Transcript MExxxElectromagnetic NDE - University of Cincinnati

5 Current Field Measurement
5.1
Alternating Current Field Measurement
5.2
Direct Current Potential Drop
5.3
Alternating Current Potential Drop
5.1 Alternating Current
Field Measurement
Principle of Operation
magnetic injection:
normal (z)
primary
ac flux
transverse (y)
axial (x)
magnetometer
magnetic
flux
density
galvanic current injection

electric field
Field Perturbation
normal (z)
Bz [a.u.]
transverse (y)
axial (x)
axial scanning
above flaw
Bz < 0
Bz [a.u.]
Axial Position
magnetometer
cw current
electric
current
axial flaw
Bz > 0
Bx0
Bx [a.u.]
Bx [a.u.]
magnetic
flux
density
ccw current
Axial Position
Uniform Field
effect of coating thickness on axial magnetic flux density Bx
(ferrous steel, 5 kHz, δ  0.25 mm, 30-mm-long solenoid)
8
advantages:
testing through coatings

depth information
6

limited boundary effects
5
ΔBx [%]

disadvantages:
slot size
7
50  5 mm
20  2 mm
20  1 mm
4

reduced sensitivity
3

sensitivity to geometry
2

flaw orientation
1
0
0
5
10
15
Coating Thickness [mm]
20
Axial Flaw
(parallel to B, normal to E)
rate of increase of the minimum of Bx with
slot depth at the center
2-mm-diameter coil, ferrous steel
30
Bx at 5 kHz
7
Bz at 5 kHz
25
6
ΔBx and ΔBz [%]
ΔBxm per 1 mm Slot Depth [%]
8
5
4
3
40-mm-long
solenoid
2
Bz at 50 kHz
20
15
10
5
12-mm-long
solenoid
1
Bx at 50 kHz
0
0
0
10
20
30
Slot Depth [mm]
40
0
changes normalized to Bx0
0.5
1
1.5
Slot Depth [mm]
2
2.5
Flaw Orientation
0.17
0.025
0.16
0.020
axial flaw
(normal to E)
0.150
Bz [T]
Bx [T]
0.15
transverse flaw
(normal to B)
0.14
0.13
0.100
axial flaw
(normal to E)
0.05
transverse flaw
(normal to B)
0.12
0
0.11
-0.05
0
1
2
3
Scanning time [a. u.]
4
5
eddy current mode
magnetic flux mode
0
1
2
3
4
Scanning Time [a. u.]
5
Magnetic Flux Mode
N
I
electromagnet
magnetometer
Normal Magnetic Field
Tangential Magnetic Field
crack
Lateral Position
Lateral Position
5.2 Direct Current
Potential Drop
Inductive versus Galvanic Coupling
magnetic field
injection
I
current
potential
drop
V
I
probe coil
specimen
specimen
eddy currents
electric current
advantages of galvanic coupling
dc and low-frequency operation
constant coupling (four-point measurement)
awkward shapes
absolute measurements
inherently directional
Thin-Plate Approximation
I (+) V (+)
2a
2b
combined electric current and potential field
V (-)
I (-)
t << a
V (+)
V (-)
I (+)
E (r )   J (r ) 
I
2r t

I   dr
V (r )   E (r ) dr 

2

t
r
r r
V (r )  
I
ln r  const
2 t
I (-)
V  V (  )  V (  )
V  2V (a  b)  V (a  b)
V 
I a  b
ln
t a  b
Lateral Spread of Current Distribution
J (r ) 
I
2r t
y
J (0,0) 
J(0,w)
V (+)
2w
V (-)
I (+)
J (0, w) 
I (-)
J(0,0)
x
I
at
2I
a
2  a 2  w2 t a 2  w2
J (0, w) 
Ia
 ( a 2  w2 ) t
J (0,0)
 2
J (0, w2 )
2a
a 2  w22
J (0,0)

2
J (0, w2 )
a2
w2  a
Thick-Plate Approximation
combined electric current and potential field
2a
2b
I (+)
V (+)
I (+) V (+)
V (-)
V (-) I (-)
I (-)

t >> a
E (r )   J (r ) 

V (r )   E (r ) dr 
r
V (r ) 
I
2r2
I   dr

2 r r2
I
 const
2r
V  V (  )  V (  )
V  2V (a  b)  V (a  b)
V 
I 1
1 

  a  b a  b 
Finite Plate Thickness
2a
2b
n = +2
I (+) V (+)
I (+)
I (-)
n = +1
V (r ) 
V (+)
n=0
V (-)

I
2
2 1/ 2
n   2 [r  (2 nt ) ]

2t
t
I  
1
V 
 
 n    [(a  b)2  (2 nt )2 ]1/ 2

n = -1
n = -2
V (-) I (-)

1

[(a  b)2  (2 nt ) 2 ]1/ 2 
Resistance versus Thickness
R 
1 ab
lim  
ln
t a  b
t 0
V
 
I
lim  
t 
2
b
 a 2  b2
Normalized Resistance, Λ
10
a = 3b
finite thickness
thin-plate appr.
thick-plate appr.
1
0.1
0.01
0.1
1
10
Normalized Thickness, t / a
100
Crack Detection by DCPD
intact specimen
I (+)
V (+)
V (-)
cracked specimen
I (-)
I (+)
V (+)
V (-)
I (-)
c
t
V ( )  V ( )  V0
V ( )  V ( )  Vc
Normalized Potential Drop, ΔVc / ΔV0
infinite slot
3
a = 3b
2
a/t=
0.44
1.2
1.8
1
0
0.2
0.4
0.6
0.8
Normalized Crack Depth, c / t
1
Technical Implementation of DCPD
power
supply
+
_
polarity
switch
+
_
electrodes
Vs
specimen
•
•
•
•
•
low resistance, high current
thermoelectric effect, pulsed, alternating polarity
control of penetration via electrode separation
low sensitivity to near-surface layer
no sensitivity to permeability
5.3 Alternating Current
Potential Drop
Direct versus Alternating Current
DCPD
ACPD
•
•
•
•
•
higher resistance, lower current
no thermoelectric effect
control of penetration via frequency
higher sensitivity to near-surface layer
sensitivity to permeability
Thin-Plate/Thin-Skin Approximation
2a
2b
I (+) V (+)
V (-)
I (-)
t << a
V
 ab

ln
t a  b
f 0 I
lim

ab
 V 
Re 
ln
 
 I  T a  b
T  min t , 
 

f
 V 
lim Re 

f 
 I 
f  a  b
ln

ab
Skin Effect in Thin Nonmagnetic Plates
analytical prediction
a = 20 mm, b = 10 mm, σ = 50 %IACS
a = 20 mm, b = 10 mm, t = 2 mm
103
1 %IACS
2 %IACS
5 %IACS
10 %IACS
20 %IACS
50 %IACS
100 %IACS
102
101
100
100
Resistance [µΩ]
Resistance [µΩ]
103
ft
101
102 103 104
Frequency [Hz]
102
101
100
100
105
( f  f t )  t
ft 
1
0  t 2
0.05 mm
0.1 mm
0.2 mm
0.5 mm
1 mm
2 mm
5 mm
ft
101
102 103 104
Frequency [Hz]
105
Skin Effect in Thick Nonmagnetic Plates
304 austenitic stainless steel, σ = 2.5 %IACS, experimental
a = 10 mm, b = 7.5 mm
104
0.05 mm
0.1 mm
Resistance [µΩ]
0.2 mm
0.5 mm
103
1 mm
2 mm
2.5 mm
6.25 mm
102
10 mm
20 mm
50 mm
101
100
101
102
103
Frequency [Hz]
104
105
Current Distribution in Ferritic Steel
FE predictions (Sposito et al., 2006)
f = 0.1 Hz
f = 50 Hz
f = 1 kHz
a = 10 mm, b = 5 mm, t = 38-mm, c = 10 mm
(0.5-mm-wide notches, two separated by 5 mm)
Thin-Skin Approximation
2a
2b
R0 
Z 
2a
2b
V
 R iX
I
 ab
ln
 a  b
c
Rc 
Rc  R* c
R0  R*  0
0  ln
ab
ab
 c  ln
2
Electrode Gain, 0
 a  b  2c
ln

ab
R* 
1
Kc 
0
1
2
Electrode Shape Factor, a / b
3
a  b  2c
ab
f 

Rc  R0
  0
 c
R0
0
1 2c
lim K c 
0 a  b
c0
Technical Implementation of ACPD
Vr
low-pass
filter
A/D
converter
oscillator
90º phase
shifter
differential
driver
+
Vq
low-pass
filter
Vs
PC
processor
_
electrodes
specimen
frequency range: 0.5 Hz - 100 kHz
driver current: 10-200 mA
resistance range: 1-10,000 µΩ
common mode rejection: 100-160 dB
.
Application Example: Weld Penetration
clamshell
catalytic converter
2 d = 0.120”
welding
current
injection
edge weld
voltage
sensing
weldment
a = 0.160”
b = 0.080”
d
w = 0.054”
w
electrode separation (b)
weld penetration (w)
80
Fracture Surface [mils]
Resistance [µΩ]
200
150
100
b=
120 mils
100 mils
80 mils
50
0
0
20
40
60
80 100
Weld Penetration [mil]
120
70
60
50
40
30
20
10
0
0
10
20
30 40 50
NDE [mil]
60
70
80
Application Example: Erosion Monitoring
Resistivity [µΩ cm]
(T )  0 [1   (T  T0 )]
internal
erosion/corrosion
pipe
130
120
110
100
90
80
70
60
50
β  0.001 [1/ºC]
301
302
303
304
309
310
316
321
347
403
0
200
400
600
Temperature [ºC]
33.0
25
33.0
24
32.8
24
32.8
23
32.6
23
32.6
22
32.4
22
32.4
21
32.2
Temperature [ºC]
25
21
32.2
erosion
erosion
20
32.0
0
5
10
Time [day]
15
20
20
32.0
0
5
10
Time [day]
15
20
Resistance [µΩ]
after compensation
Resistance [µΩ]
Temperature [ºC]
before compensation
800