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The effect of higher harmonic components on MPI process Pavel Stanˇ ek, Zbynˇ ek ˇ Skvor Department of Electromagnetic Field Czech Technical University in Prague [email protected] Pavel Stanˇ ek, Zbynˇ ek ˇ Skvor The effect of higher harmonic components on MPI process 1 / 18

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The effect of higher harmonic components on MPIprocess

Pavel Stanek, Zbynek Skvor

Department of Electromagnetic FieldCzech Technical University in Prague

[email protected]

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

Results

Thank you for attention

Questions?

Pavel Stanek, Zbynek Skvor The effect of higher harmonic components on MPI process 18 / 18