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The effect of higher harmonic components on MPIprocess
Pavel Stanek, Zbynek Skvor
Department of Electromagnetic FieldCzech Technical University in Prague
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 1 / 18
Content
1 MPI Principle
2 Magnetic field verification
3 Motivation
4 Impulse of the force
5 Magnetic field polarization
6 Results
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 2 / 18
MPI Principle
MPI Principle
MPI steps:
Generate magnetic field perpedicular to the defect (ideal case)(Verify the generated field)Apply detection particlesEvaluate the indications
Retrieved from: http://www.sssndt.com and http://shopndt.eu
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 3 / 18
MPI Principle
MPI Principle
MPI steps:
Generate magnetic field perpedicular to the defect (ideal case)(Verify the generated field)Apply detection particlesEvaluate the indications
Retrieved from: http://me.aut.ac.ir
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 3 / 18
MPI Principle
MPI Principle
MPI steps:
Generate magnetic field perpedicular to the defect (ideal case)(Verify the generated field)Apply detection particlesEvaluate the indications
Retrieved from: http://accutest-labs.com
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 3 / 18
Magnetic field verification
Magnetic field verification
Specimens with real well known defects
Measurement of tangential magnetic component by a gaussmeter
QQI - Quantitive Quality Indicators
0Retrieved from: http://www.qnde.ca
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 4 / 18
Motivation
Motivation
How to verify the field?
Need for a new method, which is
fast
clean
suitable for automation
→ Measure the field and calculate the impulse of the force
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 5 / 18
Impulse of the force
Impulse of the force
Definition:
I =
∫ t2
t1
F(H)dt
Why impulse of the force?
It combines the most critical parameters of the test
the force exert on a detection particle
time of duration
We need to know the leakage field above the defect and to calculate theforce moving the particles.
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 6 / 18
Impulse of the force
Force impulse
The leakage field components Hx, Hy and the force components Fx, Fy
were calculated by Edwards and Palmer 1
Fx = −8
3µ0πr
3H20 (∂Hx
∂x+Hx
∂Hx
∂x+Hy
∂Hy
∂x) = k(x, y, µ0, µ, a, b, r)H
20
H0
x
y
b
2a
µ0
µ
1Edwards, C., and S. B. Palmer. ”The magnetic leakage field of surface-breaking cracks.”Journal of
Physics D: Applied Physics 19.4 (1986): 657.
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 7 / 18
Magnetic field polarization
Magnetic field polarization
Example of parametricdescription of the polarization:
Hx = Acos(ωt)
Hy = Bsin(ωt)
Hx
Hy
H
A
B
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 8 / 18
Magnetic field polarization
Magnetic field polarization
Field functions are continuos and periodic→ describe them by Fourier series
H = H(Hx, Hy)
Hx =a02
+∞∑n=1
(ancos(nωt) + bnsin(nωt))
Hy =c02
+
∞∑n=1
(cncos(nωt) + dnsin(nωt))
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 9 / 18
Magnetic field polarization
Magnetic field polarization
n
H0
H
Hx
Hy
β
H0 = |H|cos(β) = |H| H · n|H| · |n|
= H · n
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 10 / 18
Magnetic field polarization
Magnetic field polarization measument2
−1 −0.5 0 0.5 1 1.5 2
−1
0
1
2
Hx(A/m)
Hy(A/m
)
2Stanek, P., Skvor Z. ”Experimental gaussmeter for circular magnetization.”NDT in PROGRESS,
IXth International Workshop of NDT Experts, Proceedings: Prague, 2017. ISBN 978-80-87012-63-5.
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 11 / 18
Results
Impulse of the force
I =
∫ T
0F(H)dt =
∫ T
0kH2
0dt =
=k
2f
[cos2(α)
(N∑
n=1
(a2n + b2n − c2n − d2n) +a202− c20
2
)+
+sin(2α)
(N∑
n=1
(ancn − bndn) +a0c0
4
)+
N∑n=1
(c2n + d2n) +c202
]
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 12 / 18
Results
Impulse of the force
The impuslse of the force terms
cos2(α)
(N∑
n=1
(a2n + b2n − c2n − d2n) +a202− c20
2
)
x
y
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 13 / 18
Results
Impulse of the force
The impuslse of the force terms
sin(2α)
(N∑
n=1
(ancn − bndn) +a0c0
4
)
x
y
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 14 / 18
Results
Impulse of the force
The impuslse of the force terms
N∑n=1
(c2n + d2n +c202
)
x
y
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 15 / 18
Results
Impulse of the force
Circular polarization
Polarization Impulse
Hx
Hy
x
y
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 16 / 18
Results
Impulse of the force
Elliptical polarization
Polarization Impulse
Hx
Hy
x
y
Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 17 / 18