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Magnetic Flux Leakage Method 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 DefinitionThe 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 SpecimenThe 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 CurrentThe 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.
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
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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