tH H=

tan

tan

II

I

II

I=


11/15

Toroid of Different Materials

electromagnet or permanent magnet

air gap

core

Ampre's law

d N I=H

total magnetic flux

0 rH A =

magnetomotive force

0 r

MMF N I dA

= =

magnetic flux

MMF

R =

magnetic reluctance

0 0

1 i

ir ri i

dR

A A=


12/15

Excitation Methods

yoke with adjustable legs

electromagnet

crack

N I I

magnetometer

Lateral Position

Tangen

tialMagneticField

Lateral Position

Norm

alMagneticField


13/15

Subsurface Flaw Detection

saturation method

electromagnet

crack

N I I

low magnetic field

crack

high magnetic field


14/15

Detection Methods

magnetic particle

(gravitation, friction, adhesion, cohesion, magnetization

magnetic particle with ultraviolet paint

coil

Hall detector

fluxgate

etc.


15/15

Hall Detector

I I

a

b

x

yzx x

Bz

VH

Lorentz Force:

( )Q= + F E v B

( ) 0y y x zF e E v B= + =

Hy

VE

a=

x xI en v a b=

xH y x z zI

V a E a v B Benb= = =

H x zH

R I BV

b=

Magnetic inspection

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