5 Magnetic Inspection
Transcript of 5 Magnetic Inspection
5 Magnetic Inspection
5.1 Magnetic Laws
5.2 Magnetic Properties
5.3 Magnetic Measurements
5.4 Magnetic Materials Characterization
5.5 Magnetic Flaw Detection
5.1 Magnetic Laws
Magnetic Field
B
Q
Fm
dv
e QF E
m Q F v B
( )Q F E v B
F Lorentz force
v velocity
B magnetic flux density
Q charge
+I -I
B
pm magnetic dipole moment
(no magnetic monopole)
N number of turns
I current
A encircled vector area
m N Ip Apm
Magnetic Dipole in a Magnetic Field
+I
-I
pm
Fm
B m Q F v B
m m T p B
pm magnetic dipole moment
Q charge
v velocity
R radius vector
B magnetic flux density
Fm magnetic force
Tm twisting moment or torque
Fm
m1
2N I Q p A R v
Ampère’s Law
infinite straight wire
d
I
dℓ
R
H r ℓ
s
encd I H s
2H ds H R I
2
IH
R
24r
I dd
r
H e e
2 2 2 3/ 244 ( )
I d R I R dd
rr R
H e e
2 2 3/ 202 2( )
I R d IH
RR
Biot-Savart Law:
H magnetic field
I current
Induction, Faraday’s Law, Inductance
Φ magnetic flux
B magnetic flux density
Є induced electromotive force
S surface area of the loop
t time
B
Є
S
d B S
Єd
dt
I N
V
μ magnetic permeability
N number of turns
I current
Λ geometrical constant
L (self-) inductance
N I
Єd
V Ndt
I L
N
dIV L
dt
2L N
5.2 Magnetic Properties
Magnetization
M magnetization
V volume
χ magnetic susceptibility
H magnetic field
B magnetic flux density
μ0 permeability of free space
μr relative permeability
μ magnetic permeability
pm magnetic dipole moment
N number of turns
I current
A encircled vector area
m N Ip A+I -I
m
V
pM
M H
0 0 r( ) B H M H
r 1
B H
0 r
Classification of Magnetic Materials
Diamagnetism:
μr < 1
no remanence
orbit distortion
e.g., copper, mercury, gold, zinc
Paramagnetism:
μr > 1
no remanence
orbit and spin alignment
e.g., aluminum, titanium, platinum
Ferromagnetism:
μr >> 1
remanence, coercivity, hysteresis
self-amplifying paramagnetism
e.g., iron, nickel, cobalt
pm magnetic dipole moment
pspin electron spin
porb electron orbital motion
N number of turns
I current
A encircled area
e charge of electron
τ orbital period
r orbital radius
v orbital velocity
Ei induced electric field
Fe decelerating electric force
m mass of electron
χ magnetic susceptibility
Diamagnetism
v e
Fm
B
v e Fe
B
ieF eE
mF ev B
m orb spin p p p
2
orb2
e A e r vp N I A
r
orb2
er vp
2 22 20
orb4 4
e re rp B H
m m
ei2 2
Fdr E r
dt e
2d m dv
rdt e dt
2 2m
B r r ve
2
erv B
m
- χ ≈ 1-10 ppm
Paramagnetism
m orb spin p p p
pm magnetic dipole moment
B magnetic flux density
Fm magnetic force
Tm twisting moment or torque
U potential energy of the dipole
kB Boltzmann constant
T absolute temperature
N moments within unit volume
χ magnetic susceptibility
m m T p B
mU p B
m0 0
( ) sinU T d p B d
m (1 cos )U p B
m m sinT p B
B( )
U
k Tp U e
20
B3
N mM C
H k T T
Langevin model:
χ ≈ 5-50 ppm
+I
-I
pm
Fm
B
Fm
Tm
θ
Ferromagnetism
(i) magnetic polarization is produced by collective action of
similarly oriented spins within magnetic domains
(ii) very high permeability
(iii) magnetic hysteresis
(v) remnant magnetic polarization (remanence)
(vi) coercive magnetic field (coercivity)
(iv) depolarization above the (magnetic) Curie temperature
H
B
Br
Hc
first magnetization
Magnetic Domains in Single Crystals
easy magnetic axes
H = 0
H
H
H
1 demagnetization
(spontaneous magnetization)
4 technical saturation
3 “knee” of the
magnetization curve
2 partial magnetization
domain wall
movement
irreversible
rotation
reversible
rotation
H
B
1
2
3 5 4
5 full saturation
(no precession) thermal precession not shown
5.3 Magnetic Measurements
Magnetic Sensors
10-2
10-1
100
101
102
103
104
105
0 5 10 15 20 25
Frequency [Hz]
Flu
x D
ensi
ty [
pT
/Hz1
/2]
Hall
GMR
SDP
fluxgate
SQUID
noise threshold of key magnetic detectors
axialaxial
dV N i N AB
dt
coil:
ferromagnetic powder, filing
Hall Detector
.
I I
a
b
x
y z
x x
B z
VH
Fm
Fe
( )Q F E v B
( ) 0y y x zF e E v B
Hy
VE
a
x xI env ab
Hx
y x z zI
V a E av B Benb
HH
x zR I BV
b
H1
Ren
5.4 Magnetic Materials
Characterization
Magnetic Properties
-1.5
-1
-0.5
0
0.5
1
1.5
-5 -4 -3 -2 -1 0 1 2 3 4 5
Magnetic Field [kA/m]
Flu
x D
ensi
ty [
Tes
la]
hardened steel
soft iron
( , )pB B H Mferromagnetic materials:
para- and diamagnetic materials: 0 ( )B H M
M H
0 rB H
r 1
Initial Magnetization
anhysteretic initial magnetization curve
Flux Density
Differential Permeability
Magnetic Field
Flu
x D
ensi
ty
B magnetic flux density
H magnetic field
M magnetization
µ0 permeability of free space
µd differential permeability
M0 saturation magnetization
n dipoles per unit volume
pm magnetic dipole moment
ddB
dH
0limH
M M
0 ( )B H M
0 mM n p
Texture, Residual Stress
-2
-1
0
1
2
-300 -200 -100 0 100 200 300 Magnetic Field [A/m]
Flu
x D
ensi
ty [
T]
σ = 0 MPa B||
B
-2
-1
0
1
2
-300 -200 -100 0 100 200 300 Magnetic Field [A/m]
Flu
x D
ensi
ty [
T]
σ = 36 MPa B||
B
-2
-1
0
1
2
-300 -200 -100 0 100 200 300 Magnetic Field [A/m]
Flu
x D
ensi
ty [
T]
σ = 183 MPa B||
B
-2
-1
0
1
2
-300 -200 -100 0 100 200 300 Magnetic Field [A/m]
Flu
x D
ensi
ty [
T]
σ = 110 MPa B||
B
mild steel
Barkhausen Noise
H = 0
H
domain wall
movement H
B
magnetic field Barkhausen noise
Am
pli
tud
e
Time
• magnetic Barkhausen noise
• acoustic Barkhausen noise
5.5 Magnetic Flaw Detection
Magnetic Flux Leakage
Advantages:
fast
inexpensive
large, awkward shaped specimens (particle)
Disadvantages:
material sensitive
poor sensitivity
poor penetration depth
ferromagnetic test piece
sensor
Hall cell, etc.)
(small coil,
exciter coil
Magnetic Boundary Conditions Ampère's law:
H J
Gauss' law:
0 B
I,n II,nB B I,t II,tH H
xt
medium I
medium II
BI I
boundary
BII
BII,t
BII,n
II
BI,n
BI,t
xn
xt
medium I
medium II
HI
I
HII
HII,t
HII,n
II
HI,n
HI,t
xn
I I,n II II,nH H I I,n II II,ntan tanH H
I II
I II
tan tan
Magnetic Refraction
I II
I II
tan tan
µI/µII =
10
30
100
0 15 45 60 75 90 0
15
30
45
60
75
90
30
Ferromagnetic Angle, θI [deg]
Nonm
agnet
ic A
ngle
, θ
II [
deg
]
medium I
(ferromagnetic)
BI
BII II
I
medium II
(air)
medium I
(ferromagnetic) BI
BII
II
I
medium II
(air)
Exciter Magnets
electromagnet
air gap
ferromagnetic core
H d N I MMF
0 r H A
0 r
MMF dA
mMMF
R
m0 r 0 r
1 1 i
i i i
dR
A A
H magnetic field
N number of turns
I excitation current
MMF magnetomotive force
Φ magnetic flux
ℓ length of flux line
µ0 µr magnetic permeability
A cross section area
Rm magnetic reluctance
Yoke Excitation
Detection Methods:
magnetic particle
(gravitation, friction, adhesion,
cohesion, magnetization)
magnetic particle with ultraviolet paint
coil
Hall detector, GMR sensor
fluxgate, etc.
Lateral Position
Tan
gen
tial
Mag
net
ic F
ield
Lateral Position
Norm
al M
agnet
ic F
ield
electromagnet
crack
N I
magnetometer
Subsurface Flaw Detection
H
B
1
2
saturation greatly reduces the differential permeability
crack
1) low magnetic field
crack
2) high magnetic field