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Magnetic Flux Leakage Method I

Magnetic Flux Leakage Method II

Eddy Current I

Eddy Current II

Benchmark Problem I

Magnetic Flux Leakage Method I

Objective:

The purpose of the benchmark study is to compare simulation results predicted by models developed and/or used by member centers. The ground truth for the study will be obtained through careful experimental work.

Problem Definition

The problem involves prediction of the radial, axial and circumferential components of the magnetic flux leakage signal around defects machined on a steel pipe. The excitation field is provided by passing D.C. current through a copper rod that runs the entire length of the pipe and is concentrically located along the pipe’s axis. Figure 1 shows a diagram of the test specimen.

Test Specimen

The pipe, which has an external diameter of 29.85 mm and has wall thickness of 4.77 mm, is made from steel. Table I describes points along the magnetization characteristic. Four defects are machined on the outer surface of the pipe. The first defect consists of an axisymmetric slot on the outer diameter that is 1 mm wide and 1.2 mm deep. The second defect is a rectangular slot that is 10 mm long, 0.25 mm wide and 1.2 mm deep. The defect is oriented longitudinally along the axis of the pipe. The third and fourth defects are similar to the second defect, except that they are 0.25 mm wide 2.4 mm deep and 0.5 mm wide and 2.4 mm deep. The third and fourth defects are also oriented longitudinally along the axis of the pipe. The copper rod is 14.35mm in diameter and is located concentrically along the axis of the pipe, as shown in Figure 1.

Excitation Current 

The copper rod carries an excitation current of 500 Amperes DC.

Scan Plan

Defect 1 – Radial and circumferential components of the leakage field will be measured, directly above the axisymmetric defect. A total of 101 measurements of each component, spaced 0.2 mm apart, with 50 points on either side of slot, will be taken. The lift-off is 1mm.

Defects 2, 3 and 4 – Radial, axial and circumferential components of the leakage field will be measured by scanning the pipe along five paths in the circumferential direction. The first scan will pass through the mid-point of the slot, and the remaining four on the end-points of the slot, and two points half way between the mid-point and the end-points. Each scan will have a  total of 101 measurements spaced 0.2 mm apart, with 50 points made on either side of the defect. The lift-off is 1 mm.

Sensors

The leakage field measurements will be made using a Hall sensor with an active area of 0.5mm x 0.5mm.

Problem

Predict the radial, axial and circumferential components of the field for each of the defects. The results will be compared with experimental results.

 

 

Benchmark Problem II

Magnetic Flux Leakage Method II

Objective:

 The purpose of the benchmark study is to compare simulation results by models developed and/or used by member centers, and validate them with laboratory measurements.

 Problem Definition

 The problem involves the prediction of the radial component of the magnetic flux leakage signal in the vicinity of notches machined on a rotating steel pipe. A photo of the experimental setup is shown in Fig. 1 of reference [1]. A sketch of the yoke and pipe is shown in the enclosed figure (not in scale). The coordinate origin in this figure lies on the tube surface. The problem is approximately 2-dimensional in the x-z plane, but involves a moving notch. Measurements with angular velocities higher than the values given below will be attempted, but we are not sure that they will be possible. A table with the approximate correspondence between the field H and the induction flux density B for the steel pipe is given in the appendix.

 

 

The average gap between the yoke and the tube is equal to 10 mm. The remaining set-up parameters are:

 Yoke vertical span:   153 mm

Yoke horizontal span:   405 mm

External pipe radius:   88.7 mm

Internal pipe radius:    81.1 mm

Pipe angular velocity:  20 and 40 RPM.

(The upper side of the pipe moves in the positive x direction, parallel to the applied magnetic field).

 Notch 1:

            location: external

            width (in the x direction):   0.965  mm

            depth  (in the z direction):   0.96   mm

            length (in the y direction):   25     mm

Notch 2:

            location: internal

width (in the x direction):   0.96  mm

            depth  (in the z direction):   0.96   mm

            length (in the y direction):   25     mm

 

The vertical component of the magnetic field  Hz  will be measured using a Hall probe at a sampling rate of 4Khz at the following location:

x =   0.0 mm

z =   1.0 and 2.0 mm (therefore. 1.0 and 2.0 mm are the values of the lift-off)

y =   half-way across the yoke horizontal span; also half way along the notch length.

 

The magnetizing current will be adjusted so that with a stationary pipe the value of Hx in the absence of notch will be equal to 20.0 kA/m.

 

 

  Sketch of the experimental set-up

 

 

Reference [1]: R. Perazzo et al., “Feature extraction in MFL signals of machined defects in steel tubes”, Review of Progress in QNDE, AIP Conference Proceedings, Vol 20A, pp.619-626,  july 2000.

 

Appendix

A table with the approximate correspondence between the field H and the induction flux density B for the steel pipe follows:

 Field H          Induction B

   (A/m)         (Tesla)

   0000.000      0.00

   69.31499     0.037192

   138.6272     0.074186

   207.9449     0.110785

   276.6213     0.146654

   343.7324     0.181711

   408.6425     0.216253

   472.4385     0.250532

   537.0279     0.284769

   604.3266     0.319188

   676.2394     0.354010

   754.6848     0.389459

   840.8746     0.425764

   933.9939     0.462787

   1032.314     0.500260

   1134.825     0.538021

   1241.691     0.575871

   1353.063     0.613615

   1469.112     0.651054

   1589.986     0.687991

   1716.621     0.724552

   1848.958     0.761117

   1986.476     0.797806

   2129.772     0.834512

   2279.177     0.870986

   2434.999     0.906984

   2597.566     0.942255

   2767.191     0.976554

   3010.402     1.015572

   3221.556     1.055990

   3406.917     1.085904

   3597.585     1.114930

   3795.630     1.143262

   4003.121    1.171100

   4222.128     1.198642

   4455.046     1.225981

   4703.831     1.253198

   4969.650     1.280644

   5250.915     1.308347

   5544.920     1.335982

   5848.951     1.363232

   6160.309     1.389772

   6476.283     1.415282

   6796.000     1.439404

   7118.265     1.461762

   7443.048     1.482327

   7771.922     1.501418

   8104.087     1.519206

   8438.743     1.535865

   8775.096     1.551568

   9112.357     1.566489

   9450.965     1.580742

   9792.127     1.594475

   10138.88     1.607623

   10492.49     1.620023

   10850.55     1.631745

   11210.68     1.642867

   11570.50     1.653461

   11927.61     1.663601

   12162.92     1.678606

   12979.76     1.704768

   13853.83     1.729369

   14775.76     1.752588

   15735.84     1.774606

   16724.61     1.795601

   17732.54     1.815756

   18749.93     1.835251

   19748.24     1.853644

   20724.30     1.870575

   21706.71     1.886345

   22724.10     1.901254

   23805.24     1.915601

   24978.66     1.929689

   26273.14     1.943817

   27717.29     1.958285

   29319.02     1.973223

   31054.61     1.988402

   32904.74     2.003582

   34850.41     2.018520

   36872.55     2.032978

   38952.00     2.046715

   41069.60     2.059491

   43206.36     2.071065

   45282.63     2.081138

   47282.43     2.089809

   49282.24     2.097439

   51358.51     2.104387

   53587.63     2.111016

   56045.99     2.117684

   58810.05     2.124752

   61956.29     2.132582

   65535.57     2.141203

   69497.03     2.150285

   73764.18     2.159646

   78260.58     2.169108

   82909.83     2.178489

   87635.55     2.187611

   92361.26     2.196292

   97010.51     2.204352

   101643.9     2.211741

 

Eddy Current Problem I

 

In Figure 1 the support plate is presented.

In the first step I propose calculations for the model presented in Figure 2. Two identical coils (each coil is wounded by N=1000 turns, diameter of wire is equal to 0,1mm, material Cu)   connected differentially move along the infinitely long tube. The changes of the impedance DZ should be calculated and presented in a complex plane. The same calculations should be done for the models presented in Figures 3, 4 and 5.

Coils are energised by an impressed AC current. Frequency of the impressed current f=1, 10, 100 and 200 kHz.

Another data for the calculations:

D1=19,7mm, D2=22,24mm, D3=9mm, D4=19mm, D5=D2 or 24,24mm, h1=0,2mm, h2=0,3mm, h3=0; 0,1 or 1mm, h4=2mm, h5=4mm, I=10mA, tube made of INCONEL 600 s1=106S/m, m1=m0, supporting plate made of ferromagnetic steel d=20mm, s2=106S/m, m2=103m0, d1@d2>>D2 .

In the second step I propose experiments made by using the differentially connected coils or using probes constructed by participants.

The third step: solution of the inverse problem.

 

 

Eddy Current Benchmark Problem II

 

The second eddy current benchmark problem is shown in Figure 1. The objective of the exercise is to predict the change in the impedance of the pancake coil impedance, DZ, as it moves past the defect. The Inconel tube has an inside diameter Di =19.69 mm and an outside diameter D0 = 22.23 mm.  The tube contains a flaw whose depth h can vary between 20% and 60% of the tube wall thickness. Other dimensions of the flaw are shown in Figure 1.

 The dimensions of the pancake coil are defined in Figure 2. The coil consists of 400 turns and is energised by an AC current (I=100mA) whose frequency is f =100, 150and 200 kHz. The probe is moved in 1 mm steps along the axial direction and in steps of 10° along the circumferential direction. The coil movement is restricted to a range of 10 mm and 40° on either side of the defect. This corresponds to 10 steps along the axial direction and 4 steps along the circumferential direction on either side of the defect.

 

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