design and analysis of rotating field eddy current probe for tube inspection

DESIGN AND ANALYSIS OF ROTATING FIELD EDDY CURRENT PROBE FOR TUBE INSPECTION By Junjun Xin

A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering—Doctor of Philosophy 2014

ABSTRACT DESIGN AND ANALYSIS OF ROTATING FIELD EDDY CURRENT PROBE FOR TUBE INSPECTION By Junjun Xin Steam generator unit in nuclear power plant comprise thousands of heat exchange tubes whereby heat from primary coolant is transferred to water circulating on the secondary side. A variety of tube degradation due to mechanical vibration and chemical interactions compromises the integrity of steam generator tubes. The rupture of these tubes may result in leakage of radioactive water to the environment. Periodic inspections aimed at timely detection and characterization of the degradation is a key element for ensuring tube integrity and safe operation of nuclear power plant. Eddy current testing has proved to be an effective technique to detect defects occurring in the tube wall. In the past two decades, three types eddy current probes developed for steam generator tube inspection include bobbin coil probe, rotating probe and array probe. Each of these probes has their own limitations. The bobbin coil probe is insensitive to circumferential cracks, and rotating probe is slow and involves complex mechanical rotation whereas the array probe has poor resolution and high cost of instrumentation. This dissertation presents the design and validation of a new rotating field eddy current probe. The probe is composed of three phase rectangular windings and pickup sensor, that can be chosen to be a simple bobbin coil or a GMR array sensor placed at the probe center. The probe avoids mechanical rotation and has fast scan speed. The rotating field probe is sensitive to all orientation defects. The axial component of magnetic field along the tubing due to a defect is measured by the pickup sensor. The probe design and performance are evaluated using an experimental validated finite element model. A reduced magnetic vector potential formulation

is used for simulating the different commercial probe as well as the proposed new probe design. A probe prototype is built to validate the simulation results with respect to different defects. A parametric study is conducted using the model to optimize the design and evaluate its performance. An encircling rotating field eddy current probe utilizing similar principles is also studied in this research. A design of a rotating field probe that encircles a cylindrical sample is presented and studied. Differences in the performance in cases of magnetic and nonmagnetic tube materials are described. Initial results show the feasibility of rotating field probes to detect a variety of defect geometries.

Dedicated to: My Parents Tao Xin and Fengzhen Shu My Wife Qin Lei

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ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to my PhD advisor, Dr. Lalita Udpa, for her continuous support and always encouragement during my graduate study. I am also very grateful for her financial support, academic guidance, intellectual and insightful discussions for my dissertation. Dr. Lalita Udpa inspires me deeply with her own passion and dedication to be an outstanding scientific researcher and excellent teacher. I really appreciate all the helps from her every time when I encountered with difficulties. I also would like to express my sincere gratitude to Dr. Satish Udpa for his numerous guidance and support as my professor within NDEL and my committee member. I also would like to thank my committee members: Dr. Edward Rothwell, Dr. Guowei Wei and Dr. S. Ratnajeevan H. Hoole for taking the time to serve on my committee and for providing invaluable comments and suggestions to my dissertation. My studies were partly supported by Electrical Power Research Institute (EPRI). Their support is gratefully acknowledged. I would like to thank Jim Benson and Rick Williams for continuous financial support and numerous discussions. Their support is a key factor for me to finish my dissertation and my research project. I would like to thank all the people who have helped and inspired me during my graduate study. Thanks Dr. Zhiwei Zeng, Dr. Yiming Deng and Dr. Xin Liu for paving the way for us on the EPRI project and theoretical and practical guidance though the emails. Thanks Naiguang Lei, Chuck Bardel, Dr. Guang Yang, Dr. Tariq Khan, Dr. Anton Khomenko, Morteza Safdarnejad and Saptarshi Mukherjee for the close collaboration and numerous discussions on the SGTSIM and finite element modeling work. Thanks Eric Tarkleson, Jeremy Phillips, Charles Maines, Ruizhi

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Mao, Chaofeng Ye and Apita Chand for building the probe prototype and experimental measurements. Thanks Brian Wright and Gregg Mulder for their help on setting up the probe auto scan system. Thanks Dr. Young-Kil Shin and Dr. Theodoros Theodoulidis for discussing on modeling, simulation and experiments. I also would like to thank all the other colleagues Zhiyi Su, Gerges Dib, Pavel Roy Paladhi, Amin Tayebi, Portia Banerjee, Oleksii Karpenko and Ahmed Zaki Alsinan in NDEL for the cooperation and friendship. Finally and most importantly, I would particularly like to thank my wife Qin Lei for her unlimited support, encouragement and love. I also would like to thank my beloved parents Tao Xin and Fengzhen Shu for their unconditional love and care for years. Their love to me and my love to them are always my greatest motivation in my life. Thank you!

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TABLE OF CONTENTS

LIST OF TABLES............................................................................................................. x LIST OF FIGURES ......................................................................................................... xi CHAPTER 1 INTRODUCTION ..................................................................................... 1 1.1. Introduction ............................................................................................................ 1 1.1.1. Steam Generator Tubes .................................................................................. 1 1.1.2. Defect Types ..................................................................................................... 5 1.2. Introduction to Eddy Current Testing ................................................................. 6 1.2.1. Principles ......................................................................................................... 6 1.2.1.1 Penetration Depth ......................................................................................8 1.2.1.2 Equivalent Circuit ......................................................................................9 1.2.2. Applications ................................................................................................... 10 1.2.3. Advantages and Disadvantages.....................................................................11 1.3 Scope of the thesis ..................................................................................................11 CHAPTER 2 REVIEW OF EDDY CURRENT PROBES AND SENSORS ............. 14 2.1. Introduction .......................................................................................................... 14 2.1.1. Bobbin Probe ................................................................................................. 14 2.1.2. Full Saturation Probe ................................................................................... 17 2.1.3. Rotating Probe .............................................................................................. 18 2.1.4. Array Probe ................................................................................................... 19 2.1.5. Rotational Magnetic Flux Sensor ................................................................ 26 2.1.6. Rotating Magnetic Field Probe .................................................................... 28 2.2. Review of Manufacturing of Eddy Current Probes .......................................... 33 2.2.1. ZETEC .......................................................................................................... 33 2.2.1.1 Bobbin Probe ............................................................................................33 2.2.1.2 Rotating Probe .........................................................................................34 2.2.1.3 X-probe .....................................................................................................34 2.2.2. Olympus (R/D tech) ...................................................................................... 35 2.3. Comparison of eddy current probes................................................................... 35 2.4 Summary ................................................................................................................ 41 CHAPTER 3 FINITE ELEMENT MODELING FOR TIME HARMONICS EDDY CURRENT PROBLEMS ............................................................................................... 42 3.1. Introduction to Analytical and Numerical Methods for Eddy Current Problem ........................................................................................................................ 42 3.1.1. Analytical Method ......................................................................................... 42 3.1.2. Numerical Method ........................................................................................ 42 3.1.2.1. Finite Element Method ...........................................................................43 3.1.2.2. Integral Equation Method ......................................................................43 3.1.2.3. Hybrid Method ........................................................................................44 3.1.3. Summary ........................................................................................................ 44 vii

3.2. Formulation of Finite Element Method ............................................................. 46 3.2.1. Eddy Current Problem ................................................................................. 46 3.2.2. Formulations - Magnetic Vector Potential .................................................. 48 3.2.3. Reduced Magnetic Vector Potential ............................................................ 51 3.2.4. Source Coil Modeling ................................................................................... 52 3.2.5. Reduced Magnetic Vector Potential for Ferrite-core Probes .................... 54 3.2.6. Galerkin Weak Formulation ........................................................................ 55 3.2.7. Mesh Generation ........................................................................................... 57 3.2.8. Linear Equations Solver ............................................................................... 58 3.2.9. Post-processing .............................................................................................. 59 3.2.10. Calibration of Simulated Signals ............................................................... 60 3.2.10. Summary ...................................................................................................... 63 CHAPTER 4 FINITE ELEMENT SIMULATION AND VALIDATION OF EDDY CURRENT PROBES FOR TUBE INSPECTION ....................................................... 64 4.1 Introduction ........................................................................................................... 64 4.2 Tube and Defect Geometries ................................................................................ 64 4.2.1 Tube Geometries............................................................................................. 64 4.2.1.1 Free Span ..................................................................................................64 4.2.1.2 Top Tube Sheet (TTS) ..............................................................................65 4.2.1.3 Tube Support Plate (TSP) .......................................................................67 4.2.2 Defect Geometries .......................................................................................... 68 4.2.2.1 Elliptical and Circular Holes ..................................................................69 4.2.2.2 Real Crack Model ....................................................................................70 4.2.2.3 360 Degrees Dent ......................................................................................72 4.2.2.4 Circular Dent ............................................................................................74 4.3 Eddy Current Probes ............................................................................................ 78 4.3.1 Bobbin Probe .................................................................................................. 78 4.3.2 Plus Point Probe ............................................................................................. 83 4.3.3 Rotating Pancake Probe ................................................................................ 84 CHAPTER 5 DESIGN OF ROTATING FIELD EDDY CURRENT PROBE .......... 85 5.1 Introduction ........................................................................................................... 85 5.2 Operational Principles .......................................................................................... 86 5.3 Simulation .............................................................................................................. 88 5.3.1 Three Phase Windings Excitation................................................................. 88 5.3.2 Rotating Magnetic Field ................................................................................ 90 5.3.3 Induced Eddy Current in Tube Wall ............................................................ 92 5.3.4 Bobbin Pickup Coil ........................................................................................ 93 5.3.5 GMR Sensor Array ...................................................................................... 107 5.3.6 Nonlinear Material Simulation ................................................................... 109 5.3.7 Parametric Study ..........................................................................................119 CHAPTER 6 DEVELOPMENT OF ROTATING FIELD EDDY CURRENT PROBE AND EXPERIMENT ..................................................................................... 145 6.1 Introduction ......................................................................................................... 145 6.2 Three Phase Sine Wave Excitation Source ....................................................... 145 viii

6.2.1 Phase Shift Circuit ....................................................................................... 145 6.2.2 Power Amplifier ........................................................................................... 148 6.3 Probe Prototype................................................................................................... 150 6.4 Test Bench ............................................................................................................ 152 6.4.1 Tubes with Defects........................................................................................ 152 6.4.2 Probe Pusher ................................................................................................ 153 6.4.3 Data Acquisition System .............................................................................. 154 6.5 Experimental Results .......................................................................................... 157 6.6 Summary .............................................................................................................. 170 CHAPTER 7 DESIGN OF ENCIRCLING ROTATING EDDY CURRENT PROBE ......................................................................................................................................... 171 7.1 Introduction ......................................................................................................... 171 7.2 Operational Principles ........................................................................................ 172 7.3 Finite Element Simulation .................................................................................. 175 7.4 Simulation Results .............................................................................................. 176 7.4.1 Nonmagnetic samples .................................................................................. 176 7.4.2 Ferromagnetic Tube Sample ....................................................................... 182 7.5 Summary .............................................................................................................. 189 CHAPTER 8 CONCLUSIONS AND FUTURE PLAN ............................................. 191 8.1 Conclusions .......................................................................................................... 191 8.2 Future Plan .......................................................................................................... 192 APPENDIX .................................................................................................................... 194 BIBLIOGRAPHY ......................................................................................................... 213

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LIST OF TABLES

Table 2.1 Advantages and disadvantages of eddy current probes and sensors for tube inspection ............................................................................................................................................... 36 Table 4.1 Parameters of tube geometries and material properties ............................................... 66 Table 4.2 Commercial bobbin probe parameters settings ............................................................. 80 Table 4.3 Parameters of Plus Point Probe for validation .............................................................. 83 Table 4.4 Parameters of rotating pancake coils for validation ...................................................... 84 Table 5.1 Simulation parameter settings for the modeling ........................................................... 88 Table 5.2 Excitation current phase for the three phase windings ................................................. 89 Table 5.3 Amplitude and phase for ID/OD defects at the same circumferential location............. 99 Table 5.4 Defects parameters .......................................................................................................113 Table 5. 5 Normalized amplitude and phase change of induced voltage with the probe coil eccentricity along x axes with the offset -0.6mm and 0.6 mm with the reference that the probe in the center ............................................................................................................... 142 Table 5. 6 Normalized amplitude and phase change of induced voltage with the probe coil eccentricity along y axes with the offset -0.6mm and 0.6 mm with the reference that the probe in the center ............................................................................................................... 144 Table 6.1 DC resistance and turns of three phase windings and bobbin coil .............................. 151 Table 6.2 The depths and diameters for flat bottom holes defects .............................................. 153 Table 6.3 Volume and signal amplitude of 10 defects on the tube sample ................................. 158 Table A. 1 Parameter of defects for the bobbin probe validation ............................................... 195 Table A. 2 Quantitative analysis of simulation and experimental signals for 610 MR probe .... 198 Table A. 3 Parameters settings for dent simulation..................................................................... 199 Table A. 4 Quantitative analysis of simulation and experimental signals for 360 dent inspection ............................................................................................................................................. 203 Table A. 5 Quantitative analysis for simulation and experimental signals for spherical dent inspection ............................................................................................................................ 205 x

LIST OF FIGURES

Figure 1.1 Nuclear power plant with steam generator tubes [1] ..................................................... 2 Figure 1.2 Steam Generator in nuclear power plant [2].................................................................. 3 Figure 1.3 San Onofre Nuclear Generating Station Unit 2 an 3 at San Onofre State Beach, south of San Clemente, California .................................................................................................... 4 Figure 1.4 Principle diagram for eddy current testing .................................................................... 7 Figure 1.5 Equivalent Circuit for eddy current testing ................................................................... 9 Figure 2.1 Differential and absolute bobbin probes for tube inspection: (a) absolute, (b) differential ............................................................................................................................. 15 Figure 2.2 Bobbin probe signals: (a) absolute, (b) differential ..................................................... 16 Figure 2.3 Rotating Probe with Plus Point Coils .......................................................................... 18 Figure 2.4 Rotating Pancake Coil Probe ....................................................................................... 19 Figure 2.5 Axial and circumferential channels of array probe: (a) Axial channel, (b) Circumferential channel ........................................................................................................ 21 Figure 2.6 General setting for the C-Probe: (a) C-3, (b) C-4 ........................................................ 22 Figure 2.7 X-Probe combined with differential bobbin probe (From Zetec)................................ 23 Figure 2.8 Axial and circumferential channels of array probes .................................................... 24 Figure 2.9 Smart array probe ........................................................................................................ 25 Figure 2.10 Intelligent probe from Mitsubishi Heavy Industries: (a) Probe schematic, (b) Real probe ..................................................................................................................................... 25 Figure 2. 11 Induced eddy current in tube wall by inclined transmit coil .................................... 26 Figure 2.12 Excitation coils and search coils for rotating magnetic flux sensor .......................... 27 Figure 2.13 One type of excitation coils and search coils for rotating magnetic flux sensor ....... 27 Figure 2.14 Rotating magnetic flux sensor for tube inspection .................................................... 28 Figure 2.15 Schematic view of encircling rotating magnetic flux probe: 1, 2, 3, transmit windings, 4, 5, receive coil, 6, high permeability ferrite core .............................................. 29 xi

Figure 2.16 Sketch of encircling rotating magnetic field probe ................................................... 30 Figure 2.17 Two phase rotating field eddy current probe by T.E. Capobianco ............................ 31 Figure 2.18 Rotating field probe response to decreasing notch depth .......................................... 31 Figure 2.19 Inner rotating magnetic field eddy current transducer: (a) a, b, c: three phase rectangular coils, (b) 1, 2, 3, …, 8: flat rectangular pickup coils.......................................... 32 Figure 2.20 Inner eddy current transducer with rotating magnetic field ...................................... 32 Figure 2.21 Zetec bobbin probes .................................................................................................. 34 Figure 2.22 Zetec motorized rotating pancake coil probes ........................................................... 34 Figure 2.23 Zetec X-probe with different bobbin on the same head 0.725” OD .......................... 35 Figure 2.24 Multi-frequency technologies for the excitation of eddy current probe: (a) Multiplexed four frequency signal, (b) simultaneous injection four frequency signal ......... 39 Figure 3.1 Typical eddy current problem ...................................................................................... 46 Figure 3. 2 Discretization of Coil separated from tube mesh ....................................................... 54 Figure 3. 3 Configuration of Nondestructive Testing with Ferrite-Core Coil .............................. 55 Figure 3. 4 Illustration of Modeling Method in Case of Ferrite Core........................................... 55 Figure 3. 5 Finite Element Meshes for Free-Span Tube (Half Geometry) (a) Axial Rectangular Crack: 0.5” (12.7 mm) Long, 0.005” (0.127 mm) Wide, and 100% Depth (b) Circumferential Rectangular Crack: 0.5” (12.7 mm) Long, 0.005” (0.127 mm) Wide, and 100% Depth (c) Circular Hole: 0.067” (1.702 mm) Diameter and 100% Depth .................. 58 Figure 4. 1 Tube mesh generation – Free Span ............................................................................. 65 Figure 4.2 Geometry of TTS, transition and free span with loose part ........................................ 66 Figure 4.3 Carbon steel loose parts for top tube sheet mock-up ................................................... 66 Figure 4. 4 Tube mesh generation - TTS ..................................................................................... 67 Figure 4. 5 Tube mesh generation - TSP....................................................................................... 68 Figure 4. 6 Rectangular crack: (a) axial notch; (b) circumferential notch .................................... 68 Figure 4. 7 Elliptical and circular holes: (a) elliptic through hole; (b) four through circular holes ............................................................................................................................................... 69 Figure 4. 8 Axial real crack (ID) ................................................................................................... 71 xii

Figure 4. 9 Axial real crack (OD) ................................................................................................. 71 Figure 4. 10 Circumferential real crack (ID) ................................................................................ 72 Figure 4. 11 Circumferential real crack (OD) ............................................................................... 72 Figure 4.12 360 degrees dent geometries of the tube .................................................................. 73 Figure 4.13 2D profile for 3D dent modeling: (a) parabola profile; (b) and (c) cross section of tube wall for demonstration of 3D dent ................................................................................ 73 Figure 4. 14 Spherical dent .......................................................................................................... 74 Figure 4. 15 Measurement of real spherical dent .......................................................................... 74 Figure 4. 16 Measurement of spherical dent by laser system: local 3D dent profile .................... 75 Figure 4. 17. Views of 2D and 3D modeling of dent in the tube wall: the maximum depth in the dent center is OO’ (h) and the axial length of dent opening is AB (l). ................................. 75 Figure 4. 18. Mathematical model for 3D dent for mesh generation ........................................... 76 Figure 4. 19 Spherical dent modeling on the tube wall cross section ........................................... 77 Figure 4. 20 Axial profile for spherical dent ................................................................................. 78 Figure 4. 21 Mesh of spherical dent in frees-pan: 3D model of spherical dent ............................ 78 Figure 4.22 Finite element modeling of absolute bobbin probe: (a) Coil model, (b) Excitation current, (c) Integration path for post-processing................................................................... 81 Figure 4.23 Finite element modeling of differential bobbin probe: (a) Coil model, (b) Excitation current, (c) Integration path for post-processing................................................................... 82 Figure 4.24 Plus point eddy current probe: orthogonal coils (red) and ferrite core (green) ......... 83 Figure 4.25 Mesh for Rotating Pancake Coil................................................................................ 84 Figure 5.1 Rotating field windings and bobbin pickup coil: (a) Three phase excitation windings; (b) 3D model of bobbin pickup and three windings inside the tube; .................................... 87 Figure 5.2 Rotating magnetic field generated inside the tube: (a)~(i): resultant rotating magnetic field at different instant time, the labeled numbers indicate the orientation of field ............ 89 Figure 5.3 Magnetic flux density decay along diameter direction................................................ 91 Figure 5.4 Amplitude contour of magnetic field component on the xy plane: (a) defect-free, (b) defect at 90° .......................................................................................................................... 91

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Figure 5.5 Induced eddy current in the tube wall due to the rotating magnetic field ................... 93 Figure 5.6 Simulation results of induced eddy current in the tube wall ....................................... 93 Figure 5.7 Amplitude and phase of induced voltage in bobbin coil vs. circumferential location of square holes: (a) Circumferential location of square holes in tube wall, (b) Induced voltage plotted by real and imaginary parts, (c) amplitude vs. circ. angles, (d) phase vs. circ. angles ............................................................................................................................................... 95 Figure 5.8 ID and OD defects signals by bobbin pickup coil (Frequency 35 kHz): (a) Induced voltage plot, (b) amplitude vs. depth, (c) phase vs. depth..................................................... 98 Figure 5.9 Axial notches of ID/OD with depth range from 20%~80%, at 35 kHz: (a) Induced voltage plot, ID, (b) induced voltage plot, OD, (c) amplitude vs. depth, (d) phase amplitude vs depth ............................................................................................................................... 100 Figure 5.10 Axial notches of ID/OD with depth range from 20%~80%, at 300 kHz: (a) Induced voltage plot, (b) amplitude vs. depth, (c) phase vs. depth................................................... 102 Figure 5.11 Circumferential notches of ID/OD with depth range from 20%~100%, at 35 kHz: (a) Induced voltage plot with real and imaginary parts, ID, (b) induced voltage plot, OD, (c) amplitude vs. depth, (d) phase vs. depth ............................................................................. 104 Figure 5.12 Circumferential notches of ID/OD with depth range from 20%~100%, at 300 kHz: (a) Induced voltage plot by real and imaginary parts, (b) amplitude vs. depth, (c) phase vs. depth .................................................................................................................................... 106 Figure 5.13 Coordinate transform from Cartesian to Cylindrical coordinate ............................. 108 Figure 5.14 Experimental B-H curve of ferromagnetic material ................................................ 109 Figure 5.15 Flow chart of updating permeability of ferromagnetic material ..............................112 Figure 5.16 Schematic of the geometry with probe inside a tube ................................................114 Figure 5.17 Induced radial and axial components of magnetic flux density measured by GMR sensors for non-ferromagnetic material, notch: (a) radial; (b) axial; square hole: (c) radial; (d) axial ................................................................................................................................115 Figure 5.18 Induced radial and axial components of magnetic flux density measured by GMR sensors for ferromagnetic material, notch: (a) radial; (b) axial; square hole: (c) radial; (d) axial ......................................................................................................................................117 Figure 5.19 Height of three phase rectangular windings vs. induced voltage amplitude and phase at different frequencies: (a), (d), (g) induced voltage plot with real and imaginary parts at 35 kHz, 100 kHz and 300 kHz; (b), (e), (h) height vs. amplitude at 35 kHz, 100 kHz and 300 kHz; (c),(f), (i) height vs. phase at 35 kHz, 100 kHz and 300 kHz. ................................... 120

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Figure 5.20 Peak magnitude of radial and axial magnetic flux density versus coil heights (a) radial component; (b) axial component .............................................................................. 125 Figure 5.21 Diameter of three windings vs. amplitude of induced voltage in the bobbin coils at 35 kHz and 300 kHz: (a), (c) induced voltage plot with real and imaginary parts at 35 kHz and 300 kHz; (b), (d) diameter vs. amplitude at 35 kHz and 300 kHz ............................... 126 Figure 5.22 Peak magnitude of radial and axial magnetic flux density versus coil diameter (a) radial component; (b) axial component .............................................................................. 128 Figure 5.23 Skin depth versus excitation frequency for the tube specimen ............................... 129 Figure 5.24 Excitation frequencies for the three phase windings vs. induced voltage in the bobbin coil: (a) induced voltage plot with real and imaginary parts, (b) absolute amplitude of induced voltage along axial distance (the defect is located from -2mm to 2mm), (c) maximum amplitude of induced voltage vs. frequency, (d) phase vs. frequency for same defect ................................................................................................................................... 130 Figure 5. 25 Model of coil crossover for three phase windings.................................................. 133 Figure 5. 26 Induced voltage with the three phase windings crossover for 0mm, 1mm and 2 mm ............................................................................................................................................. 133 Figure 5. 27 Normalized amplitude and phase of induced voltage with the three phase windings crossover 0mm, 1mm and 2mm with each other: (a) normalized amplitude vs. crossover height, (b) phase vs. crossover height ................................................................................. 134 Figure 5. 28 Bobbin pickup coil offset along tube axes (Z direction) ........................................ 135 Figure 5. 29 Induced voltage with the bobbin pickup coil z offset -1 mm, 0mm and +1 mm.... 135 Figure 5. 30 Induced voltage with the bobbin coil z offset -3 mm and +3 mm .......................... 136 Figure 5. 31 Induced voltage with the bobbin coil z offset -5 mm and +5 mm .......................... 136 Figure 5. 32 Normalized amplitude and phase of induced voltage for bobbin coil with the z offset -5 mm, -3 mm, -1mm, 0mm, +1mm, +3mm, and +5mm: (a) normalized amplitude vs. bobbin z offset, (b) phase vs bobbin z offset ...................................................................... 137 Figure 5. 33 Model of probe coil tilt along tube axes: (a) +5°, (b) -5° ....................................... 138 Figure 5. 34 Induced voltage of probe coil tilt along tube axes for -5°, -2.5°, 0°, +2.5° and +5° ............................................................................................................................................. 139 Figure 5. 35 Shifted Induced voltage of probe coil tilt along tube axes for -5°, -2.5°, 0°, +2.5° and +5° ................................................................................................................................ 139 Figure 5. 36 Normalized amplitude and phase of induced voltage for probe coil tilt along tube axes with -5°, -2.5°, 0°, +2.5° and +5°: (a) normalized amplitude vs. tilt angle, (b) phase vs. xv

tilt angle .............................................................................................................................. 140 Figure 5. 37 Probe eccentricity along x and y axes .................................................................... 141 Figure 5. 38 Probe eccentricity along x axes (changed distance to defect) ................................ 142 Figure 5. 39 Induced voltage for probe eccentricity along x axes with the offset -0.6mm, 0mm and 0.6 mm.......................................................................................................................... 142 Figure 5. 40 Probe eccentricity along y axes (distance to defect keeps the same) ..................... 143 Figure 5. 41 Induced voltage for probe eccentricity along y axes with the offset -0.6mm, 0mm and 0.6 mm.......................................................................................................................... 143 Figure 6.1 Phase shift circuit: (a) phase lag, (b) phase lead ....................................................... 146 Figure 6.2 Circuit diagram for phase shift circuits: (a) cascaded phase lag circuits, (b) parallel phase lag and lead circuits .................................................................................................. 148 Figure 6.3 Power amplifier circuits: (a) non-inverting amplifier, (b) combined non-inverting amplifier .............................................................................................................................. 149 Figure 6.4 Plastic cores for the phase windings: (a) CAD model, (b) plastic core printed by 3D printer .................................................................................................................................. 151 Figure 6.5 Prototype of RoFEC probe ........................................................................................ 151 Figure 6.6 Test bench for the rotating field eddy current probe (RoFEC) .................................. 152 Figure 6.7 Steam generator tube sample for the experiment ...................................................... 153 Figure 6.8 SR844 RF Lock-in amplifier ..................................................................................... 154 Figure 6.9 Basic function diagram of Lock-in amplifier ............................................................ 154 Figure 6.10 LabVIEW control panel for lock-in amplifier ......................................................... 156 Figure 6.11 LabVIEW control panel for signal display .............................................................. 156 Figure 6.12 Real and imaginary parts of experimental signal of RoFEC probe ......................... 158 Figure 6.13 Induced voltage trajectory of defect 1 measured by probe prototype and simulation signals from finite element model....................................................................................... 159 Figure 6.14 Real and imaginary parts of induced voltage comparison for experimental and simulation signals for defect 1 ............................................................................................ 159 Figure 6.15 Induced voltage trajectory of defect 2 measured by probe prototype ..................... 160

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Figure 6.16 Induced voltage trajectory of defect 3 measured by probe prototype ..................... 161 Figure 6.17 Induced voltage trajectory of defect 4 measured by probe prototype ..................... 161 Figure 6.18 Induced voltage trajectory of defect 5 measured by probe prototype ..................... 162 Figure 6. 19 Induced voltage trajectory of defect 6 measured by probe prototype .................... 162 Figure 6.20 Induced voltage trajectory of defect 7 measured by probe prototype ..................... 163 Figure 6.21 Induced voltage trajectory of defect 8 measured by probe prototype ..................... 163 Figure 6.22 Induced voltage trajectory of defect 9 measured by probe prototype ..................... 164 Figure 6. 23 Induced voltage trajectory of defect 10 measured by probe prototype .................. 164 Figure 6.24 Comparison of induced voltage trajectories of defect 1 ~ 5 measured by prototype probe ................................................................................................................................... 165 Figure 6.25 Signals amplitude and phase versus depth for defect 2~5 ....................................... 166 Figure 6.26 Comparison of induced voltage trajectories of defect 7 ~ 10 measured by prototype probe ................................................................................................................................... 166 Figure 6.27 Signals amplitude and phase versus depth for defect 7~9 ....................................... 167 Figure 6.28 Real and imaginary parts of experimental signal for defect 2 and 3 at 150 kHz .... 168 Figure 6.29 Induced voltage measurement in the bobbin coil for defects at different circumferential locations: (a) probe prototype, (b) induced voltage plot by real and imaginary parts, (b) amplitude vs. defect circumferential location, (c) phase vs. defect circumferential location ...................................................................................................... 169 Figure 7. 1 Rotating Field Eddy Current Probe: (a) 3D model, (b) Magnetic flux contour ....... 173 Figure 7. 2 Magnetic flux density due to three phase windings and total magnetic flux density 174 Figure 7. 3 Rotating magnetic field (clockwise) at different current excitation phase angle: (a) 0°, (b) 45°, (c) 90°, (d) 135°, (e) 180° ...................................................................................... 174 Figure 7. 4 Finite element modeling of probe and tube: (a) 3D mesh, (b) top view of 3D mesh 176 Figure 7. 5 Simulation results of Bobbin pickup signals from square hole, axial and circumferential notches at 35, 150, 300 kHz: (a) square hole, (b) axial notch, (c) circumferential notch .......................................................................................................... 177 Figure 7. 6 Signals for different depths square hole at different excitation frequency: (a) 35 kHz, (b) 150 kHz, (c) 300 kHz .................................................................................................... 179

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Figure 7. 7 Phase and amplitude of different depths square hole at 35, 150 and 300 kHz: (a) amplitude, (b) phase ............................................................................................................ 180 Figure 7. 8 Axial magnetic flux density due to different defect with 100% depth measure by GMR sensors: square hole (a) 2D, (b) 3D, axial notch (c) 2D, (d) 3D, circumferential notch (e) 2D, (f) 3D. Note that black box indicate the defect size and location. .......................... 181 Figure 7. 9 2D model for encircling probe with ferrite core and ferromagnetic tube ................. 183 Figure 7.10 GMR sensor signal for amplitude of magnetic flux density around circumference versus the relative permeability of the ferromagnetic tube sample: (a) magnetic flux density vs. circ. Angular position, (b) maximum magnetic flux density vs. relative permeability . 184 Figure 7.11 Magnetic flux contour and flux density for (a) nonmagnetic and (b) ferromagnetic samples (µr = 100) ............................................................................................................... 186 Figure 7.12 Nonmagnetic and ferromagnetic tube samples with two defects at circumference: (a) defects at 90° and 270°, (b) defects at 45° and 225°........................................................... 186 Figure 7. 13 Amplitude of magnetic flux density from GMR array from nonmagnetic/ferromagnetic tube with air/ferrite core with 100% defect ........................... 187 Figure 7. 14 Ferromagnetic tube with two defects (90° and 270°) at different frequencies (60 Hz ~ 300 kHz): (a) magnetic flux density vs. circ. Angular position, (b) maximum amplitude of magnetic flux density vs. frequency ................................................................................... 188 Figure 8. 1 RoFEC probe with GMR sensor array as pickup in the center ................................ 193 Figure A. 1 610 MR bobbin probe experimental and simulation signals (60% depth defect) at 270 kHz: (a) Liz plot; (b) real plot; (c) imaginary plot. ............................................................. 195 Figure A. 2 610 MR bobbin probe experimental and simulation signals (100% depth defect) at 270 kHz: (a) Liz plot; (b) real plot; (c) imaginary plot. ...................................................... 197 Figure A. 3 3D mesh for the tube with 360 degrees dent ........................................................... 199 Figure A. 4 Comparison of simulation and experiment signals of 3D dent at 400 kHz: (a) impedance trajectory, (b) real and imaginary parts ............................................................. 200 Figure A. 5 Comparison of simulation and experiment signals of 3D dent at 200 kHz: (a) impedance trajectory, (b) real and imaginary parts ............................................................. 201 Figure A. 6 Comparison of simulation and experiment signals of 3D dent at 100 kHz: (a) impedance trajectory, (b) real and imaginary parts ............................................................. 202 Figure A. 7 LIZ plot comparison of Bobbin probe impedance from experiment and simulation at five different excitation frequencies: (a) 550 kHz, (b) 400 kHz, (c) 300 kHz, (d), 130 kHz ............................................................................................................................................. 203 xviii

Figure A. 8 Free span axial real crack profile from EPRI Database: (a) Measured profile, (b) simulation model ................................................................................................................. 205 Figure A. 9 3D images of real channel from Plus Point probe: (a) experimental signal, (b) simulation signal ................................................................................................................. 206 Figure A. 10 3D images of imaginary channel from Plus Point probe: (a) experimental signal, (b) simulation signal ................................................................................................................. 207 Figure A. 11 Line scan of real channel in the center of crack ..................................................... 208 Figure A. 12 Line scan of imaginary channel in the center of crack .......................................... 208 Figure A. 13 Free span axial real crack profile from ETSS database (TMI1_91_55): (a) measured profile, (b) simulation model .............................................................................................. 209 Figure A. 14 3D images of real channel from Plus Point probe: (a) experimental signal, (b) simulation signal ................................................................................................................. 210 Figure A. 15 3D images of imaginary channel from Plus Point probe: (a) experimental signal, (b) simulation signal ..................................................................................................................211 Figure A. 16 Line scan of vertical channel in the center of crack ...............................................211 Figure A. 17 Line scan of horizontal channel in the center of crack .......................................... 212

xix

CHAPTER 1 INTRODUCTION 1.1. Introduction 1.1.1. Steam Generator Tubes Steam generator (SG) units in nuclear power plants comprise thousands of tubes transfer heat from the primary reactor side coolant to the secondary side clean water, generating non-radioactive steam to drive the turbines for electric power production, as shown in Figure 1.1 [1].

The SG tubes constitute a barrier between primary and

secondary sides and confine the radioactivity inside of the reactor core to the primary side. There are approximately 3,000 to 16,000 tubes, 70 feet (21 m) in height and 3/4’’ (19.05 mm) or 7/8’’ (22.23 mm) in diameter inside a typical heat exchange tower. Inside of these tubes, there are pressurized heavy water at high temperature and high fluid flow rate. The flow induced mechanical vibration and chemical interactions on the secondary side can cause corrosion deposits as well as defects in the tube wall. Typical defect types are mechanical wear between tubes and support plates, outer diameter stress corrosion cracking (ODSCC), pitting, denting, and primary water stress corrosion cracking (PWSCC) [2].

1

Figure 1.1 Nuclear power plant with steam generator tubes [1]

2

Wear

U-bend

Axial ODSCC in free span

Tube Support Plate (TSP)

Intergranular Attack

Steam Generator Tube (SG Tube)

Pitting Loose Parts Top Tube Sheet (TTS)

Axial PWSCC

Figure 1.2 Steam Generator in nuclear power plant [2] Since steam generator tubes carry radioactive water inside degraded tubes, it presents a potential safety problem. Severe tube defects could result in the leakage of radioactivity to the secondary side and to the environment. A rupture could lead to a much more serious situation since radiation can escape into the atmosphere. Nuclear Regulatory Commission (NRC) reports steam generator tubes in nuclear plants between 1975 and 2000 that vented as much as 630 gallons of radioactive steam per minute [2]. As of 2013, there are 104 commercial nuclear power reactors in the United States. In the past 20 years, these ruptures occurred at a rate of about one every 2-3 years and may continue to occur. In 1991, SG tubes at Bruce Nuclear Generating Station failed due to circumferential outer diameter stress corrosion cracking (ODSCC) in U-bend section and leaked radiation 3

material to environment. Recent leakage of SG tubes occurred on March 15, 2012. At the Nuclear Generating Station Unit 3 in San Onofre State Beach, south of San Clemente, California, 3 steam generator tubes in Unit 3 failed pressure stress tests by Southern California Edison. Steam leaked at the rate of 82 gallons per day. The unit has been shut down since a leak is detected in one of the steam generator tubes on January 31, 2012 and the shutdown has lasted over a year. There are 8.7 million people who live within 50 miles of the San Onofre plant affected by the rolling power blackouts in summer due to the lengthy shutdown plan.

Figure 1.3 San Onofre Nuclear Generating Station Unit 2 an 3 at San Onofre State Beach, south of San Clemente, California Degradation of steam generator tubing due to both mechanical vibration and corrosion result in extensive repairs and replacement of steam generators. The variety of degradation mechanisms challenge the integrity of SG tubing and hence the stations’ reliability. Periodic inspection and monitoring aimed at timely detection and characterization of the degradation is a key element for ensuring tube integrity. The aim

4

of the steam generator tube integrity program (SGTIP) was to experimentally evaluate the margin-to-failure and inspection reliability of degraded steam generator tubes. The program was initiated in 1976. Nondestructive evaluation has evolved from simple detection tools to diagnostic tools that provide input into integrity assessment decisions, fitness-for-service and operational assessment. 1.1.2. Defect Types Nuclear plants using pressurized water reactor (PWR) design have struggled for more than 30 years with degradation problems, such as 

Axial or circumferential inner/outside diameter stress corrosion cracking (ID/OD SCC)



Primary water stress corrosion cracking (PWSCC)



Volumetric material loss due to fretting wear



Tube wall thickness thinning



Pitting corrosion



Denting



High-cycle fatigue



Wastage



Flow accelerated corrosion (FAC)



Intergranular attack (IGA)



Volumetric material loss due to fretting wear Eddy current techniques are indispensable in the In-Service Inspection of steam

generator tube of nuclear power plants. Their reliability ensures safety of SG tubes in pressurized water nuclear reactor, making eddy current testing techniques very critical. 5

For example, by using phase analysis from eddy current testing results, defects such as pitting can be assessed to an accuracy of about 5% of tube wall thickness, which allows accurate estimation of the remaining life of the SG tubes in the plant [3]. Eddy current probes work well on thin-walled tubes of the sort used in PWR and Canada Deuterium Uranium (CANDU) steam generators. Until early 70’s, the in-service inspection of SG tubes were carried out using single-frequency eddy current bobbin coils, which were adequate for the detection of volumetric degradation. By mid-80’s, additional degradation such as pitting, intergraular attack, axial and circumferential inside or outside diameter stress corrosion cracking were found in these tubes. Since bobbin probes cannot detect circumferential cracking, new rotating pancake coil (RPC) probes were developed to solve that problem. However, the RPC uses a helical scan, and the scan speed is more than 50 times slower than that of the bobbin probes. In the 90’s, the requirement for timely, fast detection and characterization of degradations resulted in the development of array probes and other advanced inspection probes and systems with advanced instrumentation, fast computers and remote communication system[2]. 1.2. Introduction to Eddy Current Testing 1.2.1. Principles Eddy current testing is based on electromagnetic induction. When a coil carrying alternating current is brought close to the metallic specimen, the time-varying primary magnetic field associated with the alternating current induces eddy currents in the specimen. The eddy current flows parallel to the coil winding in the specimen, but opposite in direction to that of primary current in the coil. The secondary magnetic field associated with the eddy current opposes the primary magnetic field. Defects in the

6

specimen perturb the eddy current flow which decrease the resistance of the coil and change its effective reactance. Monitoring the voltage induced in the coil and keeping current constant, the impedance change can be recorded to locate defects in a conducting specimen, such as metallic pipes and structural frames. From the amplitude and phase variations of coil impedance, the defect can be characterized. Note that the defect must interrupt the eddy current path to be detected, and defect lying parallel to the current path will not cause any significant interruption and may not be detected. Coils

Tubes

Alternating current

Eddy current (opposite direction)

Primary magnetic field

Oppose

Secondary magnetic field

Change in impedance (amplitude and phase)

Figure 1.4 Principle diagram for eddy current testing There are 4 steps to illustrate the magnetic field interaction between primary and induced fields. 

Coil carrying alternating current generate primary magnetic field;



Alternating primary magnetic field induce eddy current in the conductive specimen;



Eddy current generates secondary magnetic field in opposite direction



Defects in the specimen perturb the eddy current and weaken the secondary magnetic field, which cause the variation of impedance change of the coil. Two different conducting materials, non-ferromagnetic and ferromagnetic metals,

7

have different effects on the eddy current testing. The secondary magnetic field by induced eddy currents in non-ferromagnetic material weakens the primary magnetic field. So the reactance is smaller than that of the coil in the air. Whereas with ferromagnetic materials, due to its high permeability, the primary field is highly reinforced, thus the reactance increases in spite of reverse effect of the secondary magnetic field. In the presence of defects, the resistance of both materials decreases due to less eddy current losses and reactance increase because of less reverse effects of secondary magnetic field on the primary magnetic field. 1.2.1.1 Penetration Depth The density of induced eddy current decreases exponentially from the surface with depth into the specimen. The standard depth of penetration is the depth from the surface at which the eddy current strength has dropped to 37% of the value at the surface. It depends on the testing frequency, as well as test specimen properties such as electrical conductivity and permeability. Penetration depth is defined as

1  f 

 Where,

 : skin depth; f : excitation frequency;  : conducting material permeability;  : conducting material conductivity;

 : conducting material permeability;

8

(1.1)

Skin depth is a critical parameter for selecting excitation frequency for a given test specimen: (1) Each frequency is sensitive up to a certain depth of test sample. (2) Low frequency corresponds to large skin depth, for example in SG tube inspection applications, the low frequency is used for detection of support plates and other support structures outside of the tubes due to the large penetration depth. (3) At a fixed frequency, there is also a well-defined relationship between the signal phase and defect depth. The phase is hence used to detect, classify and characterize the defect. 1.2.1.2 Equivalent Circuit

R

I

M

I2

1

U

L1 Primary Coil

L2

R2

Conducting Specimen

Z Figure 1.5 Equivalent Circuit for eddy current testing According to the circuit theorem

 R1I  j L1I  j MI 2  U   j MI  j L2 I 2  R2 I 2 The impedance of the probe coil is given by[4]

9

(1.2)

Z

U  2M 2  2M 2  R  jX  ( R1  R2 )  j ( L1  L2 ) I R22   2 L22 R22   2 L22

(1.3)

The phase angle between the excitation voltage and current is given by X R

  tan 1( )

(1.4)

Factors affecting eddy current testing are the following: 

Material Conductivity - Greater the conductivity of a material, greater the flow of eddy currents and hence probe coil resistance.



Permeability - Changes the coupling of coil with conductive specimen, and thus affects the reactance of the coil.



Frequency - Affects eddy current penetration depth and impedance phase.



Geometry - Curvature, edges and grooves affect eddy current response. For example, in order to test an object edge for cracks, the probe will normally be moved parallel to the edge so that small changes may be easily seen.



Lift-off - Lift-off is the spacing between the coil and specimen. Larger the liftoff, weaker induced eddy current intensity, less eddy current loss and hence effect of secondary magnetic field. Lift-off increases noise in the response signals and results in a reduction of sensitivity.

1.2.2. Applications Typical applications of eddy current testing in industry today are in: 1) Sorting material with different conductivity and permeability. 2) Detecting defects in conductive specimen, such as plates, tubes, rods and bars a. Surface and near-surface defect detection. b. Safety-critical systems depend on early detection of fatigue cracks which 10

are small, deeply buried defects to avoid major failures. 3) Measurement of non-conductive and conductive coating thickness (>= 10 um), and also in detecting defects, which are under insulating coatings. 4) In-service inspection of heat exchanger tubes (internal probes with multifrequency method to detect corrosion and cracking at inside and outside surface, and estimate depth of these defects). 1.2.3. Advantages and Disadvantages The advantages for the eddy current testing are: 

Noncontact ( no couplant required )



High inspection speeds



High sensitivity



Gives good discrimination



Easy to automate



Simple to use



Low cost sensors



Environmentally friendly Disadvantages:



Only applicable for thin, conductive materials.



Tends to generate large noise due to variations in factors such as probe lift-off

1.3 Scope of the thesis The objective of this thesis is to investigate a design of novel rotating field eddy current probe for steam generator tube inspection that overcomes drawbacks of existing eddy current probes. The probe design is optimized using a simulation model and a 11

prototype of this probe is built to validate the design. A rotating field probe is also designed for inspection of cylindrical rods and its operation for the cases of magnetic and nonmagnetic samples are studied. The design and analysis of the proposed probe is conducted using an experimentally validated finite element modeling. In order to reduce the computational time involved in simulating the scan process of the eddy current probe in a real experiment, an efficient formulation using reduced magnetic vector potential is implemented. Using finite element modeling, the eddy current signals from different probe designs and test geometries and a variety of defects can be generated. Chapter 2 review the eddy current probes which have been used for the tube (some of them are especially for steam generator tubes) or plate inspection. This chapter also reviews the manufacture in industry to produce the commercial probes for practical tube inspection. A comparison about the performance, detectability and cost is summarized for the bobbin probe, rotating probe and array probe for the steam generator tube inspection is presented. New technique trends for the eddy current testing are also discussed in the summary. Chapter 3 reviews the analytical and numerical methods for the eddy current problems. A finite element modeling with reduced magnetic vector potential formulation is presented. Chapter 4 presents experimental validation of finite element modeling w.r.t different probes Bobbin, Plus Point and Rotating Pancake coils probes applied for different tube geometries free span, tube support plate and top tube sheet to detect different defect geometries flat bottom holes, real crack, dent and loose part.

12

Chapter 5 presents a new design and analysis of rotating field eddy current probe for the steam generator tube inspection. The probe design is optimized using a simulation model, and the parametric studies of probe dimension and offset are also presented. Chapter 6 presents the development of a prototype of the rotating field eddy current probe. The probe is used for detecting 10 machined defects on a tube sample. The simulation results by the modeling are validated by these experiment measurements. Chapter 7 present a design and modeling of an encircling rotating field eddy current probe for cylindrical sample inspection. The probe is analyzed by simulation model for its operation for magnetic and nonmagnetic samples. Chapter 8 summarizes the contribution of the research and some future work about the rotating field probe on modeling and experiments.

13

CHAPTER 2 REVIEW OF EDDY CURRENT PROBES AND SENSORS 2.1. Introduction There are mainly two types of eddy current probes: impedance variation probe and transmit-receive probe. Impedance variation probe coils induce eddy current in the specimen. The secondary flux created by eddy currents changes the flux coupling the exciting coils and thus the coil’s impedance. The impedance variation is monitored and measured by instrumentation. In transmit-receive probe, the transmit coils induce eddy currents within the specimen, and the voltage induced in the receive coil by the time varying magnetic field forms the measured signal. In the past few decades, three different commercial probes have been used widely in the market for the inspection of SG tubes: absolute and differential bobbin probes; motorized rotating probe coil (MRPC) with pancake and plus point coils; and array probe, such as X-probe, smart array probe and intelligent probe. Among these probes, the bobbin probe and rotating probe are the impedance variation probes. Array probe belongs to a class of transmit-receive probe. 2.1.1. Bobbin Probe In late 70’s and 80’s, bobbin probes began to be used for in-service inspection. Bobbin probe is reliable and capable of detecting and sizing volumetric defects such as fretting wear and pitting corrosion. The typical scanning speed is up to 1 m/s (40 inch/sec). Large numbers of tubes in steam generator are inspected by bobbin probes. Bobbin probes are connected to analog single-frequency instruments with a scope for impedance trajectories display. Bobbin probes have fast scan speed of approximately 40’’/sec and are mainly used for initial detection of possible degradation to determine the

14

areas requiring additional inspection using other probes with improved ability to size and characterize degradation. Two types of bobbin probes are commonly used in tube inspection: Absolute bobbin and differential bobbin probes. Absolute bobbin operates with single bobbin coil and a second identical reference coil, which is used for electronic balancing and electromagnetically shielded from the inspected tubing, as shown in Figure 2.1(a). The probe is sensitive to axial cracks in tube wall. Material property variations, and gradually varying wall thinning, are not detected by differential bobbin probe. Defect

Defect Scan Metallic Shileds Reference Coil

Tube Wall

Tube Wall

(a) (b) Figure 2.1 Differential and absolute bobbin probes for tube inspection: (a) absolute, (b) differential Differential bobbin probe have two coils that are differentially connected. The typical probe outer diameter ranges from 12~30 mm, thickness from 0.7~3mm and liftoff from 0.8~1.5mm. The probe operates with the current in one coil 180 degrees out of phase with the current in the other. The recorded signal is the total impedance of two coils. Differential bobbin probe is sensitive to small defects and abrupt anomalies such as pitting corrosion and fretting wear, relatively unaffected by lift-off (although the 15

sensitivity reduced), probe wobble, temperature variations, gradual tube conductivity changes and external interference. The probe is not sensitive to gradual changes such as metallurgical variations, geometry and slowly increasing cracks. Typical absolute and differential bobbin signals are shown in Figure 2.2(a) and (b). The amplitude and phase differences of impedance trajectories are used to detect and size the defects. Differential bobbin probes have the following advantages and disadvantages.

(a)

(b)

Figure 2.2 Bobbin probe signals: (a) absolute, (b) differential Advantages: 1) Inexpensive, fast scanning (typically up to 1m/s). 2) Reliably detects and size volumetric defects, such as fretting wear and pitting corrosion. Disadvantages: 1) Limited sensitivity at expansion and transition zone, U-bend, top tube sheet (TTS) and tube support plates (TSP) in SG tube inspection, because large signals generated by geometrical tube wall distortions obscure the defect signals significantly. 2) Insensitive to circumferential cracks, because induced eddy current is parallel to defects and inherently unaffected by the presence of such defects.

16

3) Limited resolution with respect to defect location and characterization. 4) High sensitivity to lift-off. 2.1.2. Full Saturation Probe It is not possible to use standard eddy current probes to inspect ferrous or magnetic stainless steel tubes, such as Monel 400 (ferromagnetic copper-nickel alloy) used in CANDU, because little or no penetration of eddy current fields at practical test frequencies due to the high permeability. Furthermore, variations in permeability of these tubes cause eddy current response which are orders of magnitude greater than defect indications. In order to detect the defects in these tubes, it is necessary to magnetically saturate the tube material using a strong static magnetic field and reduce the effective permeability of tube to 1. This increases the penetration depth and also reduces indication due to permeability variations. Saturation eddy current probes are conventional eddy current probes with integrated strong permanent magnet bias to magnetize the tube material. Magnetic saturation to reduce the permeability ensures the adequate eddy current depth of penetration in order for internal probe to detect defects that start from the outer diameter surface of the tube. These types of probe are used in the case of partially ferromagnetic materials, such as copper-nickel alloy and stainless steel. The problem with full saturation eddy current probe is the need for ensuring that ferromagnetic material is saturated. However, with a reference calibration tube, this can be verified.

17

2.1.3. Rotating Probe Bobbin probes are fast and effective in initial detection and sizing the degradation but insensitive to circumferential cracks and defects around transition zones. Surfaceriding probe such as Rotating Pancake Coil (RPC) and Plus Point (+ Point) are the supplemental probes used in examination of tube defects and other areas of concern, such as transition and U-bend area. The pancake and Plus Point coils are connected to motor units, pressed to tube surface by spring and rotated by motor circumferentially inside tube in a helical pattern, as shown in Figure 2.3 and Figure 2.4. These probes can detect both axial and circumferential cracks and provide information about defect morphology[5, 6]. Rotating Pancake Coil probe typically contains 3 surface-riding pancake coils placed around the circumference. Plus Point coils are two orthogonal coils connected in differential mode crossing at a point, as shown in Figure 2.3, which are affected simultaneously by material and geometrical distortions such as lift-off and defects during the inspection.

Helical Scan

Figure 2.3 Rotating Probe with Plus Point Coils

18

Helical Scan

Figure 2.4 Rotating Pancake Coil Probe In commercial rotating probe, there are 3 coils placed spatially 120 degrees apart, including one Plus Point differential eddy current coils, and two high and low frequency pancake coils. Each scans the inner surface of the tube in a helical path, thus a C-scan image is obtained from these probes. The three coils are excited at multiple frequencies, typically, 200, 300 and 400 kHz. The rotating probe is sensitive to defects of all orientation, and has high resolution and improved sensitivity to characterize and size defects. However, it is sensitive to probe lift-off. In order to minimize the effect of lift-off, the pancake/Plus Point coils are spring loaded to contact with the tube wall inner surface. The mechanical rotation of the coils cause serious wears so that the probe is prone to failure. In some cases such as CANDU reactor tubes, the situation is even worse, because there are internal magnetite deposits on tube wall which reduce the probe life significantly by the wear. Furthermore, these magnetic deposits can also obscure the signals from defects. Since the probe has a helical scan pattern, the scan speed is slow, which is around 0.6’’/sec and 120~80 times slower than that of bobbin probes. Hence, the inspection time and cost increase significantly. 2.1.4. Array Probe During 1990s, number of tubes exhibiting SCC increased dramatically. In 1991, the rotating pancake coil (RPC) failed to detect the circumferential ODSCC crack which

19

caused the radiation leakage of SG tubes at Bruce Nuclear Generating Station (CANDU plant). The cracks were located in the deformed section of the tubes. Some magnetic deposits inside of tube also obscured crack signals. In order to detect and characterize these degradations, the array probe was developed. The array probes built for the market includes: C-probe, X-probe, smart probe, and intelligent probe. The array probe belongs to transmit-receive type. The transmit and receive coils of array probe coils are magnetically coupled. The transmit (active primary) coils are driven by time-harmonic ac at several frequencies. Induced voltages in receive (passive secondary) coils are generated by the change of magnetic flux through the coil windings. Anomalies in the test specimen that affect the flow of eddy current and alter the magnetic flux through the windings of the receive coil are detected and characterized. A typical array probe is composed of an array of pancake eddy current coils. These pancake coils forms axial and circumference channels separately at different time slots. Figure 2.5(a) and (b) shows the axial and circumferential channels of an array probe. The axial defects disturb the eddy current induced by axial channel transmit coil and is detected by this channel’s two receive coils. The circumferential defects cut the eddy current induced by the circumferential channel transmit coil and the indication of the defects are present in the corresponding receive coil.

20

Circ. flaw

Axial flaw

Axial

Circ.

(b)

(a)

Figure 2.5 Axial and circumferential channels of array probe: (a) Axial channel, (b) Circumferential channel C-Probe The C-Probe C-3 was the first initial array probe built by Cecco in 1990s, and later C-4, C-5 probes [7]. Two circumferential arrays of transmit and receive pancake coils are arranged with a small degrees shift along the circumference to improve the resolution along circumferential direction, as shown in Figure 2.6. Since 1992, The C-probe is routinely used for SG in-service inspection at four CANDU plants.

21

Axial 1

2 Circ. (a)

Axial Receive Circ.

Transmit

Figure 2.6 General setting for the C-Probe: (a) C-3, (b) C-4 X-Probe The X-Probe was built in 1990s. There are number of coils in each row from 8~19 (depending on tube diameter). Special designs are also made for tight radius U-bends. Array probes are usually a combination of X-Probe and bobbin probe on the same head, so the inspection times decrease largely and re-visiting tubes with different probes is eliminated, as shown in Figure 2.7. It has a complicated excitation and data acquisition system, which makes the probe costly[8].

22

X-probe

Differential bobbin

Figure 2.7 X-Probe combined with differential bobbin probe (From Zetec) An array of pancake coils covers 360 degrees of the circumference of inner tube surface, as shown in Figure 2.8. There are three rows of pancake coils with 16 in each row. Instead of rotating a single pancake probe circumferentially by motor over the circumference as is done in RPC, multiplexing techniques are used to switching on axial and circumferential channels separately at different time slots around the circumference. The first two axial channels are obtained by transmitting from C1 to A1 and A2. The first two circumferential channels are obtained by transmitting from B1 to B3 and B15 and from C1 to C3. The transmit and receive coils are activated at different multiplexed times, enabling each receive coil to detect a signal from one transmit coil at a time. The other channels are generated in the same manner after incrementing the numbers by one, giving a total of 32 axial and three sets of 16 circumferential channels in this example (with a 22.5° angular step-size for circumferential channels and 11.25° step-size for axial channels). Note that each of the 32 axial channels covers 11.25° around the circumference of the tube, and each circumferential channel covers 22.5°. Data are collected as the probe is pulled along the axis of the tube, giving circumferential and axial defect information at each axial and circumferential location in the tube. Thus, the data collected are in the form of 2D image. Since C01 works both on transmit and receive

23

mode, thus the control circuit becomes much more complicated. The array probe is capable of detecting and characterizing circumferentially and axially oriented defects such as cracks, as well as volumetric defects. It has 10 times faster inspection speed than RPC. Multiple identical pancake coils uniformly spaced ensures equal sensitivity over circumference.

1

2

3 4

5

6

7

8 9

10 11 12 13 14 15 16

A B C 1

2

3 4

5

6

7

8

9

10 11 12 13 14 15 16

Axial Channel: C1->A1 & A2 Circ. Channel: B1->B3 & B15, C1->C3 Figure 2.8 Axial and circumferential channels of array probes Smart array probe The smart array probe is an improved version of the X-probe with the following characteristics that are different from the X-probe: 

One transmitter four receivers



Every coil works on either transmit or receive mode



Simple DAQ circuits



Circumferential mode with higher resolutions



No need for axial position correction



Less time slots

24

Figure 2.9 Smart array probe From the Figure 2.9, there are only one transmitter, and four different receivers. This new design highly simplifies the control and DAQ circuits and also reduces the time slots by half. Intelligent probe The intelligent probe was built by Mitsubishi Heavy Industries and the first field trail took place in 1997. As shown in Figure 2.10, the transmit coils are specially designed as inclined coil, which is effective in both axial and circumferential defects, as explained in Figure 2. 11. The receive coil are thin film pickup coils connected with build-in electronic preamplifier circuit. The probe also combines bobbin coil with array coils together. It can detect all orientation defects in a single pass[9, 10].

(a) Figure 2.10 Intelligent probe from Mitsubishi Heavy Industries: (a) Probe schematic, (b) Real probe 25

Figure 2.10 (cont’d)

(b)

Figure 2. 11 Induced eddy current in tube wall by inclined transmit coil In summary, the array probes have high resolution, and relatively faster scanning speed compared with rotating probe, however, they are costly and have complicated control circuit and signal post-processing schemes. If specimen’s shape and size is changed then a new probe design is required. 2.1.5. Rotational Magnetic Flux Sensor The rotating magnetic flux sensor was proposed by Enokizono in 1997. This sensor is transmit-receive type. Two pairs of pancake-type coils with iron cores are arranged orthogonally with each other and are excited by two phase alternating currents with 90 degrees phase shift. Thus rotational magnetic flux with constant amplitude is generated in the specimen. Three axis searching coils measure magnitude of magnetic leakage flux density, which is perturbed by the defect in the plate or tube. Two type of probe designs are used for the flat plate inspection, as shown in Figure 2.12 and Figure 2.13. In Figure 26

2.13, the iron cores are replaced by two ferromagnetic yokes. Two pairs of excitation coils and the search coils both are wound on the yoke as represent in the figure. A modified design of the probe renders it possible to inspect a tube with the same principle as shown in Figure 2.14. However, this type of sensor is only applicable for ferromagnetic material, since it needs the return path for the magnetic flux [11-13].

Figure 2.12 Excitation coils and search coils for rotating magnetic flux sensor

Figure 2.13 One type of excitation coils and search coils for rotating magnetic flux sensor 27

Figure 2.14 Rotating magnetic flux sensor for tube inspection 2.1.6. Rotating Magnetic Field Probe Compared with an array probe, the rotating magnetic field probe has no time multiplexing. The probe belongs to transmit-receive type. No coils or sensors are need to work on both transmit or receive modes. The rotating field transmitting coils generate the rotating field during the scanning. And the pickup coils or array sensor measure the magnetic field or impedance changes at each axial scan position. The received signals with defects information can be visualized directly without complicated post-processing. The instrumentation for the probe can be simple and total cost for the system is cheap. The encircling rotating magnetic field eddy current probe was proposed by Grimberg in 1997, as shown in Figure 2.15. Three pairs of series-opposition connected coils are placed 120 degrees apart spatially on a ferrite core torus, and excited by threephase balanced sinusoidal alternating currents. The ferrite core with high-permeability homogenizes the magnetic field at the probe center. Thus a radial leakage field is created by each pair of coils separately. By vectorially combining the three magnetic fields, a resultant rotating magnetic field is produced with constant amplitude and the rotation 28

frequency of electric currents passing through the coils. Two receive coils surround the specimen to detect the magnetic leakage flux density. The probe is used for the inspection of high permeability tube or steel wire, which are placed in the middle of the encircling area [14-17].

Figure 2.15 Schematic view of encircling rotating magnetic flux probe: 1, 2, 3, transmit windings, 4, 5, receive coil, 6, high permeability ferrite core F. Ferraioli presents a new approach to build the rotating magnetic field for the encircling probe in 2010, as shown in Figure 2.16. Three phase distributed windings are wound on the inner surface of a laminated iron cylinder as transmit coils. Large number of magnetic field probes, such as Hall or fluxgate sensor, are placed all around the inner bore for the receive coils. The tubular structure to be inspected passes through the bore of the device. The probe operation has two different modes: 29



Detection: in order to assess the integrity of the tube, rotating magnetic field is generated for detecting anomalies and cracks, and a subset of MFP (magnetic flux probe) are sampled.



Inspection: when the presence of a defect is detected, synchronize three phases and generate a sinusoidal steady field, with a peak in the defect area, and MFP only in defect area is sampled.

Figure 2.16 Sketch of encircling rotating magnetic field probe A rotating field eddy current probe was built and tested by Capobianco in 1988 for use in small diameter, non-magnetic tubing. The probe is transmit-receive type with two orthogonally wound transmit coils and a pancake receive coil underneath, as shown in Figure 2.17. The transmit coils are excited by two sinusoidal currents with 90 degrees phase shift with each other, thus a rotating magnetic field is created in the specimen under the transmit coils. The probe produces a bipolar response in the presence of cracks 30

or notches. The phase angle of response signals is measured and used for estimating depth of volumetric defects [18].

Figure 2.17 Two phase rotating field eddy current probe by T.E. Capobianco Three different frequencies are used for the excitation, such as 100, 210,300 kHz. The specimen is 0.5 inch OD tube with 0.047 inch tube wall thickness. The tube material is Inconel Alloy 600. There are four electrical discharged machine (EDM) defects, which are 0.01 inch in width and 45 degrees in circumferential extent, with different depths varying between 40% ~ 100%. The receive pancake coil is 0.5 inch in diameter. From the test results shown in Figure 2.18, the phase of the signals relates to the depth of the defect when 210 kHz is used as the excitation frequency.

Figure 2.18 Rotating field probe response to decreasing notch depth An inner eddy current transducer with rotating magnetic field is also proposed by

31

Grimberg for the SG tube inspection, as shown in Figure 2.19 (a) and (b). The transmit coils are three rectangular windings with same turn numbers and placed 120 degrees spatially apart. These windings are then excited by three phase balanced sinusoidal alternating currents. Thus a rotating magnetic field is generated by these three windings. The receive coils are 8 flat coils placed on external surface of the probe cylinder and connected to a multi-channel eddy current control equipment. A prototype of the probe is built in the lab for the inspection of SG tube, as shown in Figure 2.20. The probe is pushed and pulled by a computer controlled system for the tube inspection [19-23].

(a) (b) Figure 2.19 Inner rotating magnetic field eddy current transducer: (a) a, b, c: three phase rectangular coils, (b) 1, 2, 3, …, 8: flat rectangular pickup coils

Figure 2.20 Inner eddy current transducer with rotating magnetic field The probe can detect certain material discontinuities and provide information about 32

the angular position of discontinuities. Sample defects such as OD circumferential groove and other simulated corrosion on Inconel 800 tubes with OD 20 mm and thickness 1.8 mm are detected by the probe at an excitation frequency of 102 kHz. In summary, the rotating field eddy current probes are proposed to overcome the drawbacks of the conventional rotating probes and array probes. The basic idea is to produce a rotating the magnetic field electrically instead of mechanical rotation of probe. The probe generates a rotating magnetic field using three identical rectangular windings, and receive coil is used to sense the response signal from defects. The probe is transmitreceive type with high signal to noise ratio, and sensitive to defects of all orientations, which is functionally equivalent to RPC. Furthermore, the probe has higher scan speed than RPC and simpler control circuit than array probe. There are multiple configurations of transmit and receive coils according to different applications. The sensitivity and resolution are highly dependent on the receive coil. The probe can be either inside-tube probe or outer encircling probe depending on the test sample. 2.2. Review of Manufacturing of Eddy Current Probes 2.2.1. ZETEC Zetec is a one of the leading companies for development and marketing different eddy current probes for the steam generator inspection. These probes are Zetec’s compliant low noise bobbin probe, rotating probe and X-probe. 2.2.1.1 Bobbin Probe Bobbin probe provides clean eddy current data that is consistent through the life of a probe and the duration of inspection, as shown in Figure 2.21.

33

Figure 2.21 Zetec bobbin probes 2.2.1.2 Rotating Probe Motorized Rotating Probe Coil (MRPC) Prove comprise two pieces: a motor unit and a probe head, as shown in Figure 2.22. The MRPC rotating head inspects full coverage of tube circumference. The surface riding coils ensure minimum lift-off effect and maximum signal-to-noise. MRPC probes excel in finding axial and circumferential defects in critical areas of top tube sheets (TTS), tube support plates (TSP), and U-bends areas.

Figure 2.22 Zetec motorized rotating pancake coil probes 2.2.1.3 X-probe Zetec’s X-Probe design uses a combination of bobbin and array probe to provide 34

quick, simple, and comprehensive single pass inspections. The X-Probe incorporates array of pancake coils around tube circumference and takes advantage of sophisticated multiplexing techniques within the head of the probe, as shown in Figure 2.23.

(a)

(b) Figure 2.23 Zetec X-probe with different bobbin on the same head 0.725” OD 2.2.2. Olympus (R/D tech) Eddy current bobbin probes are also developed by the Olympus (previous R/D tech) for steam generator tube inspection. Full saturation probe is designed for ferromagnetic steam generator tube inspection. Array probe is available for detecting circumferential cracks with high resolution and speed. 2.3. Comparison of eddy current probes All the above eddy current probes or sensors have their advantages and disadvantages for the nondestructive testing, which is summarized in Table 2.1[24].

35

Table 2.1 Advantages and disadvantages of eddy current probes and sensors for tube inspection Probe type Advantages Disadvantage Bobbin

Fast inspection speed, sensitive to axial

Insensitive to

probe

defects, determine defect depth and length,

circumferential defect

high reliability and durability, low price

1D scan data, not direct for visualization of defects Not possible for multiple defects at same axial location

Rotating

High sensitivity to defect of all orientations

Low inspection speed

Probe

High signal to noise ratio

Low reliability and

(Pancake,

Defect orientation determination

durability

+Point)

Characterize and size defect with length and

High price

depth C-scan visualization for tube inner surface

36

Table 2.1 (cont’d) Array probe

High sensitivity to defects of Very high price with

(C-Probe, X-Probe, smart all orientation probe, intelligent probe)

complicated instrumentation

High inspection speed Insensitive to lift-off effect Defect orientation determination Characterize and size defect with length and depth C-scan visualization for tube inner surface

Rotating field probe

Avoid rotating probe

Need field test approve

mechanically Sensitive to defects of all orientations Fast inspection speed

In order to utilize the advantages and disadvantages of eddy current probes, some concepts can be considered for improving the performance of these probes. Multi-probe Different types of probes can be combined together to get advantages of both. For example, absolute and differential bobbin probes are integrated into one probe header.

37

Then the probe can be both sensitive to the large defects so that gradual geometry changes are detected in absolute channel and abrupt anomalies and small defects are detected in differential channel. The X-probe combines array of coils with a differential bobbin coil. The bobbin probe detects the initial defect region and array probe is used for fine scan data useful to characterize the defect. Multiple identical X-probes can also be integrated into one probe together to increase the circumferential resolution during onepass inspection. Multi-frequency Single-frequency eddy current tests offer excellent sensitivity to a number of different types of SG tubing under normal conditions. However, conditions are often complicated by a number of factors, and consequently inspection needs cannot be effectively solved by single-frequency examinations. State-of-the-art multi-frequency ET overcomes most of the single-frequency limitations. The multi-frequency technique consists of collecting data simultaneously using several excitation frequencies from just one probe pull. The data are analyzed using multi-frequency mixing. The technique not only allows the effect of extraneous discontinuities to be nullified but also improves the classification and characterization results. Each single frequency is sensitive up to a certain depth of the test sample. Low frequencies have large skin depths and hence generate strong indications of support structures that are located outside the tube. Thus, they are often used to determine the location of support plates and other support structures along the tube. They can also be used to detect depositions of corrosion products on the outside of the tubes. Higher frequencies have a much smaller skin depth. The relationship between the phase angle of

38

the eddy current signal and the depth of defects, can be obtained and plotted in a phase calibration curve, which is exploited to detect, classify, and characterize defects. Due to the different skin depths at different frequencies (skin effect), signals from defects and support features change with frequency. In effect, this means that multi-frequency response signals have more information that can be analyzed to extract relevant features. For instance, suppression of unwanted response due to tube support plates is realized by subtracting lower frequency signal (greater response from support plate) from a scaled and rotated high frequency signal (more response from defects), so that the mixed signal show little or no support plate indication but retain information about small defects. The multi-frequency mixing algorithms can also reduce noise from internal surface[6]. There are two methods to apply the multi-frequency excitation to the probe coils, as shown in Figure 2.24: (a) multiple frequencies signals are applied to the coils by multiple time slots with multiplexing technology; (b) all the frequencies signals are injected to the coils at the same time.

(a)

(b) Figure 2.24 Multi-frequency technologies for the excitation of eddy current probe: (a) Multiplexed four frequency signal, (b) simultaneous injection four frequency signal The advantages of multi-frequency techniques can be summarized as follows: 

Data collections at several test frequencies simultaneously. This decreases the inservice inspection time. 39



Separation of discontinuities that give dissimilar signals at different frequencies.



Improvement in sensitivity to different types of discontinuities.



Improvement in detection, interpretation, and sizing of defects even in the presence of artifacts that complicate the analysis procedure.

Multi-probe and Multi-frequency Multi-frequencies techniques can be applied to probes which integrate multiple different types of probe into one header. For example, a rotating probe head includes three different diameter coils, 2 pancake coils and 1 plus point coil, and operate at different frequencies. Since the bigger size of coil, deeper the penetration depth, the largest diameter coil is excited by lowest frequency and has deepest penetration depth. The smallest diameter coil is excited by highest frequency, so maximum spatial resolution is achieved. The probe is rotated helically through the inner surface of Inconel tubing, and can detect diverse kinds of defects such as cracks, pits or regions of thinning, and also defects located at different depths throughout the tube wall due to multifrequencies techniques [25]. Multi-inspections Different probes are used in multiple scans in each inspection. For example, the bobbin probe initially detects the existence of defects on the full-length of the tubing, and then additional inspection with best available and qualified probes such as RPC/array probes are used for the re-scanning only around these defects areas. Any unusual or new indications of potential defects found by bobbin probe are re-inspected to provide further information that can help the detection.

40

Multi-technologies Often, additional techniques such as ultrasonic testing (UT) are also deployed for reinspection and characterization after the eddy current testing. For example, it is difficult for eddy current probe to detect defect within ferromagnetic tubes, in which case ultrasonic probes are considered as complementary tools for the inspection. 2.4 Summary In summary, eddy current probes have evolved along several directions such as multi-probe, multi-frequency excitation and multi-inspections based on the needs of different applications. The probes also tend to take advantage of multi-technologies other than eddy current. In order to have better performance, the probes are designed to collect additional channels of data, faster inspection speed and acquisition rates, greater bandwidth, higher resolution and higher signal to noise ratio. Small thin film sensors such as giant magnetoresistive (GMR) sensors with high sensitivity can measure a magnetic field from eddy current transit coil over an area comparable to the size of the coil itself. Recent development in probes is aimed to provide them with the capability to characterize defect types and their morphologies, assess tube integrity and help identify degradation mechanisms easily.

41

CHAPTER 3 FINITE ELEMENT MODELING FOR TIME HARMONICS EDDY CURRENT PROBLEMS 3.1. Introduction to Analytical and Numerical Methods for Eddy Current Problem 3.1.1. Analytical Method In the past few decades, a lot of research has focused on the analytical analysis of eddy current testing problems. Dodd and Deeds gave closed form solutions of magnetic vector potential for axially symmetric eddy current problems. The analytical solution for coil above a semi-infinite conducting plane is calculated in [26]. Grimberg uses transfer matrix method to calculate electromagnetic field created by an arbitrary current distribution placed in the proximity of a multi-layer conductive cylinder. The general results obtained are adapted for the special case of an eddy current transducer with a rotating magnetic field[15]. Theodoros provides closed-form expressions for both impedance and induced eddy current density of rectangular coils located above a conducting half-space. The formulation is general and can be also used for coils with different shapes [27]. His software TEDDY is posted on his website. 3.1.2. Numerical Method Analytical methods are limited in their application to relatively simple specimen and defect geometries. Numerical methods including finite element, finite volume, boundary element and integral equation methods have been investigated and implemented by many research groups, such as SGTSIM by NDEL from MSU[28-35], CIVA in France[36, 37], VIC3D[38, 39], integral equation methods by John Bowler from ISU[40-43], and AECL in Canada[44-46].

42

3.1.2.1. Finite Element Method Finite element method is a versatile method for the numerical analysis of eddy current problem and its application is widely used in the past years [47-59]. From 1970s, Chari M.V.K [48, 49] used finite element analysis to model eddy current problem in magnetic structures. Vector potential and scalar potential methods are two finite element formulation methods are discussed and implemented by Biro [60-73] and other researchers for eddy current problems [51, 52, 57, 59]. R. Palanisamy and W. Lord predict eddy current probe impedance trajectories with 2D finite element method for nondestructive testing [54, 74-80]. The magnetic vector potential is used to calculate magnetic flux density in the vicinity of defects and complex impedance of a sensor placed near a defect. Z. Zeng and L. Udpa have used two and three dimensional eddy current probe modeling and simulation using magnetic vector potential and reduced magnetic vector potential and electric scalar potential [28-31, 81-93]. Other methods such as electric vector potential and magnetic scalar potential also been applied for the eddy current problems in the past years [64, 66]. The edge finite element method is investigated for eddy current problems in [68, 70]. 3.1.2.2. Integral Equation Method In 1980s, Bowler calculated eddy current probe impedance due to a volumetric defect by integral equation methods [40-42, 94, 95]. A theoretical prediction for electromagnetic field of eddy current probe response for three dimensional surface cracks is expressed by volume integral with dyadic kernel. The integral equations are approximated by a discrete form using moment method and solved using conjugate gradients. Albanese and Rubinacci propose an integral formulation using two-component

43

current density vector potential for the numerical analysis of thin cracks[96]. However, it is hard for integral equation to deal with complex geometries. In some cases, there are no explicit Green’s function for the eddy current problems. 3.1.2.3. Hybrid Method CIVA [97-99] apply the volume integral method combined with finite element method for the eddy current probe simulation. The primary field is calculated using finite element method, whereas the defect response is efficiently computed through volume integral method using dyadic Green’s formulation. The integral equation methods are also combined with boundary element method for the eddy current problems[43]. So the method has short computational time and very efficient compared with the finite element method especially for large scale eddy current problem. The drawback of these methods is the need to calculate the equivalent current and dyadic Green’s functions. As in the case of integral equation methods, the Green’s function may not exist for some cases. 3.1.3. Summary Analytical methods are computationally efficient and accurate for the analysis of eddy current problems with simple geometries composed of homogeneous materials, and are very helpful for understanding the basic underlying physics. Compared with analytical methods, numerical methods have high computational cost. However, unlike analytical methods, finite element method is not restricted by irregular geometry or inhomogeneity of the domain. The method can handle awkward boundaries and shapes with ease. In finite element methods for electromagnetic field computation, one of the most commonly used approaches is magnetic vector potential (MVP) formulation. The MVP

44

formulation has several advantages such as (1) avoiding the need of interface coupling since the surface boundary for different materials is natural in this formulation and fits very well with eddy current testing problems where the conductor surfaces and defect boundaries have a very complicated shape; (2) the source current is assumed as ideal current in free space with no induced eddy current inside and thus easily modeled; (3) applicable for multi-connected conductors; (4) high accuracy compared with electric scalar potential methods. However, magnetic vector potential and electric scalar potential in conducting region yield relatively ill-conditioned systems as high number of iterations is needed for solution. With higher frequency, the conditioning number deteriorates considerably. The reduced magnetic vector potential is a modified version of magnetic vector potential methods. It has all the advantages as the magnetic vector potential methods, especially in the simulation of eddy current probe scan. Reduced magnetic vector potential can avoid the re-meshing the probe at different scan positions. The primary magnetic field can be calculated analytically using Biot-Savart law with fast computational speed and high accuracy. The magnetic scalar potential method also reduces the number of unknowns in the non-conducting region due to use of only one magnetic scalar potential for each node. It renders the method more computationally economical and effective for nonhomogeneous problems in contrast to magnetic vector potential that uses threecomponent unknowns in the non-conducting region. However, the method cannot be applied for multi-connected conductors.

45

3.2. Formulation of Finite Element Method 3.2.1. Eddy Current Problem The typical eddy current problem consists of a conducting (eddy current) region 1 with nonzero conductivity and a surrounding non-conducting region  2 free of eddy currents which may contain source currents J s , as shown in Figure 3.1. Assume there is no eddy current in the current source such as excitation coils, the excitation current source is always located in the non-conducting region  2 . SH : H  n  0

n12

 0 1

Js  0 2

S12

Conducting region

 0

SB : B  n  0 Figure 3.1 Typical eddy current problem Where, J s : excitation source current density.  : conductivity of the conducting region.

1 : conducting region with nonzero conductivity.  2 : non-conducting region, contains source current, free of eddy current. S12 : interface between 1 and  2 .

S B : boundary, norm component of magnetic flux density is prescribed. S H : boundary, tangential component of magnetic field intensity is given.

46

n:

the outer normal on the boundaries S B and S H .

Because   is always satisfied at the low frequencies in eddy current problems, the displacement current is neglected and the Maxwell equation can be written as  H   E  E  

B t

B  0

(a)    (b)  in 1  (c )  

 H  J s  B  0

(a)   in 2 (b)  B  n  0 on S B H  n  0 on S H

B1  n12  B2  n12 H1  n12  H 2  n12

(a )   on S12 (b) 

(3.1)

(3.2) (3.3) (3.4) (3.5)

where, the subscripts 1 and 2 refer to quantities in regions 1 and  2 respectively. Boundary conditions impose the continuity of normal component of flux density and the tangential component of magnetic field intensity. The eddy current finite element model solves for the magnetic flux density, magnetic field intensity and the induced eddy current in the solution domain for the case where the geometry, source current distribution and the material properties such as permeability and conductivity are prescribed. The above equations are known to ensure the uniqueness of B and E , provided S B and S H are simply connected. When the source current and field oscillate at single frequency, each quantity can be expressed as a sinusoidal function with an amplitude and phase, which is the generally case for the eddy current testing. Then all the quantities in the Maxwell equations can be expressed by phasors. Once these phasor quantities are solved, then the corresponding instantaneous quantities can be obtained. Assume 47

 t

j

(3.6)

Then the Maxwell equations can be re-written as

H  E   E   jB

(3.7)

B  0

(a)   (b)  in 1 (c) 

 H  J s  B = 0

(a)   in 2 (b) 

(3.8)

Bn  0

on S B

(3.9)

H  n  0 on S H

(3.10)

B1  n12  B2  n12 H1  n12  H 2  n12

(a )   on S12 (b) 

(3.11)

3.2.2. Formulations - Magnetic Vector Potential Three-dimensional magnetic vector potential finite element method for modeling of eddy current nondestructive testing is described in [100]. The method predicts differential eddy current bobbin probe impedance plane trajectories for defects in PWR steam generator tubing. Isoparametric hexahedral elements are used in the simulation. Let magnetic vector potential be represented by A and electrical vector potential by V, then

B   A

(3.12)

H   A

(3.13)

 E   jB

(3.14)

 (E  j A)  0

(3.15)

E   jA  V

(3.16)

48

where  is the reluctance. A is used in both conducting region 1 and non-conducting region  2 , while V is used in conducting region only. The magnetic vector potential reduces the number of unknowns to be solved compared with the method to solve the magnetic and electric field components directly. So the governing equations for the 3D eddy current problem can be presented by  ( A)  j A  V  0

in 1

(3.17)

 ( A)  J s

in 2

(3.18)

n  ( A)  0

on SB

(3.19)

( A)  n  0

on SH

(3.20)

n12  A1  n12  A2 (1 A1)  n12  ( 2 A2 )  n12

(a)   on S12 (b) 

(3.21)

Because  ( A)  0 is always satisfied, so  B  0 is included. If A is continuous, then equation (a) is satisfied automatically. At each node in the conducting region, A and V are unknowns, and the degrees of freedom is 4, whereas for non-conducting region, A is the only unknown, and degrees of freedom is 3. Coulomb Gauge In the governing equations, the curl of A is determined; however, divergence of A is undetermined. There are two methods to fix the divergence: Coulomb Gauge and Lorentz Gauge. The Coulomb Gauge is more convenient than Lorentz Gauge for the numerical computations at quasi-static frequencies in electromagnetics. In order to ensure the uniqueness of A, the divergence and boundary condition for A also need to be prescribed.

 A  0

(3.22)

After imposing the Coulomb Gauge, the governing equation cannot guarantee the current 49

continuity, which should be listed as a separate equation.

 ( A)  (  A)  j A  V  0   ( j A  V)  0  ( A)  ( A)  J s

( a)   in 1 (b) 

(3.23)

2

(3.24)

in

n A  0   A  0

(a)   (b) 

on S B

(3.25)

nA  0 ( A)  n  0

( a)   (b) 

on S H

(3.26)

on S12

(3.27)

A1  A 2

1  A1   2  A 2 1  A1  n12   2  A 2  n12 n  ( j A  V )  0

(a)  (b)   (c )  (d ) 

Equation (3.27) (d) ensures the norm current density to be zero on the surface of conductor. The governing equation can be merged into one equation:  ( A)  ( A)  j A  V  Js  0  ( j A  V)  0

in  : 1  2

(3.28)

in 1

(3.29)

where,  and J s can be defined element by element. In conducting region 1 , Js  0 , and in non-conducting region  2 ,   0 . The A, V - A method has stable numerical solution for harmonic quasi-static magnetic field because of the uniqueness of A and V . The inner interface S12 condition is the natural boundary condition, which is satisfied automatically in finite element discretization. The method can be applied for multiply connected conducting regions.

50

3.2.3. Reduced Magnetic Vector Potential In order to decouple the magnetic field due to induced eddy current from the field due the excitation source current, the total magnetic vector potential A is decomposed into

As and Ar , where As is the magnetic vector potential due to excitation source current in free space and Ar is the magnetic vector potential due to induced current in the conductor, respectively. The total magnetic flux density B is the summation of the corresponding terms Bs and Br and similarly, the magnetic field intensity H can be expressed in terms of source and induced components.

A  As  Ar

(3.30)

B  Bs  Br

(3.31)

Bs   As

(3.32)

Br   Ar

(3.33)

H  Hs  Hr

(3.34)

Hs   0Bs   0 As Js   Hs

(3.35) (3.36)

Then the governing equation can be derived from the A, V - A method by substituting A by As and Ar as  (As  Ar )   (As  Ar )  j (As  Ar )  V  Js  0  ( j (As  Ar )  V)  0

(3.37) (3.38)

Incorporating Coulomb gauge into the governing equation:   (As  Ar )  0

51

(3.39)

  As  0

(3.40)

  Ar  0

(3.41)

J s   H s

(3.42)

B s  0H s 

   A s    B s   

1

0

Hs

(3.43)

 H s    r H s 0

 Ar    Ar  j Ar  V   Hs  

(3.44) Hs

0

 j As

 Ar   Ar  j Ar  V  (1  r ) Hs  j As  ( j Ar  V)   ( j As )

(3.45) (3.46) (3.47)

where  0 is the reluctance in free space and  r is the relative reluctance of the conductor. It is important to note that all the variables on the left hand side of equation is independent of excitation source, and only rely on induced current in the conducting region. This implies that there is no need to re-generate the mesh for the probe coils at different scan positions during inspection. From the above equations, there is no need to mesh the current source together with solution domain. It is therefore efficient to simulate the probe scan, since there is no need to re-mesh the probe at different scan positions. Thus, the total computation time is largely reduced. In simulation of eddy current inspection of tubes, the tube and probe are meshed separately, as shown in Figure 3. 2. 3.2.4. Source Coil Modeling In the Ar, V-Ar formulation, the contribution of the current source (probe coil) to the 52

system of equations (solution domain, tube and surrounding air mesh) is described by As and Hs . According to the Biot-Savart law, the As and Hs on the right hand side of the equation can be calculated analytically with highly reduced computation time as,

 J s (r ) As  0  d 4  r  r 

Hs   0 As 

1 r  r Js (r )  d  3 4  r  r

(3.48)

(3.49)

where, r and r’ are the coordinates of observer (tube mesh) and source (probe coil mesh) points. J(r’) is the excitation current density, and  is the volume of excitation source (probe coil mesh),  is the volume of tube mesh. At each scan point, the field in the tube mesh due to the probe coil is calculated by the equation (3.48) and (3.49). Numerical integration is performed to calculate As and Hs . To this end, the coil is discretized into elements, as shown in Figure 3. 2. The coil mesh is different from the tube mesh generation in the FEM and is done independently from the tube. The magnetic field in each element of the tube mesh due to all the probe coil current source mesh elements is calculated analytically at each scan point by summation and interpolation of the coil mesh into the tube mesh with fast computation time.

53

Figure 3. 2 Discretization of Coil separated from tube mesh On the interfaces between ferromagnetic and non-ferromagnetic regions, the normal component of the Ar should be allowed to be discontinuous in order to improve the accuracy of the computations. Dirichlet boundary conditions are imposed only at the far boundaries, namely the tangential components of Ar are set to zero there, and no Dirichlet boundary conditions are imposed on V. 3.2.5. Reduced Magnetic Vector Potential for Ferrite-core Probes The method presented above only considers an air-core coil. If the probe has a ferrite core, the calculation of source coil magnetic field in free space cannot be done simply by using Biot-Savart law. If a coil has a ferrite core, as shown in Figure 3. 3 and only the coil mesh is decoupled from the sample mesh then the ferrite core needs to be meshed with the test sample. Then re-meshing and matrix factorization are necessary for 54

each coil/core position. Therefore the above method cannot be directly applied. Core Coil

Sample

Figure 3. 3 Configuration of Nondestructive Testing with Ferrite-Core Coil To make use of the Ar, V-Ar formulation, the ferrite core should not be meshed with the test sample. To this end, we decompose the magnetic field intensity into three parts: H  Hcoil + Hcore + Hsample where Hcoil, Hcore, and Hsample are field intensities due to coil, core, and test sample, respectively. So H can be rewritten as 𝑯 = 𝑯𝑐𝑜𝑖𝑙 + 𝑯𝑐𝑜𝑟𝑒 + 𝑯𝑠𝑎𝑚𝑝𝑙𝑒

(3.50)

A procedure is illustrated in Figure 3. 4. The iterative procedure continues until the value of coil voltage calculated from the total field converges.

Figure 3. 4 Illustration of Modeling Method in Case of Ferrite Core 3.2.6. Galerkin Weak Formulation Galerkin method belongs to the class of weighted residuals methods, which is an approximate approach to solve differential equations. Define[101, 102] Js  (1  r ) Hs  j As

 Ni [ Ar  (  Ar )  j Ar  V  Js ]dV  0, i  1, 2,..., NP 55

(3.51) (3.52)

n  Ar  0

  Ar  0 n  Ar  0 ( Ar )  n  0

(a)   (b) 

on S B

(3.53)

(a)   (b) 

on S H

(3.54)

on S12

(3.55)

A1r  A 2r 1  A1r   2  A 2r

(a)  (b)   (c )  (d ) 

1  A1r  n12   2  A 2r  n12 n  ( j A r  V )  0 n  Ni  0 n  Ni  0

on SB

(3.56)

on SH

(3.57)

[ Ni  Ar   Ni (  Ar )  j Ni  Ar   Ni V  Ni  Js ]dV  0 (3.58) 

Ni   ( j Ar  V)dV  0

(3.59)

1

  [ Ni ( j Ar  V)]dV   Ni  ( j Ar  V)dV  0 1

(3.60)

1

 Ni  ( j Ar  V)dV  S 1

Ni ( j Ar  V)  nds  0

(3.61)

12

n  ( j Ar  V)  0

on S12

 Ni  ( j Ar  V)dV  0

(3.62) (3.63)

1

The coefficient matrix is not symmetric. In order to ensure the symmetry of the coefficient matrix, the electrical scalar potential can be presented as V  j

(3.64)

So the Galerkin weak form for the reduced magnetic vector potential formulation can be written as

 ( Ni  Ar   Ni  Ar  j Ni  Ar  j Ni   Ni  Js )dV  0 56

(3.65)



jN i  ( Ar  )dV  0

(3.66)

1

E

  (  Nie   Aer   Nie  Aer  j Nie  Aer e

e 1

(3.67)

 j N ie e  N ie  Jse )dV  0 E

 

e 1

e

jN ie  ( Aer  e )dV  0

(3.68)

3.2.7. Mesh Generation A hexahedral element is used to discretize the 3-D domain of interest. The mesh is so designed that when the probe scans along either the axial direction or the circumferential direction, the interpolation error due to different relative positions between the probe and the local mesh lines remains consistent. Thus the computed signal should not be noisy. The mesh generator allows incorporation of cracks of different types. Figure 3. 5 shows examples of cracks: axial, circumferential notches or circular hole. Cracks can be introduced on different sides of the tube wall (ID, OD, and through-wall).

57

Figure 3. 5 Finite Element Meshes for Free-Span Tube (Half Geometry) (a) Axial Rectangular Crack: 0.5” (12.7 mm) Long, 0.005” (0.127 mm) Wide, and 100% Depth (b) Circumferential Rectangular Crack: 0.5” (12.7 mm) Long, 0.005” (0.127 mm) Wide, and 100% Depth (c) Circular Hole: 0.067” (1.702 mm) Diameter and 100% Depth 3.2.8. Linear Equations Solver Expanding the magnetic vector and electric scalar potentials in terms of shape functions, applying Galerkin techniques, and imposing appropriate boundary conditions, we get the following system of algebraic equations. 58

{G}{U }  {Q}

(3.69)

where, {G} is a complex and sparse matrix, and only its nonzero entries need to be stored when we use an iterative solver to obtain the solution. {U } is the vector of unknowns consisting of three components of magnetic vector potential and electric scalar potential at each node of the finite element mesh. {Q} is the load vector incorporating the current source. To solve the linear equations, two types of methods are used: direct method and iterative methods. Direction methods are Gauss elimination, LU, LDU (or LDLT if matrix is symmetric) decomposition methods, frontal and multifrontal methods. They can be used for some small dimensional matrices with high efficiency. For large sparse matrix, iterative methods are used for solving the equations, such as CG, BiCG, GMRES, QMR, CGS, BiCGSTAB and TFQMR [103-114].TFQMR method quasi-minimizes the residual norm in the space spanned by the vectors generated by CGS methods. It has smoother convergence with a convergence rate similar to CGS method[105]. The TFQMR matrix has transpose free feature for the implementation. In the simulation tools, TFQMR method is used to solve the linear equations. 3.2.9. Post-processing After solving the linear equations, the solutions for the magnetic vector potential and scalar potential are obtained. For the reduced magnetic vector potential method, the solutions from the linear equations are values of Ar and V. In order to get the total magnetic vector potential, the magnetic vector potentials As of each node are added into Ar as A = Ar + As

59

(3.70)

Then three components of magnetic flux density and magnetic intensity are calculated from A as. A z A y  y z A x A z By   z x A y A x Bz   x y

(3.71)

H = νB

(3.72)

Bx 

The induced eddy current density in the conducting region can be calculated by A and V as (3.73) E   jA  V J   E   j A  V

(3.74)

The induced voltage in the bobbin coil, used as pickup sensor, can be calculated as V   N 

B

S t

 ndS   N  j A  dl

(3.75)

where, S is the encircling area of bobbin coil, n is the outward normal direction of bobbin coil plane, and N is the number of bobbin coil turns. 3.2.10. Calibration of Simulated Signals Signals computed by the simulation model are first calibrated in order to compare with experimental measurements. The calibration procedure is as described below. Calibration procedure for bobbin probe signals: a) Simulate a 0.06” diameter (0.067” for 720MR, 0.052 for 510 TF) flat bottom hole (FBH) through wall (100% depth) defect and calculate maximum amplitude of the signal. b) Simulate four 0.188” diameter, FBHs with 20% depth defect and calculate

60

phase c) Scale the maximum amplitude to 4V to 100% FBH signals and determine the amplitude calibration factor (scaling). d) Rotate the 4 FBHs signal phase to 40 degrees (from the WEST direction) and determine the phase calibration factor (rotation). e) A set of simulations of 100% and 20% FBHs have been run for the type of Bobbin probes with specific tube dimensions at different frequencies. f) The simulation signals (amplitude and phase) at different frequency are used in a curve fitting procedure to determine the scaling factors from 100% FBHs and rotation factors from 20% FBHs with respect to frequency. g) Simulate the tube with target defect and calculate the defect signal. h) Then the corresponding scaling and rotation factors for calibration at target frequency are calculated by interpolation on the two curves from step (f), and thus the calibration coefficients of magnitude and phase are obtained i) Apply amplitude scaling factor to the result from step (e). j) Apply the phase rotation from step (d) to the result from step (e). Calibration procedure for pancake probe signals a) Simulate a 0.06” by 0.06” square through wall (100% depth) defect and calculate the phase and amplitude of the signal at maximum vertical location. b) Rotate the phase to 35 degrees and determine the phase calibration factor (rotation). c) Simulate the tube with target defect and calculate the defect signal. d) Apply the phase rotation from step (b) to the result from step (c).

61

e) Apply amplitude scaling to 20 Volts to the result from step (d) and get the final results. Calibration procedure for Zetec PP11A +Point probe signals a) Simulate a 0.5” length, 40% depth of the tube wall thickness, I.D. axial defect and calculate the phase at the maximum vertical signal location. b) Rotate the phase to 15 degrees and determine the phase calibration factor (rotation). c) Simulate the tube with target defect and get the defect signal. d) Apply the phase rotation from step (b) to the result from step (c). e) Apply amplitude scaling to 20 Volts to the result from step (d) and get the final results. Calibration procedure for Array probe signals a) Simulate a 0.5” length, 30% depth of the tube wall thickness, O.D. groove and calculate the amplitude at the maximum signal location. b) Scale the amplitude from step (a) to 4 volts and determine the amplitude calibration factor (scaling). c) Simulate a transition part of tube with tube I.D. 0.665”, tube O.D. 0.75”, transition O.D. 0.765” and calculate the phase at the maximum vertical signal location. d) Rotate the phase from step (c) to 0 degree and determine the phase calibration factor (rotation). e) Simulate the tube with target defect and get the defect signal. f) Apply the amplitude scaling from step (b) to the result from step (e).

62

g) Apply the phase rotation from step (d) to the result from step (e) and get the final results. 3.2.10. Summary The steps for modeling procedure using the Ar, V-Ar formulation are as follows: 

Generate mesh without meshing coil, an example shown in Figure 3. 5.



Discretize coil, an example shown in Figure 3. 4.



Choose basis functions



Generate stiffness matrix G



Impose Dirichlet boundary condition on G



Perform preconditioning on G



Loop over coil positions o Calculate As and Hs (if r  1) o Generate right hand side b o Impose Dirichlet boundary condition on b o Solve system of equations Gx = b o Calculate coil impedance o Auto calibration for amplitude and phase by scaling and rotating factors

63

CHAPTER 4 FINITE ELEMENT SIMULATION AND VALIDATION OF EDDY CURRENT PROBES FOR TUBE INSPECTION 4.1 Introduction In order to make the software user friendly for SG analysts, it is important to: (1) make the software interactive so as to enable modeling of different defect and tube geometries with ease; (2) validate with experiment. This chapter presents modeling of different tube, regions, defect and probe geometries using finite element model. The user interaction the defects are characterized by few parameters. The experimental validation of model w.r.t different probes Bobbin, Plus Point and Rotating Pancake coils probes and various defect scenarios along with quantitative error analysis are reported in Appendix 1. 4.2 Tube and Defect Geometries 4.2.1 Tube Geometries 4.2.1.1 Free Span The free span geometry is the segment of steam generator tube that is free geometrical structures, as shown in Figure 4. 1. The geometry is divided into a region with uniform mesh and the outer region with varying element size. The probe scan is performed in the uniform region during the simulation. The scan step size is generally set as 1 mm. User specified parameters for free span mesh generation are: (1) tube outer/inner diameter, (2) number of uniform mesh element, and (3) number of element layers in tube wall thickness.

64

Figure 4. 1 Tube mesh generation – Free Span 4.2.1.2 Top Tube Sheet (TTS) In steam generators, U-shaped heat exchange tubes are inserted into a thick plate called tube sheet. The tube sheet is approximately 21 inches thick and has two holes for each tube (one hole on the hot-leg side of the steam generator and one hole on the cold-leg side). The tube bundles connect to a tube sheet on each end of the tubes. The lower end of the tubes is tack-expanded into the tube sheet for approximately 0.70 inch. This tack expansion is performed to facilitate welding of the tube to the tube sheet and forms a temporary expansion transition, as shown in Figure 4.2. Both the tube sheet and the exterior of the tubes at TTS tend to accumulate sludge, and show excessive fatigue cracking. Further, some loose parts or foreign object inside of the steam generator are often found around the tube sheet region. A rotating probe is normally used to inspect the tube sheet for loose part detection [115, 116].

65

Top Tube Sheet (TTS) Transition

Free span

Rotating Pancake coils Loose part

Figure 4.2 Geometry of TTS, transition and free span with loose part Table 4.1 Parameters of tube geometries and material properties Tube Free Span Transition Tube Sheet

Material ID OD OD (expanded) Length ID

0.775" 0.875" 0.890" 0.25" 0.890"

Relative Permeability

Conductivity (S/m)

inconel 600

1.01

696000

carbon steel

100

6990000

Figure 4.3 Carbon steel loose parts for top tube sheet mock-up User specified parameters for TTS meh generation are: (1) inner diameter of tube sheet, (2) length of transition, (3) expanded inner/outer diameter of tube diameter, (4) tube outer/inner diameter, (5) number of uniform mesh element, and (6) number of element layers in tube wall thickness.

66

Figure 4. 4 Tube mesh generation - TTS 4.2.1.3 Tube Support Plate (TSP) Tube support plate (ferromagnetic material, generally carbon steel) is a structure to hold the steam generator tube from vibration. The tubes go through the support plate, with a small air gap between the tube and the plate, as shown in Figure 4. 5. User specified parameters for TSP mesh generation are: (1) the thickness and inner diameter of support plate, (2) tube outer/inner diameter, (3) number of uniform mesh element, and (4) number of element layers in tube wall thickness.

67

Figure 4. 5 Tube mesh generation - TSP 4.2.2 Defect Geometries A long rectangular crack oriented along axial or circumferential directions is modeled as shown in Figure 4. 6. The width of the crack generally is 0.005”. The length and depth is user specified.

(a) Figure 4. 6 Rectangular crack: (a) axial notch; (b) circumferential notch

68

Figure 4.6 (cont’d)

(b) 4.2.2.1 Elliptical and Circular Holes The elliptical and circular holes are used to simulate the machined flat bottom holes as shown in Figure 4. 7. The diameter and the depth is user specified. The model can generate four flat bottom holes at 0, 90, 180 and 270 degrees as shown in Figure 4. 7(b) for the probe signal calibration.

(a) Figure 4. 7 Elliptical and circular holes: (a) elliptic through hole; (b) four through circular holes

69

Figure 4.7 (cont’d)

(b) 4.2.2.2 Real Crack Model The module for interactive generation of a real crack is described in this section. The width of the real crack introduced is assumed to be 0.001 inches. For the axial crack the user can define the axial length and depth profile of the crack. For the circumferential crack the user can define the circumferential length and depth profile along the circumferential direction. In the SG tube inspection application, EPRI has database of metallurgically profiled real cracks. The simulation code can accept the profile in format from the database or allow the user to draw the profile on a grid using a cursor. The red curves are drawn by the user to simulate the axial or circumferential real crack profiles as shown in Figure 4. 8 - 4.11. In order to simulate axial or circumferential real cracks, an element based method is applied. First, a uniform mesh is generated for the tube wall. Then a pre-defined curve for approximate the axial real crack profile is load as the reference for comparison, so that all the element below that curve are chosen to be marked as air elements to represent the real crack. All the elements under the curve are marked as element as air, as shown in Figure 4. 8. The method for modeling of circumferential crack is similar as that of axial cracks. Note that these two models are two dimensional representations, since the width of the real crack is 0.001 inches.

70

Figure 4. 8 Axial real crack (ID)

Figure 4. 9 Axial real crack (OD)

71

Figure 4. 10 Circumferential real crack (ID)

Figure 4. 11 Circumferential real crack (OD) 4.2.2.3 360 Degrees Dent Dent is another type of physical deformation defects occurring in tube wall of the steam generator tubes. The Figure 4.12 presents typical 360 degrees dent geometry, where both the ID and OD decrease because of the deformation on the outer surface of the tube wall.

72

ID

Figure 4.12 360 degrees dent geometries of the tube A 360 degrees dent around the tube wall is used as the calibration standard for the detection of dent in industry. The 2D profile for 3D dent modeling can be represented by parabola described by equation (4.7) as shown in Figure 4.13(a), where, ri represents the deformation of the tube wall along radial direction of a tube wall. If the maximum depth in the dent center is OO’ and the axial opening of the dent is AB, then the constant k can be calculated using equation (4.8). r A

O

B ri

O’

ID x

A ri r

xi

(a) B

ri

r (b) (c)

Figure 4.13 2D profile for 3D dent modeling: (a) parabola profile; (b) and (c) cross section of tube wall for demonstration of 3D dent 73

ri  OO ' kxi2

(4.1)

OO '

(4.2)

k

OB 2

4.2.2.4 Circular Dent Circular dent is local defect of spherical shape in the tube wall outer surface, as shown in Figure 4. 14. Dent dimensions from actual tube dents were used for the dent modeling. The maximum depth of the dent is 0.02”, the maximum angle of the deformed circumferential profile is around 45° and axial length of the dent is 0.55”.

Figure 4. 14 Spherical dent

Figure 4. 15 Measurement of real spherical dent

74

Figure 4. 16 Measurement of spherical dent by laser system: local 3D dent profile Axial profile Circ. Profile C

E

A

D

E

C

F

O

G

A D

E

H

O

F O’

Axial (x) B

B

OO’: maximum depth in the dent center, h AB: axial length of dent opening, l

Circ. (y) C A

E

O

B

D F

O’

Figure 4. 17. Views of 2D and 3D modeling of dent in the tube wall: the maximum depth in the dent center is OO’ (h) and the axial length of dent opening is AB (l).

75

y

A

A’

y

A

y

A’

ny z

x

O

z O

O’

h

z

hx

nx

B’

B

B z  hx  k y y 2

y

h

B’

ky 

hx xi

hx ny 2

x

hx  h  k x x 2

kx 

h nx 2

Figure 4. 18. Mathematical model for 3D dent for mesh generation In order to model the 3D spherical dent modeling, the tube cross section is shown in the Figure 4. 19. The tube wall dent deformation along the radial direction is calculated by:

76

-3

x 10 12

10

y  ax 2  (r  hr )

h r

( x0 , y0 )

8

6

4

( x* , y* )

2

0

-2 -8

-6

-4

-2

0

2

4

6

8 -3

x 10

Figure 4. 19 Spherical dent modeling on the tube wall cross section y  ax 2  (r  hr )

(4.3)

y0  (r  hr )

(4.4)

a

x02

( x0 , y0 ) ,

x0  r cos 0 y0  r sin 0

(4.5)

 y  ax 2  (r  hr )  ( x* , y* , * )   y  x  tan 

(4.6)

r  r  (r cos  *  x* )2  (r sin  *  y* )2

(4.7)

The deformation profile along the axial direction is defined by a parabola, which can be defined by the maximum depth in the dent center and the length of the opening along the axial directions. The profile is shown in Figure 4. 20. The maximum depth of the dent is h, and halflength of axial opening is represented by Zm. The depth (deformation) at other axial location is calculated by:

77

r

hr

h

zm

z

Figure 4. 20 Axial profile for spherical dent hr  h  kr z 2

kr 

h zm2

(4.8) (4.9)

Figure 4. 21 Mesh of spherical dent in frees-pan: 3D model of spherical dent 4.3 Eddy Current Probes 4.3.1 Bobbin Probe Bobbin probe generates circumferentially oriented eddy current flowing in the tube wall.

78

Axial notch or volumetric defect perturb the eddy current, and cause the probe impedance to change during the scan. Therefore circumferential notches that are parallel to eddy current do not produce a significant signal. The bobbin probe generally has two modes: absolute mode with single coil and differential mode with two identical coils. The bobbin coil is excited by alternating sinusoidal current at single or multiple frequencies. Four typical frequencies are used for the excitation of bobbin probes in steam generator inspection, namely 10, 100, 200, 300 kHz. The frequencies cover low, middle and high frequency range and different frequency components have different penetration depths, which are sensitive to different defects and structures. The model first calculates the magnetic field due to the excitation current flowing in the bobbin coils. The induced eddy current then generate reverse magnetic field which is affected by defects. The reverse alternating magnetic field changes the impedance of the bobbin coil, which contributes the eddy current probe signal. In the simulation, the impedance of the bobbin coil can be calculated during post-processing by Z

j  A  dl I

(4.10)

where, A is the magnetic vector potential, dl is the integration path along the circumference of bobbin coils, which is also the current flow direction, I is the excitation current with constant amplitude, and  is the angular frequency. The differential bobbin coils are connected so that the excitation currents flowing in the two coils are in opposite direction. Thus the magnetic fields exactly cancel each other where there is no defect in the tube wall. The probe is sensitive to small abrupt changes or anomalies such as pitting corrosion. The probe is also insensitive to probe wobble, temperature variations, and gradual variations in tube’s conductivity. To understand the differential bobbin probe coils 79

operation, a simple circuit model including the coupling between the two coils can be developed. The output voltage V1 and V2 for both coils are presented by

V1  IZ11  IZ12

(4.11)

V2  IZ 22  IZ 21

where, Z11, Z 22 are self-impedance, and Z12 , Z 21 are mutual impedance. Because of law of reciprocity, Z12  Z21 . The total output voltage for the oppositely connected coils is Vdiff  V1  V2  I (Z11  Z22 )

(4.12)

Two commercial bobbin probes are modeled and simulated for tube inspection. Tubes with the same defects as used in experiment are modeled using finite element analysis. The simulation results are validated with the experimental data. The commercial bobbin probes have different inner and outer diameters for inspecting different diameter tubes. The parameters for the two commercial bobbin probes are listed in Table 4.2, including the spacing between two differential coils. The finite element modeling for the absolute and differential bobbin coils are shown in Figure 4.22 and Figure 4.23. In these figures, the source current vectors and integration path for the induced voltage in these coils are represented by Figure 4.22(b), (c) and Figure 4.23 (b), (c). Table 4.2 Commercial bobbin probe parameters settings Bobbin type 510 TF 720 MR

ID (inch) 0.39 0.6

OD (inch) 0.48 0.702

Height (inch) 0.06 0.06

80

Spacing between coils (inch) 0.06 0.06

core

Turns

air air

39 60

(a)

(b)

(c) Figure 4.22 Finite element modeling of absolute bobbin probe: (a) Coil model, (b) Excitation current, (c) Integration path for post-processing

81

(a)

(b)

(c) Figure 4.23 Finite element modeling of differential bobbin probe: (a) Coil model, (b) Excitation current, (c) Integration path for post-processing 82

4.3.2 Plus Point Probe The Plus Point probe is composed of two orthogonal coils wound on a ferrite core, and is opposite-series connected, as shown in Figure 4.24. The probe rotates helically around the tube wall along the tube axes when scanning. The probe is sensitive to all orientation defects in the tube wall. A commercial Plus Point eddy current probe is modeled and used to simulate inspection of a real axial crack obtained from EPRI ETSS database. The parameter for the plus point probe is listed in Table 4.3. The real crack profiles are obtained using destructive inspection and metallographic profiling. Width

Length

Height

Figure 4.24 Plus point eddy current probe: orthogonal coils (red) and ferrite core (green) Table 4.3 Parameters of Plus Point Probe for validation Plus Point Coils Height 0.1" Width 0.046" Length 0.065" Current Density 1.5e7A/m^2 Frequency 300 kHz

83

Ferrite Core height 0.07" Width 0.07" Length 0.035" Relative Permeability 2000

4.3.3 Rotating Pancake Probe A Rotating Pancake Coil probe is a surface-riding probe. It is composed of pancake coil, rotating motor and a ferrite core to enhance the probe magnetic field. A pancake coil is loaded to close to surface of the tube wall with small lift-off. The probe is motorized and scans the tube in a helical path. A commercial Rotating Pancake Coil is modeled and used to simulate inspection of Top Tube Sheet with loose part.

Ferrite Core

Pancake Coil Figure 4.25 Mesh for Rotating Pancake Coil Table 4.4 Parameters of rotating pancake coils for validation Pancake Coil OD 0.23" ID 0.07" Height 0.05" Current Density 1e6 A/m^2 Frequency 15 kHz

84

Ferrite Core Diameter 0.035" Height 0.125" Relative Permeability 800

CHAPTER 5 DESIGN OF ROTATING FIELD EDDY CURRENT PROBE 5.1 Introduction Eddy current inspection has proved to be a fast and effective nondestructive technique to detect and size defects that occur in steam generators tubes. Conventionally, eddy current probes such as bobbin coil probes cannot detect circumferentially oriented defects; rotating coil probes can obtain an eddy current C-Scan of tube so that the circumferential defects are detected but the inspection using rotating probe coils scanning along a helical path takes too much time. Also the complex mechanical rotation affects the data quality and reliability of the probe. Array probes are capable of determining circumferential location of defects on the tube and have high inspection speed, but need complicated excitation and data analysis system. This thesis describes the design, analysis and development of a rotating field eddy current (RoFEC) probe that generates a rotating field electronically without mechanical movement and hence combines the merits of previous three types of probes and avoids their disadvantages. The RoFEC probe generates a rotating magnetic field by using three balanced identical rectangular windings inside the tube. Different pickup sensors can be located in the center plane of the excitation coils, such as bobbin coil or an array of Giant Magnetoresistance (GMR) sensors. These GMR sensors are characterized by high sensitivity to fields along the easy axis of the element. A three dimensional finite element model is developed to investigate the operation of the RoFEC probe and optimize its design for maximizing defect detection probability. The RoFEC probe is smaller, simpler to build and can be used for non-ferromagnetic and ferromagnetic tube defect inspection. The chapter first describes the theoretical principles of RoFEC with excitation and reception coils. The modeling of nonlinear material properties, using an iterative procedure is also discussed. Simulation results for defects with different pickup

85

sensors are provided. Optimization of probe design is discussed using results from a systematic parametric study. Experimental validation of the simulation results is also presented. 5.2 Operational Principles The principle of rotating fields necessary for the probe design is a fundamental property, which is similar with that of rotating electrical machines. The RoFEC works in a send-receive mode with excitation and pickup coils. The excitation coil consists of three identical rectangular windings located on same axes physically 120 degrees apart. The excitation sources for driving the three windings are three-balanced alternating currents with adjustable amplitude, phase and frequency. The currents through these windings are represented as i A  2 I cos t 2 iB  2 I cos(t   ) 3 4 iC  2 I cos(t   ) 3

(6.1)

The magneto-motive force (MMF) due to these three windings can be calculated by the following equations.

1 1 F cos(t   )  F cos(t   ) 2 2 2 2 1 1 4 f B (t ,  )  F cos(   ) cos(t   )  F cos(t   )  F cos(t     ) 3 3 2 2 3 4 4 1 1 2 fC (t ,  )  F cos(   ) cos(t   )  F cos(t   )  F cos(t     ) 3 3 2 2 3 f A (t ,  )  F cos  cos t



f  f A  f B  fC 

3 F cos(t   ) 2

(6.2)

(6.3)

The vector summation of these MMFs has constant amplitude and rotates at the same angular frequency  , which is similar as a magnetic dipole. It rotates circumferentially at a rate dictated by the excitation frequency.

86

Defect B

*

Ba

Diamete r

B Z

Bb

Bc

*

Bobbin coil

A

X

* C

Y Tube wall

(a)

Scan direction

Height

Thicknes s

(b)

Figure 5.1 Rotating field windings and bobbin pickup coil: (a) Three phase excitation windings; (b) 3D model of bobbin pickup and three windings inside the tube; The principle can also be explained from a point of view of magnetic flux density. The magnetic flux density components Ba, Bb, and Bc associated with the three windings AX, BY and CZ are perpendicular to the plane of each windings, as shown in Figure 5.1(a). The three components synthesize a total magnetic flux density vector B with constant amplitude at any given time, which rotates at the same rate as the excitation source. The rotating magnetic field in the cross section of the tubing is mainly in the radial direction, inducing eddy currents in the tube wall, which flow circularly about the radial axis, which makes the probe sensitive to cracks of all orientations. The response signal due to defects can be picked up by bobbin coil on the outside and at the center of excitation windings, as shown in Figure 5.1(b), or an array of GMR sensors around the same location in the middle. If there is no defect on the tube wall, the magnetic flux is mainly radial direction, and there is no axial magnetic flux on the cross section. However, if a defect is present close to the center plane, which causes variation in radial magnetic fields, an axial component of magnetic field occurs. Therefore, the defect is detectable by the probe with pickup sensors, such as bobbin coil or array of Giant Magnetoresistance (GMR) sensors oriented to measure the axial component.

87

In summary, the probe generates a rotating magnetic field in the tube wall without mechanical rotation of probe, and needs a fast single scan along the axial length of tubing for defect detection. The probe is sensitive to defects of all orientations, such as axial and circumferential notches. Finally, the probe has high operation speed, simple excitation, signal acquisition and post-processing system, and it is cheap to build compared to rotating probes and array probes. 5.3 Simulation 5.3.1 Three Phase Windings Excitation In order to investigate the operation of RoFEC probe, the finite element simulation model is modified and used for the modeling and simulation of steam generator tube inspection using the probe. The geometry for the tube is the same as used before in Chapter 4. All the parameter settings are listed in the Table 5.1. The definitions for the diameter, thickness, and height for the RoFEC probe can be found in Figure 5.1. Table 5.1 Simulation parameter settings for the modeling

Tube Geometry Outer diameter 22.225 mm Wall thickness 0.127 mm Material Inconel 600 RoFEC Probe Diameter Thickness Height

Excitation Current density 1e7 A/m^2 Frequency 35 kHz

Bobbin pickup Outer diameter inner diameter coil height

17 mm 2 mm 30 mm

19 mm 17 mm 2 mm

The excitation windings consist of three identical rectangular windings, as shown in Figure 5.1(b). The coils A-X, B-Y and C-Z are placed 120° apart around the circumference of the tube. Three phase sinusoidal current is introduced into these windings following the phase sequences as presented in the third column of Table 5.2. The magnetic field rotating along a counter88

clockwise direction is generated, as shown in Figure 5.2. Table 5.2 Excitation current phase for the three phase windings Phase

(a) 0°

(d) 135°

A-X

Spatial Angle (degrees) 0°

Current Phase (radian) 0

B-Y

120°

-2/3 

C-Z

240°

-4/3 

(b) 45°

(c) 90°

(e) 180°

(f) 225°

(g) 270° (h) 315° (i) 360° (0°) Figure 5.2 Rotating magnetic field generated inside the tube: (a)~(i): resultant rotating magnetic field at different instant time, the labeled numbers indicate the orientation of field

89

5.3.2 Rotating Magnetic Field The magnetic flux density of the rotating field is uniformly distributed in the center plane of the windings (near the axis of tube), and decays exponentially in radial direction, as shown in Figure 5.3, within the double red lines representing the tube wall. The figure presents the magnetic flux density amplitude distribution along the radial direction on the plane of pickup sensor. The presence of through wall square hole (3.5×4mm) in the tube wall is shown in the zoomed-in area of the magnetic field on the left hand side of the curve. If there is no defect in the tube wall, the total magnetic field at the center of the coil is purely radial with no vertical component. The vertical component arises from the eddy current perturbations caused by the defect in the tube wall. In this manner, the probe is automatically self-nulling. The rotating magnetic field vector is sinusoidal in time as well as space along the circumference of the tube wall. Figure 5.4(a) shows the magnetic flux density contour around the tube wall at an instant of time for the case with no defect. Figure 5.4 (b) shows the field contour in the presence of a through wall hole. The defect disturbs the induced eddy current and cause a variation in the magnetic flux density around defect area in the tube wall, as shown in red box in Figure 5.4 (b).

90

x 10

-4

14 12

|B| (T)

10 8 6 4 2 -30

-20

-10 0 10 Relative radial location (mm)

20

Figure 5.3 Magnetic flux density decay along diameter direction

(a) Figure 5.4 Amplitude contour of magnetic field component on the xy plane: (a) defect-free, (b) defect at 90°

91

Figure 5.4 (cont’d)

10

y(mm)

5

0

-5

-10 -10

-5

0 x(mm)

5

10

(b) 5.3.3 Induced Eddy Current in Tube Wall

The radially oriented rotating magnetic field induces circularly flowing eddy currents around radial axis in the tube wall. The rotating magnetic field is similar to the magnetic dipole, which has a front head and back tail. When the dipole rotates around the tube wall, eddy current will move with the rotating filed from 0 to 360 degrees along circumferential direction, as shown in Figure 5.5. Any defect in the tube wall, axial or circumferential, perturbs the induced current paths and generates an axial component of magnetic field which in turn will induce a voltage in a bobbin pick up coil sensor or detected by the GMR sensor array. In the absence of defects, there is no axial component in the probe center then the bobbin coil signal will be very close to zero or GMR sensors cannot measure an axial magnetic field. Figure 5.6 shows induced eddy currents in the tube wall, illustrating the perturbation of currents near the through wall square hole in the red 92

box at 90 degrees in circumferential direction. Tube wall Notches

B

Induced eddy current

Rotating magnetic field

Je

Figure 5.5 Induced eddy current in the tube wall due to the rotating magnetic field [wt = 1 degrees] Jzc 15

Axial(mm)

10 5 0 -5 -10 -15 0

50

100

150 200 Circ.(degrees)

250

300

350

Figure 5.6 Simulation results of induced eddy current in the tube wall 5.3.4 Bobbin Pickup Coil The induced voltage in the coil can be presented as V  N

  B  ndS   N  S t t

 A  dl

(6.4)

where, B represents the axial magnetic flux density. Notice that the bobbin pickup coil on the plane of rotating field is only sensitive to changes of axial magnetic flux. The induced voltage drop in the bobbin coil will be zero if there are no defects, which means no axial magnetic flux in the tube wall. A non-zero induced voltage results only in the presence of a defect. So the probe is self-nulling. In addition, the phase of the induced voltage in the coil is correlated with 93

circumferential location of defects in the tube wall. The reason is that the main magnetic field is rotating around the circumference of the tube wall. The defect signals results in the interaction of crack and magnetic field. That instant time is the moment when the rotating field encounter with the crack which determine the phase of the defect signal, so that it is relevant to the circumferential location of the defects. This is validated by the simulation and experiments in later discussion. The free span region of steam generator tube with the RoFEC probe inside the tube is modeled to simulate the scanning process in a practical eddy current inspection. The inner diameter of tube is 0.775’’ (19.685 mm), and wall thickness is 0.051’’ (1.295 mm), the material of tube is Inconel 600, with conductivity is 9.69×105 S/m. A three-phase source is applied to the excitation coils. The induced voltage in the bobbin pickup is computed by post-processing after finite element simulation. The default geometry of the three phase rectangular windings is with 20 mm height, 16 mm in diameter, and 0.5 mm in thickness. The diameter of the bobbin coil is 17 mm, and thickness is 2mm. The bobbin coil located at the center of three phase windings. It has a self-nulling property and produces near zero output in the absence of defects. The bobbin coil output voltage is induced largely by changes of axial magnetic flux only when there is a defect in tube wall. The magnitude of the induced voltage is proportional to depth of the defect. In addition, the phase of the voltage is relative to the circumferential location of the defect in the tube wall. The probe has high spatial resolution for discriminating circumferential volumetric defects since phase changes due to these defects are continuous. Simulations have been conducted to validate this hypothesis. The probe is excited by sinusoidal current source at 35 kHz, with an equivalent current density in the three phase windings of 5×107 A/m2. A square hole of area 3.5×4 mm and two different

94

depths, namely, 100% and 60% of tube wall thickness inner surface defects, are introduced at different circumferential positions as shown in Figure 5.7(a). Figure 5.7 (b) presents induced voltage in the bobbin coil with respect to scan positions. The simulation results show that the phase of the induced voltage in the bobbin pick up coil is correlated with the circumferential location of defect around the tube wall, whereas, the amplitude remains invariant with different circumferential location as shown in Figure 5.7 (c)(d). These results are validated using experimental measurements in later discussion. Bobbin coil 135

Z

B

Defects

Three phase windings

90

45 Tube wall

180 A

X C

Y

225

0

315

270

(a) Figure 5.7 Amplitude and phase of induced voltage in bobbin coil vs. circumferential location of square holes: (a) Circumferential location of square holes in tube wall, (b) Induced voltage plotted by real and imaginary parts, (c) amplitude vs. circ. angles, (d) phase vs. circ. angles

95

Figure 5.7 (cont’d) Defect at different circ. location 0.2 0.15

0 45 90 135 180 225 270 315

ID 60%

Imaginary part (V)

0.1

100% 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.2

-0.1

0 Real part (V)

0.1

0.2

(b) 0.2 100% 60%,ID

Amplitude(V)

0.15

0.1

0.05

0

0

50

100 150 200 Circ. angle(degree)

(c)

96

250

300

Figure 5.7 (cont’d) 50 100% 60%,ID

0

Phase(degree)

-50 -100 -150 -200 -250 -300 -350

0

100

200 300 Circ. angle(degree)

400

(d) In order to further validate the idea, the signal phase change with defect depth, when the defect is at the same circumferential location is studied. The simulation results for square defects with different depth but in the same circumferential location are shown in Figure 5.8, where ID means inner surface defect, and OD represents outer surface defect. The excitation source and frequency are the same as that used before. Although the amplitudes of the induced voltage in the bobbin coil change proportionally according to the depth, the phase of induced voltage is almost unchanged, as shown in Figure 5.8(c) and Table 5.3. Therefore it is clear that the phase of the induced voltage in bobbin coil could be used for estimating the circumferential location of defects in the tube wall, whereas, the amplitude includes the depth information of defects. Since the excitation frequency is comparably low, the penetration depth is much larger than the tube wall thickness. So the phase of the defect signal mainly depends on the circumferential location of defects but not the depth, and the probe may have difficulty to distinguish the defect depth or whether it is an ID or OD defect.

97

Defect with different depth OD_20 OD_40 OD_60 OD_80 OD_100 ID_20 ID_40 ID_60 ID_80 ID_100

Imaginary part (V)

0.1 0.05 0 -0.05 -0.1 -0.2

-0.1

0 Real part (V)

0.1

0.2

(a)

Amplitude(V)

0.2 OD ID

0.15 0.1 0.05 0 20

40

60 Defect depth(%)

80

100

(b) Figure 5.8 ID and OD defects signals by bobbin pickup coil (Frequency 35 kHz): (a) Induced voltage plot, (b) amplitude vs. depth, (c) phase vs. depth

98

Figure 5.8 (cont’d) OD ID

Phase(Degrees)

150

100

50

0 20

40

60 Defect depth(%)

80

100

(c) Table 5.3 Amplitude and phase for ID/OD defects at the same circumferential location Location Depth (%) Amplitude(V) Phase(degree) 20 0.012 95.29 40 0.030 94.58 60 0.054 94.40 OD 80 0.088 95.01 100 0.145 97.24 20 0.016 81.01 40 0.037 83.52 ID 60 0.064 86.68 80 0.097 90.84 Axial notches of length 8 mm and width 0.254 mm and different depths ranging from 20% ~ 80% (both ID/OD) are simulated at 35 kHz and 300 kHz. The amplitudes of the induced voltage increase with the depth of the defect. Also higher the excitation frequency, higher the amplitude for the same defect depth, as shown in Figure 5.9 and Figure 5.10. However, when the frequency is higher, the penetration depth is comparable with the tube wall thickness. The phase of the defect signal not only depends on the circumferential location but also the defect depth. So the phase of the induced voltage varies with depth of the defect located at the same circumferential location as shown in Figure 5.10(c). 99

Imaginary part (V)

0.05 ID_20% ID_40% ID_60% ID_80% 0

-0.05 -0.02

-0.01

0 Real part (V)

0.01

0.02

(a)

Imaginary part (V)

0.05

0

-0.05 -0.02

OD_20% OD_40% OD_60% OD_80%

-0.01

0 Real part (V)

0.01

0.02

(b) Figure 5.9 Axial notches of ID/OD with depth range from 20%~80%, at 35 kHz: (a) Induced voltage plot, ID, (b) induced voltage plot, OD, (c) amplitude vs. depth, (d) phase amplitude vs depth

100

Figure 5.9 (cont’d) 0.04 ID notch OD notch

Amplitude(V)

0.03

0.02

0.01

0 20

30

40

50 Depth(%)

60

70

(c)

ID notch OD notch

160

Phase(degree)

140 120 100 80 60 40 20 0 20

30

40

50 Depth(%)

(d)

101

60

70

80

0.04

Imaginary part (V)

0.02

0

-0.02

ID 20% ID 40% ID 60% ID 80% OD 20% OD 40% OD 60% OD 80%

-0.04

-0.06 -0.06 -0.04 -0.02

0 0.02 Real part (V)

0.04

0.06

0.08

(a) 0.1 ID notch OD notch

Amplitude(V)

0.08 0.06 0.04 0.02 0 20

30

40

50 Depth(%)

60

70

80

(b) Figure 5.10 Axial notches of ID/OD with depth range from 20%~80%, at 300 kHz: (a) Induced voltage plot, (b) amplitude vs. depth, (c) phase vs. depth

102

Figure 5.10 (cont’d) 180 160

Phase(degree)

140 120

ID notch OD notch

100 80 60 40 20 0 20

40

60 Depth(%)

80

100

(c) Circumferential notches of width 0.254mm and length 8mm with different depths ranging from 20% ~ 100% ID/OD are simulated at 35 kHz and 300 kHz. The resulting signals are shown in Figure 5.11 and Figure 5.12 respectively. Similar conclusions can be drawn as presented above for axial notches. The difference is that the amplitude of induced voltage in the bobbin coil due to circumferential notches is one order of magnitude smaller than that due to axial notches, because a smaller axial component of magnetic field is generated by circumferential defects. So the conclusion is drawn that with low frequency excitation, the phase of defect signal depends mainly on the circumferential location. Defect at same circumferential location results in same phase of signals, and phase can be used to detect the circumference location of defects. The amplitude of the signal is proportional to the depth of the defect depth, which can be used for the depth estimation. However, with high frequency excitation, the phase of defect signal not only depends on the circumferential location of defect but also the depth. So the phase is no longer a single function of either the circumferential location or the depth. For such probe design, a low frequency excitation that the penetration depth is much larger than the tube wall thickness is an appropriate choice for the frequency. Since the frequency is related with detection 103

resolution and defect signal amplitude, so the frequency also should not be set as too low.

Imaginary part (V)

0.01 ID 20% ID 40% ID 60% ID 80% ID 100%

0.005

0

-0.005

-0.01 -4

-2

0 Real part (V)

2

4 x 10

-3

(a)

Imaginary part (V)

x 10

-3

5

OD 20% OD 40% OD 60% OD 80% OD 100%

0

-5

-10 -2

0

2 Real part (V)

4 x 10

-3

(b) Figure 5.11 Circumferential notches of ID/OD with depth range from 20%~100%, at 35 kHz: (a) Induced voltage plot with real and imaginary parts, ID, (b) induced voltage plot, OD, (c) amplitude vs. depth, (d) phase vs. depth

104

Figure 5.11 (cont’d) 6

x 10

-3

Amplitude(V)

5 4 3 ID notch OD notch

2 1 0 20

40

60 Depth(%)

80

100

(c) 180 ID notch OD notch

160

Phase(degree)

140 120 100 80 60 40 20 0 20

40

60 Depth(%)

(d)

105

80

100

x 10

-3

10 8

Imaginary part (V)

6 4 2 ID 20% ID_40% ID_60% ID_80% ID_100% OD_20% OD_40% OD_60% OD_80%

0 -2 -4 -6 -8 -0.01

-0.005

0 0.005 Real part (V)

0.01

0.015

(a) 0.014

Amplitude(V)

0.012 0.01 0.008 0.006 ID notch OD notch

0.004 0.002 0 20

40

60 Depth(%)

80

100

(b)

Phase(degree)

150 ID notch OD notch

100

50

0 20

40

60 Depth(%)

80

100

(c) Figure 5.12 Circumferential notches of ID/OD with depth range from 20%~100%, at 300 kHz: (a) Induced voltage plot by real and imaginary parts, (b) amplitude vs. depth, (c) phase vs. depth 106

5.3.5 GMR Sensor Array Giant Magnetoresistance (GMR) is a quantum mechanical Magnetoresistance effect observed in thin-film structures composed of alternating ferromagnetic and non-magnetic conductive layers. The effect is observed as a significant change in the electrical resistance depending on whether the magnetization of adjacent ferromagnetic layers is in a parallel or an anti-parallel alignment. GMR sensor has two or more ferromagnetic thin films separated by thin nonmagnetic conducting layers. When GMR sensor is subjected to a magnetic field, its resistance can be reduced by up to 20% more than those of conventional anisotropic magnetoresistive (AMR) materials. One of the main application of GMR is magnetic field sensing [117, 118]. GMR sensor has low cost and low power consumption with small dimensions compared with hall sensor. GMR sensors offer high sensitivity over a wide range of frequencies from DC to MHz frequencies. However, GMR sensors need to be biased appropriately for bipolar operation. This can be achieved easily with electromagnetic field of DC wire or magnetic field of permanent magnets. GMR array sensors with axial sensitive axes can be located in the center plane of excitation windings to sense the axial components of magnetic field, which shares the similar idea as that of bobbin coils. With the advances in nanotechnology, it is possible to integrate a big number of small GMR sensor elements on the circumference, and then the spatial resolution of detection can be fairly high.

107

Y

By

r

 Bx

(x, y) X



Figure 5.13 Coordinate transform from Cartesian to Cylindrical coordinate In finite element simulation, the measurements of GMR array sensor can be the axial, radial and azimuth components of magnetic flux density. Since B x , B y and B z are computed as equation (3.123) and (3.124), then the radial and azimuth components B r and B are computed as shown in equation (5.6) and (5.7), whereas, the axial component is the same as B z in cylindrical coordinates. y x

  tan 1( )

(6.5)

Br  B x cos   B y sin 

(6.6)

B  B x sin   B y cos 

(6.7)

where, (x,y) are the coordinates of the observation location. The most important magnetic field is the axial component, since it also provides a good indication of circumferential location of defect in the tube wall. The simulation results for GMR pickup sensors are presented in the next chapter on tubes of non-ferromagnetic and ferromagnetic materials.

108

5.3.6 Nonlinear Material Simulation The ferromagnetic tubes are commonly used in steam generator units in CANDU nuclear power plants. These tubes have nonlinear magnetic properties. The permeability changes with the imposed magnetic field, which presents difficulties in the eddy current probe simulation model. In order to investigate the RoFEC probe performance in ferromagnetic tube inspection, a finite element simulation method is conducted for this purpose. In the finite element mesh of a non-ferromagnetic tube, the relative permeability of every element in the tube wall equals to 1. However, for ferromagnetic materials, the permeability of each element depends on magnetic flux density, which should be updated with the magnetic flux density solution in the finite element simulation. The permeability is determined using the computed magnetic field by finite element method and the B-H curve of the ferromagnetic material. The material property is updated and used in the next iteration during the solution procedure.

Figure 5.14 Experimental B-H curve of ferromagnetic material The B-H curve is typically stored in the form of a table, as shown in Figure 5.14. In order to determine the permeability corresponding to an arbitrary magnetic flux density value, linear interpolation is used on the adjacent values in the table. The initial permeability of the ferromagnetic material is estimated from linear region of the B-H curve. The new magnetic field 109

density H ( j ) of each element is computed from magnetic flux intensity B( j ) as H ( j )  Hi  ( B( j )  Bi )

Hi 1  Hi Bi 1  Bi

(6.8)

where, j  1, 2,..., n , n is the number of elements in the mesh, ( Bi , Hi ) and ( Bi 1, Hi 1) are experimental samples on the B-H curve, as shown in Figure 5.14. The permeability for each element is



( j)



B( j )

(6.9)

H ( j)

where, j  1, 2,..., n . The permeability of each element during the iteration process is updated as ( j) ( j) ( j) new  old   ( ( j )  old )

(6.10)

( j) where, j  1, 2,..., n , n is the number of elements in the model, old is the permeability obtained in

the previous iteration,  is the factor controlling the rate of convergence, generally ranges from 0.1~1.0. ( j) Using the new permeability new of each element, the global matrix is formulated and the

matrix equation is solved for magnetic vector potential A( j ) , and hence new B( j ) for each element. The convergence criteria at the end of each iteration is examined by determining the magnitude of the largest difference between magnetic vector potential of previous and present computations, which is defined as (k ) (k ) A  max Anew  Aold 1 k  N

(6.11)

(k )

where, k  1, 2,..., N , N is the number of nodes in the model, Aold is the magnetic vector potential (k ) of kth node in the previous iteration, and Anew is the corresponding updated value in the present

110

iteration. The procedure terminates when A is less than a prescribed tolerance  , which is given by



Amax 105

(6.12)

where, Amax is the maximum magnetic vector potential among all the nodes in the model. The procedure generally takes up to 21 iterations to converge. The flow chart of the updating procedure is shown in Figure 5.15.

111

Initial permeability for each element

FE solution for A and B

First Iteration

Save Amax and A_old.dat

Calculation of H for each element using Linear Interpolation on BH curve

Find  B / H

Update B and Save A_old.dat

new   (   old )  old

FE solution for A and B

NO

A   YES Process Converged

Figure 5.15 Flow chart of updating permeability of ferromagnetic material

112

In this algorithm, linear interpolation is used to locate the exact operating point rather than approximating it to the nearest known experimental samples. The only assumption is that the variation in the operation region in each interval is linear. Hence, the error in the approximation can be reduced effectively by including more samples of experimental measurements for the B-H curve. A finite element model is developed to predict the response signals of the RoFEC probe from inspection of ferromagnetic tubes with defects. The test geometry is the free span region. Both nonmagnetic and ferromagnetic tubes are modeled and corresponding signals are compared. The GMR array elements are used for the pickup sensors. The inner diameter of simulated tube is 0.775 inch (19.685 mm), and the wall thickness is 0.051 inch (1.295 mm). The material of nonmagnetic tube is Inconel 600, and the conductivity is 9.69*105 S/m. The B-H curve of ferromagnetic material is shown in Figure 5.14 and divided into 12 segments for linear interpolation, and its conductivity is 1.45*106 S/m. On the tubes, two types of defects were considered: axial notch and square hole, whose dimension can be shown in Table 5.4. The simulation model includes 454,608 hexahedral elements and 472,685 nodes. Table 5.4 Defects parameters Dimension (mm) No. Location 1 2

OD, 90° OD, 90°

Type axial square

Axial Circumferential Depth 8 4

113

0.254 3.5

0.777 0.777

-12

0

12

Z (mm)

Defect Diameter

Offset

GMR

Line scan

RoFEC Tube wall

Three windings Height

Figure 5.16 Schematic of the geometry with probe inside a tube The default diameter, height and thickness of the RoFEC probes are 16 mm, 6 mm and 0.6 mm respectively. The RoFEC probe is excited by a 320 kHz alternating current source with current density 3*106 A/m2. The frequency is chosen as the typical frequency used in the inspection of heat exchange tubes in nuclear power plants. The probe moves axially within the tube from z = -12mm to 12mm, as shown in Figure 5.16. The magnetic flux density induced by rotating fields is measured by an array of GMR sensors located at the center around the excitation coils. Each GMR sensor measures two components of magnetic flux density along the radial and axial directions. The measured radial and axial components of magnetic flux density due to axial notch and square hole are displayed in Figure 5.17 and Figure 5.18 for nonferromagnetic and ferromagnetic materials tube respectively.

114

(a)

(b) Figure 5.17 Induced radial and axial components of magnetic flux density measured by GMR sensors for non-ferromagnetic material, notch: (a) radial; (b) axial; square hole: (c) radial; (d) axial

115

Figure 5.17 (cont’d)

(c)

(d)

116

(a)

(b) Figure 5.18 Induced radial and axial components of magnetic flux density measured by GMR sensors for ferromagnetic material, notch: (a) radial; (b) axial; square hole: (c) radial; (d) axial 117

Figure 5.18 (cont’d)

(c)

(d) The signals due to a square hole are much stronger than that due to an axial notch. The signals from defects in ferromagnetic and non-ferromagnetic materials show considerable

118

differences. The axial component response signals in a ferromagnetic tube have four peaks around each corner of the defect, whereas, there are only two peaks in non-ferromagnetic tube signals, as shown in Figure 5.17(b) and (d), also Figure 5.18 (b) and (d). 5.3.7 Parametric Study In order to optimize the probe design, a parametric study of is conducted using finite element simulation. The parameters are diameter and height of the three windings of RoFEC probe. The excitation frequency of the probe is also a key factor for the amplitude and phase of the pickup sensor signals, which is also studied in this section. The effect of height, diameter and thickness of the three rectangular windings are investigated on the bobbin induced voltage at different excitation frequencies. A) Effect of Coil Height The height of the windings was varied from 4 mm to 28 mm at increments of 4 mm, and the probe was excited at frequencies 35 kHz, 100 kHz, and 300 kHz. The simulation results are shown in Figure 5.19. For different excitation frequencies, the optimal heights for the coil can be different. For example, when the excitation frequency is 35 kHz, the maximum amplitude of the induced voltage signal is optimized as the height is 14 mm. For the excitation frequencies are 100 kHz and 300 kHz, the heights are 12 mm and 10 mm respectively, as shown in Figure 5.19 (e) and (h). As shown in Figure 5.19 (c), (f) and (i), the phase of the induced voltage decrease linearly at low frequency as height increase, and decrease quadratic at high frequency excitation as height increase. 119

Imaginary part (V)

0.1 4mm 8mm 12mm 16mm 20mm 24mm 28mm

0.05

0

-0.05

-0.1 -0.04

-0.02

0 Real part (V)

0.02

0.04

(a) 0.1 max [14,0.08575]

V_max(V)

0.08 0.06 0.04 0.02 0

0

5

10

15 Height(mm)

20

25

30

(b) Figure 5.19 Height of three phase rectangular windings vs. induced voltage amplitude and phase at different frequencies: (a), (d), (g) induced voltage plot with real and imaginary parts at 35 kHz, 100 kHz and 300 kHz; (b), (e), (h) height vs. amplitude at 35 kHz, 100 kHz and 300 kHz; (c),(f), (i) height vs. phase at 35 kHz, 100 kHz and 300 kHz.

120

Figure 5.19 (cont’d)

(c)

4mm 8mm 12mm 16mm 20mm 24mm 28mm

Imaginary part (V)

0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.1

-0.05

0 0.05 0.1 Real part (V)

(d)

121

0.15

0.2

Figure 5.19 (cont’d) 0.25 max [12,0.21361]

V_max(V)

0.2 0.15 0.1 0.05 0

0

5

10

15 Height(mm)

(e)

(f)

122

20

25

30

Figure 5.19 (cont’d)

Imaginary part (V)

0.3 0.2 0.1

4mm 8mm 12mm 16mm 20mm 24mm 28mm

0 -0.1 -0.2 -0.3 -0.4 -0.2

0 0.2 Real part (V)

0.4

(g) 0.4

max [10,0.38053]

V_max(V)

0.3

0.2

0.1

0 0

5

10

15 Height(mm)

(h)

123

20

25

30

Figure 5.19 (cont’d)

(i) Effect of changing the coil height of three windings from 2mm to 12 mm in 2mm increments, on the magnitudes of radial and axial magnetic flux density is studied. The peak values of the magnitudes of the radial and axial component signals for different coil height are shown in Figure 5.20. The magnitudes are larger for bigger heights of excitation coil. However the larger dimensions will result in a bigger probe size which may not be desirable in practical implementation.

124

(a)

(b) Figure 5.20 Peak magnitude of radial and axial magnetic flux density versus coil heights (a) radial component; (b) axial component B) Effect of Coil Diameter The diameter of the three phase windings was varied from 4 mm to 16 mm at increments of 2 mm, and simulations were carried out at excitation frequencies 35 kHz and 300 kHz. The simulation results are shown in Figure 5.21. If the location and diameter of bobbin pickup coil is fixed, the amplitude increases as probe diameter increases. However, the diameter of the three windings is limited by the diameter of bobbin pickup coils and tube inner diameter.

125

0.1 4mm 6mm 8mm 10mm 12mm 14mm 16mm

0.08

Imaginary part (V)

0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 -0.03

-0.02

-0.01

0 0.01 Real part (V)

0.02

0.03

(a) Diameter vs Amplitude 0.1 max [16,0.085548]

V_max(volt)

0.08 0.06 0.04 0.02 0

0

5

10 Diameter(mm)

15

(b) Figure 5.21 Diameter of three windings vs. amplitude of induced voltage in the bobbin coils at 35 kHz and 300 kHz: (a), (c) induced voltage plot with real and imaginary parts at 35 kHz and 300 kHz; (b), (d) diameter vs. amplitude at 35 kHz and 300 kHz

126

Figure 5.21 (cont’d)

0.3

Imaginary part (V)

0.2 0.1 4mm 6mm 8mm 10mm 12mm 14mm 16mm

0 -0.1 -0.2 -0.3 -0.2

0 0.2 Real part (V)

0.4

(c) Diameter vs Amplitude max [16,0.34]

V_max(volt)

0.3

0.2

0.1

0

0

5

10 Diameter(mm)

15

(d) Effect of changing the coil diameter from 4mm to 16mm in 2mm increments, on the magnitudes of radial and axial magnetic flux density is studied. The peak values of the magnitudes of the radial and axial component signals for different coil diameters are shown in Figure 5.22. The magnitudes are larger for bigger diameters of excitation coil. However the 127

larger dimensions will result in a bigger probe size which may not be desirable in practical implementation.

(a)

(b) Figure 5.22 Peak magnitude of radial and axial magnetic flux density versus coil diameter (a) radial component; (b) axial component C) Effect of Frequency The effect of excitation frequency was also studied. The skin depth of eddy current is controlled for a specific specimen. For the non-ferromagnetic steam generator tube, with the conductive and the permeability mentioned before, the skin depth versus the excitation frequency 128

is shown in Figure 5.23. There are three typical excitation frequencies 35, 150 and 300 kHz with the penetration depth of 2.7, 1.3 and 0.933 mm respectively. Since the steam generator tube wall thickness is around 1.27 to 1.3 mm, 150 kHz has a better coverage of the thickness. However, the high frequency excitation has the ability to detect the shallow tiny cracks with high resolution.

Skin depth 6

Skin depth(mm)

5 4 3

35kHz, 2.7 mm

2

150kHz, 1.3 mm 300kHz, 0.933 mm

1 0

0

200

400 600 Frequency(kHz)

800

1000

Figure 5.23 Skin depth versus excitation frequency for the tube specimen In order to find the optimized excitation frequency for the detection, the probe is excited at different frequencies ranging from 20 kHz to 600 kHz. The defect is a through wall square hole of area 3.5×4mm. As shown in Figure 5.24(c)(d), the magnitude of the induced voltage in the bobbin coils increase exponentially with frequency at frequencies less than 100 kHz and rises linearly at frequencies larger than 100 kHz. Also, as frequency increases, the phase of the induced voltage in the bobbin due the same defect remains constant; however, the phase varies with different depth of the defects, as discussed in the previous section. So the excitation

129

frequency must be selected both considering amplitude and phase of induced voltage in the bobbin coil.

0.6 0.4

Imaginary part (V)

0.2 0 20 kHz 35 kHz 50 kHz 100 kHz 200 kHz 300 kHz 400 kHz 500 kHz 600 kHz

-0.2 -0.4 -0.6 -0.8 -0.4

-0.2

0 Real part (V)

0.2

0.4

(a) Figure 5.24 Excitation frequencies for the three phase windings vs. induced voltage in the bobbin coil: (a) induced voltage plot with real and imaginary parts, (b) absolute amplitude of induced voltage along axial distance (the defect is located from -2mm to 2mm), (c) maximum amplitude of induced voltage vs. frequency, (d) phase vs. frequency for same defect

130

Figure 5.24 (cont’d) 0.7 20 kHz 35 kHz 50 kHz 100 kHz 200 kHz 300 kHz 400 kHz 500 kHz 600 kHz

0.6

|V|(V)

0.5 0.4 0.3 0.2 0.1 0 -15

-10

-5

0 Axial dist.(mm)

5

10

15

500

600

(b) 1

Max. Amplitude(V)

0.8 0.6 0.4 0.2 0

0

100

200 300 400 Frequency(kHz)

(c)

131

Figure 5.24 (cont’d)

Phase(Degree)

150

100

50

0

0

100

200 300 400 Frequency(kHz)

500

600

(d) D) Crossover – thickness of coils The three phase rectangular windings cross at one point on the top and bottom. In practice, the outer coil’s height is larger than the inner coil due to the coil’s thickness. In order to simulate the different thickness of the three phase rectangular windings, a finite element model is developed for the parametric study as shown in Figure 5. 25. The induced voltage in the bobbin coil is shown in Figure 5. 26 when the thickness of the coil changes from 0 to 1mm and 2mm. The normalized amplitude and phase of induced voltage are shown in Figure 5. 27. As the crossover thickness increase from 0 mm to 1mm and 2mm, the amplitude decrease to be 92.4% and 85.4%. The phase variation is less than 1.4° within 2mm crossover.

132

Figure 5. 25 Model of coil crossover for three phase windings

Figure 5. 26 Induced voltage with the three phase windings crossover for 0mm, 1mm and 2 mm

133

(a)

(b) Figure 5. 27 Normalized amplitude and phase of induced voltage with the three phase windings crossover 0mm, 1mm and 2mm with each other: (a) normalized amplitude vs. crossover height, (b) phase vs. crossover height E) Bobbin Pickup Coil Offset (Z direction) The bobbin pickup coil is placed in the center cross plane of the probe. The shift along the tube axes (Z direction) may affect the induced voltage signal, as illustrated in Figure 5. 28. The induced voltages in the bobbin coil are shown in Figure 5. 29, Figure 5. 30 and Figure 5. 31

134

where the shift are -5mm, -3mm, -1mm, 0mm, +1mm, +3mm and +5mm respectively. The induced voltage plot becomes more asymmetric as the coil is shifted further away from the center plane. The normalized amplitude and phase of the induced voltage versus bobbin coil shift are shown in Figure 5. 32. The amplitude decrease exponentially with the bobbin coil is shifted along tube axes. The phases of the induced voltage also change dramatically as the coil is shifted along tube axes.

Figure 5. 28 Bobbin pickup coil offset along tube axes (Z direction) 1.5 Z=-1mm Z=0mm Z=+1mm

1

Imag(V)

0.5

0

-0.5

-1

-1.5 -1

-0.5

0 0.5 Real(V)

1

Figure 5. 29 Induced voltage with the bobbin pickup coil z offset -1 mm, 0mm and +1 mm 135

Figure 5. 30 Induced voltage with the bobbin coil z offset -3 mm and +3 mm

Figure 5. 31 Induced voltage with the bobbin coil z offset -5 mm and +5 mm

136

250 226.5174

Relative Amplitude (%)

200 175.4254

150

123.2864

100 100 80.1335 50

52.4592 35.4728

0 -6

-4

-2 0 2 Bobbin Z Offset (mm)

4

6

(a) 0 -20

Phase (Degree)

-40 -60

-72.2858 -82.2969

-80 -100

-69.507 -101.3666

-76.7868 -88.797

-120 -114.7927 -140 -160 -180 -6

-4

-2 0 2 Bobbin Z Offset (mm)

4

6

(b) Figure 5. 32 Normalized amplitude and phase of induced voltage for bobbin coil with the z offset -5 mm, -3 mm, -1mm, 0mm, +1mm, +3mm, and +5mm: (a) normalized amplitude vs. bobbin z offset, (b) phase vs bobbin z offset F) Tilt Angle along Tube Axes The ideal case for the probe during the scanning is that the probe keeps coaxial with tube axes. However, probe tilt is inevitable because of probe wobble and vibration. A finite element model is developed to simulate the probe tilt angle along tube axes, as shown in Figure 5. 33. The induced voltage in the bobbin coil is shown in Figure 5. 34 when the probe tilt for -5°, -2.5°, 0°, +2.5° and 5° respectively. The Liz plot of induce voltage becomes more asymmetric as the

137

probe tilt from 0° to 5° and from 0° to -5°. The center of the Liz plot is also shifted further away from the center as the tilt angle increases. If all the Liz plots are shifted back to the center, the plots are shown in Figure 5. 35. The normalized amplitude and phase for the shifted induced voltage are shown in Figure 5. 36. The amplitude changes linearly with the tilt angle, and the phase variation is less than 2° within tilt angle which is less than 5°.

(a)

(b)

Figure 5. 33 Model of probe coil tilt along tube axes: (a) +5°, (b) -5°

138

Figure 5. 34 Induced voltage of probe coil tilt along tube axes for -5°, -2.5°, 0°, +2.5° and +5°

2.5

x 10

-4

+ 5 Degree +2.5 Degree 0 -2.5 Degree -5 Degree

2 1.5

Imag (V)

1 0.5 0 -0.5 -1 -1.5 -2 -2.5

-1

0

1 Real (V)

2

3 x 10

-4

Figure 5. 35 Shifted Induced voltage of probe coil tilt along tube axes for -5°, -2.5°, 0°, +2.5° and +5°

139

130 122.3267

Relative Amplitude (%)

120 110

112.469

100

100

90 80 70 -6

88.2931 76.0516

-4

-2 0 2 Tilt angle (Degree)

4

6

(a) 99 98.8262

Phase (Degree)

98.5 98 97.6656

97.5 97 96.5272 96.5 96 -6

96.407 96.3604

-4

-2 0 2 Tilt angle (Degree)

4

6

(b) Figure 5. 36 Normalized amplitude and phase of induced voltage for probe coil tilt along tube axes with -5°, -2.5°, 0°, +2.5° and +5°: (a) normalized amplitude vs. tilt angle, (b) phase vs. tilt angle G) Probe Offset (Radial) Probe offset along radial direction is common during the scanning. Two possible offset along x and y axes may cause different effect on the bobbin pickup signals, as shown in Figure 5.

140

37. The probe offset along x axes is the case that the probe is closer (or further) to the defect, as illustrated in Figure 5. 38. The induced voltage in the bobbin pickup coil is show in Figure 5. 39. If the probe is 0.6 mm closer to the defect along x axis, the amplitude is 4.25% larger than that of when the probe is in the center. However, if the probe is 0.6mm further away from the defect along x axis, the amplitude is 3.88% smaller than that of when the probe is in the center. As shown in Table 5. 5, the phase variation for these two cases changes less than 2%. So probe offset along x axis mainly affect the amplitude of the induced voltage in bobbin pickup coil, and the closer the probe, the larger the amplitude. The phase of the induced voltage almost keeps the same at this circumstance.

Figure 5. 37 Probe eccentricity along x and y axes

141

Figure 5. 38 Probe eccentricity along x axes (changed distance to defect)

x = -0.6mm 1x = 0 mm x = +0.6mm 0.8 0.6

Imag(V)

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -0.2 0 0.2 Real (V)

Figure 5. 39 Induced voltage for probe eccentricity along x axes with the offset -0.6mm, 0mm and 0.6 mm

Table 5. 5 Normalized amplitude and phase change of induced voltage with the probe coil eccentricity along x axes with the offset -0.6mm and 0.6 mm with the reference that the probe in the center Offset

-0.6

+0.6

Amp (%)

-3.88%

4.25%

Phase (%)

0.95%

-1.94%

142

The probe offset along y axes mainly change the relative position of the probe to the defect, as shown in Figure 5. 40. This mainly affects the phase of the induced voltage of the bobbin pickup coil, which is also validated by the parametric study simulation results as shown in Figure 5. 41. The amplitude variation is less than 2%, as shown in Table 5.6.

Figure 5. 40 Probe eccentricity along y axes (distance to defect keeps the same)

1

y -0.6mm y 0mm y +0.6mm

0.8 0.6

Imag(V)

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -0.2 0 0.2 Real(V)

Figure 5. 41 Induced voltage for probe eccentricity along y axes with the offset -0.6mm, 0mm and 0.6 mm

143

Table 5. 6 Normalized amplitude and phase change of induced voltage with the probe coil eccentricity along y axes with the offset -0.6mm and 0.6 mm with the reference that the probe in the center Offset

-0.6

+0.6

Amp (%)

-1.33%

2.06%

Phase (%)

5.21%

-4.97%

5.4 Conclusion This chapter presents a novel design of RoFEC for nondestructive evaluation of SG tubes in nuclear power plant. The simulation results of the non-ferromagnetic and ferromagnetic SG tubes show that the RoFEC probe is sensitive to defects in both non-ferromagnetic and ferromagnetic tubes. The probe needs relatively simple control and excitation hardware. The parametric study conducted for the optimization is helpful in generating calibrating curves with respect to different design parameters that can be used in the probe design.

144

CHAPTER 6 DEVELOPMENT OF ROTATING FIELD EDDY CURRENT PROBE AND EXPERIMENT 6.1 Introduction A prototype of novel RoFEC probe was built in the lab for the validation of simulation results. In order to test the probe, a test bench was also setup in the lab. The test bench includes three phase sinusoidal waveform source, a stepper motor controller pusher, and lock-in amplifier with data acquisition. This chapter presents the development of the experimental system and test results on laboratory samples of steam generator tubes with machined defects. 6.2 Three Phase Sine Wave Excitation Source The three phase excitation source for the three phase windings was first built. The source is composed of series connection of lead or lags phase shift circuits in the first stage and power amplifiers in the second stage. The phase shift circuit shifts the phase of signal from function generator. The power amplifier circuit amplifies the voltage as well as the current that drives the three phase windings with adjustable amplitude and frequency. 6.2.1 Phase Shift Circuit In analog design, there are two types of circuits can be used for introducing a phase shift, namely, phase lag and phase lead circuits, as shown in Figure 6.1.

145

R1 R1 R

Vi

Vo

C

(a) R1 R1 C

Vo

Vi R

(b) Figure 6.1 Phase shift circuit: (a) phase lag, (b) phase lead In the phase lag circuit we have Vo 1  j RC  Vi 1  j RC

(7.1)

The transfer function for phase lag circuit is H ( j ) 

1  j RC 1  j RC

(7.2)

And the amplitude response G( ) and phase response  ( ) are G ( )  H ( j ) 

146

1  ( RC ) 2 1  ( RC ) 2

1

(7.3)

 ()  2arctan( RC) (7.4) The amplitude response is a constant value of unity at all frequencies making it an all-pass circuit. The phase shift of the circuit is lagging and varies from 0 ~ 180 over an infinite frequency range. The phase shift is a function of the product of  RC . For a given frequency, the RC product can be determined to provide a given phase shift. Similarly, the transfer function for the phase lead circuit is H ( j ) 

1  j RC 1  j RC

(7.5)

And the amplitude response G( ) and phase response  ( ) are

G( )  1

(7.6)

 ( )  180  2arctan( RC )

(7.7)

In order to generate three phase balanced current source, the phase lag and lead circuit can be combined appropriately. As shown in Figure 6.2, there are two ways: (a) cascaded phase lag circuit with 120 degrees delay; (b) one phase lag circuit for phase B, and phase lead circuit for phase C, with 120 degrees shift in both cases. Theoretically, these two methods are equivalent. However, the second method is better for the practical experiment, since the channels of phase B and phase C are independent and it is easily for phase shift debugging when switching to different frequencies.

147

Phase A

Phase B Phase-lag 120

Phase-lag 120

Phase C

(a)

Phase A

Phase-lag 120

Phase B

Phase C Phase-lead 120 (b)

Figure 6.2 Circuit diagram for phase shift circuits: (a) cascaded phase lag circuits, (b) parallel phase lag and lead circuits 6.2.2 Power Amplifier The power amplifier circuit supplies adjustable amplitude and current for driving the three phase windings. In analog circuits, the amplifier is used to increase the power of a weak signal from the function generator. Integrated chip of operational amplifiers are commonly used for building such circuits. However, different chips have their own limits, such as amplitude ranges, maximum output currents and bandwidth. To cover the eddy current testing frequency range, which is from 10 kHz to 800 kHz, the amplifier chip must have a wide bandwidth and big output currents.

148

R2 R1

Vo Vi

(a) R2 R1

I1 R

I  2 I1 Vi R

Vo

(b) Figure 6.3 Power amplifier circuits: (a) non-inverting amplifier, (b) combined non-inverting amplifier For the non-inverting amplifier show in Figure 6.3(a), the gain is expressed as Vo R  1 2 Vi R1

(7.8)

Note that in Figure 6.3(b), R  10  . The gain is always greater than 1. The non-inverting amplifier is cascaded with a voltage follower using the same power amplifier chip. Then the parallel outputs double the input current for the three phase windings, since the maximum continuous output current is not big enough (~200 mA). An integrated power amplifier chip was

149

chosen to build the circuit using operational amplifier OPA552 from Texas Instruments with following key parameters: 

Wide supply range: ±30V



High output current: 200 mA Continuous



Fast Slew Rate: 24V/  s



Wide bandwidth: 12 MHz

Connecting the phase shift circuit in series with power amplifiers, the three phase power source is built with the operational frequency from 10 ~ 800 kHz, peak output voltage up to 30V, and maximum output current up to 400 mA. 6.3 Probe Prototype A probe prototype is built in the laboratory to validate the simulations. The prototype of the RoFEC probe is composed of three phase excitation windings and bobbin pickup coil. The three phase excitation windings are wound on a plastic core, which was printed using a 3D printer, as shown in Figure 6.4. The cylinder diameter and height are 19 mm and 20 mm respectively. The slot width for three phase windings is 3mm, and for bobbin pickup coil, is 2mm. The diameter of the three windings is 16mm. The diameter of the bobbin coils is 17mm.

150

(a)

(b)

Figure 6.4 Plastic cores for the phase windings: (a) CAD model, (b) plastic core printed by 3D printer Copper wire is used for the three phase windings are gauge AWG 24. After fabrication, the DC resistance and number of turns for the windings and bobbin coil are presented in Table 6.1. Table 6.1 DC resistance and turns of three phase windings and bobbin coil Coils Phase A Phase B Phase C Bobbin coil

DC resistance (Ohm) Turns 23 24.7 25.5 14.8

160 160 160 120

Figure 6.5 Prototype of RoFEC probe

151

6.4 Test Bench The test bench comprises a stepper motor, plastic stage, steam generator tube sample, power source and data acquisition system, as shown in Figure 6.6. The stepper motor is used in the probe pusher for axial scanning. The steam generator tube is a standard calibration tube sample with machined flat bottom holes, for inspection. A lock-in amplifier is used for measuring the amplitude and phase of induced voltage in bobbin pickup coils. The lock-in amplifier has embedded data acquisition card for acquiring, digitizing and storing the measured data from the bobbin pick up coil.

Probe

Power source

Prober Pusher

Tube sample

Figure 6.6 Test bench for the rotating field eddy current probe (RoFEC) 6.4.1 Tubes with Defects The steam generator tube sample used in the experiment is the same as that used in industry, as shown in Figure 6.7. The outside and inside diameters of the tube are 0.875 and 0.775 inches. The total tubing length of the tube is around 1m. There are 10 flat bottom holes with different 152

depth and diameters on the tube wall listed in Table 6.2.

Figure 6.7 Steam generator tube sample for the experiment Table 6.2 The depths and diameters for flat bottom holes defects Number 1 2 3 4 5 Depth (inch) 0.052 0.05 0.04 0.03 0.02 Diameter (inch) 0.127 0.127 0.127 0.127 0.127 Number 6 7 8 9 10 Depth (inch) 0.01 0.04 0.021 0.018 0.016 Diameter (inch) 0.127 0.06 0.06 0.06 0.06

6.4.2 Probe Pusher An MS 23 industry standard NEMA size 23 stepper motor is used as the probe pusher. The motor is optimized for micro-stepping and offers 1.8 degrees per full step with 200 full steps per revolution. The diameter of front and rear shafts is 0.250”, and the shaft endplay has been limited to 0.010” for excellent encoder performance and minimum vibration. The device has a 4 wire connector interface for the driver board. The motor driver is STP 100 from Pontech for small to medium stepper motor applications where step precision up to 32 bit is required. It has a RS232 serial port for connection and communication with computer. For the experiment, the stepping size of the motor is set to be 6.5 micrometer.

153

6.4.3 Data Acquisition System In order to measure the amplitude and phase of induced voltage in bobbin pickup coil, a lock-in amplifier with data acquisition function is used in the experiment. The lock-in amplifier is SR844, RF lock-in amplifier from Stanford Research Systems with wide bandwidth, as shown in Figure 6.8. It’s operational frequency range is from 25 kHz to 200 MHz and provides up to 80dB dynamic reserve. It can work with internal and external reference. Two 16-bits DACs and ADCs are embedded. It has both GPIB and RS-232 interface[119]. The GPIB port can be used for transmitting data from the amplifier to computer for the data acquisition.

Figure 6.8 SR844 RF Lock-in amplifier The basic functional diagram for phase-locking is shown in Figure 6.9. Vsig

Vref

Mixer

LPF

Gain

X

90

Y

Phase shift

Mixer

Gain

LPF

Figure 6.9 Basic function diagram of Lock-in amplifier Assume the input signal Vsig and reference signal Vref are represented by Vsig  Vs sin(st   s )

154

(7.9)

Vref  Vr sin(r t  r )

(7.10)

where, Vs , Vr are the amplitudes,  s , r are the phases of the two signals respectively. Then the mixed signals of input and reference signal are represented as Vm1  VsVr sin(s t   s )sin(r t  r ) 1  VsVr {cos[(s  r )t  ( s  r )]  cos[(s  r )t  ( s   r )]} 2

(7.11)

Vm2  VsVr sin(s t   s )sin(r t  r  90 )

(7.12) 1  VsVr {sin[(s  r )t  ( s  r )]  cos[(s  r )t  ( s  r  90 )]} 2

1 Define    s  r and V  VsVr . After passing the low pass filter (LPF), the high frequency 2

components of these mixed signals are eliminated. If the input signal frequency equals that of the reference signal frequency, which means s  r , then the low frequency components become DC value. So the outputs of the lock-in amplifier are constant values, which are independent of frequency:

X  V cos

(7.13)

Y  V sin 

(7.14)

Where, X is called the in-phase component, and Y the quadrature component. So the amplitude R and phase  of the output signal is calculated by

R  X 2 Y2 V Y X

  tan 1( )   s  r

(7.15) (7.16)

Where, R is measures the signal amplitude and does not depend upon the phase between the input signal and lock-in reference signal.  is the phase between the input signal and lock-in 155

reference signal. The GPIB-USB cable is used for SR844 to communicate with computer by LabVIEW program. The lock-in amplifier is controlled by the computer for automatic data acquisition. The experimental signals are displayed as real versus imaginary parts in the complex plane, as well as the induced voltage plot a shown in Figure 6.11.

Figure 6.10 LabVIEW control panel for lock-in amplifier

Figure 6.11 LabVIEW control panel for signal display 156

6.5 Experimental Results The test bench is used for the RoFEc probe inspection of the steam generator tube sample. The three phase excitation source operates at 35 kHz. The output peak voltages for three phases are 18.4, 18.4 and 19.2 V. Because phase C is the outer winding, it has longer wires and hence larger impedance and higher terminal voltage. The peak current for the three phase excitation source is 116mA. The stepper motor drives the probe with a speed of 4 mm/s and step size of 0.65 mm. The tube sample contains 10 different machined defects on the tube wall. The real and imaginary parts of experimental data are represented in Figure 6.12. The induced voltage trajectories for those detectable defects are shown in Figure 6.13 to Figure 6.22. The real and imaginary parts of experimental signal for defect 1 is compared with the simulation results from the finite element model, as shown in Figure 6.13 and Figure 6.14. These two are match very well, which validates the finite element simulation model. The experiment signals of defects 6 and 10 are weak because these defects have small depth (defect 6: depth 0.01 inch, defect 10: depth 0.016 inch ) thus small volume (defect 6: 0.0044 inch3, defect 10: 0.0059 inch3 ) for detection, as present in Table 6.3.

157

(1)

(2)

(3)

(4)

(5)

(7)

(6)

(8)

(9)

(10)

Figure 6.12 Real and imaginary parts of experimental signal of RoFEC probe Table 6.3 Volume and signal amplitude of 10 defects on the tube sample Defect Number 1 2 3 4 5 Depth (inch) 0.052 0.05 0.04 0.03 0.02 5 3 Volume (x 10 inch ) 65.9 63.3 50.7 38 25.3 Amplitude (inch) 0.0324 0.0154 0.0116 0.0091 0.0040 Defect Number 6 7 8 9 10 Depth (inch) 0.01 0.04 0.021 0.018 0.016 5 3 Volume (x 10 inch ) 12.7 11.3 5.94 5.09 4.52 Amplitude (inch) 0.0014 0.0035 0.0034 0.0031 0.001

158

0.8

Simulation Experiment

Imagianary part (V)

0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1

-0.5

0 Real part (V)

0.5

1

Figure 6.13 Induced voltage trajectory of defect 1 measured by probe prototype and simulation signals from finite element model

Normalized real part (V)

1 Simulation Experiment

0.5

0

-0.5

-1 -15

-10

-5 0 5 Axial location (mm)

10

15

(a) Figure 6.14 Real and imaginary parts of induced voltage comparison for experimental and simulation signals for defect 1

159

Normalized imaginary part (V)

Figure 6.14 (cont’d) 1 Simulation Experiment

0.5 0 -0.5 -1 -15

-10

-5 0 5 Axial location (mm)

10

15

(b) x 10

-3

8

Imaginary part (V)

6 4 2 0 -2 -4 -6 -8 -0.01

-0.005

0 Real part (V)

0.005

0.01

Figure 6.15 Induced voltage trajectory of defect 2 measured by probe prototype

160

x 10

-3

6 Imaginary part (V)

4 2 0 -2 -4 -6 -8 -0.01

-0.005

0 Real part (V)

0.005

0.01

Figure 6.16 Induced voltage trajectory of defect 3 measured by probe prototype x 10

-3

Imaginary part (V)

4 2 0 -2 -4 -6

-4

-2 0 2 Real part (V)

4

6 x 10

-3

Figure 6.17 Induced voltage trajectory of defect 4 measured by probe prototype

161

x 10

-3

2 Imaginary part (V)

1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2

-1

0 1 Real part (V)

2

3 x 10

-3

Figure 6.18 Induced voltage trajectory of defect 5 measured by probe prototype

Figure 6. 19 Induced voltage trajectory of defect 6 measured by probe prototype

162

x 10

-3

Imaginary part (V)

2

1 0

-1 -2

-3

-2

-1

0 1 Real part (V)

2

3 x 10

-3

Figure 6.20 Induced voltage trajectory of defect 7 measured by probe prototype

x 10

-3

Imaginary part (V)

1 0.5 0 -0.5 -1 -2

-1.5

-1 -0.5 Real part (V)

0

0.5

1 x 10

-3

Figure 6.21 Induced voltage trajectory of defect 8 measured by probe prototype

163

6

x 10

-4

Imaginary part (V)

4 2 0 -2 -4 -8

-6

-4

-2 0 Real part (V)

2

4 x 10

-4

Figure 6.22 Induced voltage trajectory of defect 9 measured by probe prototype

Figure 6. 23 Induced voltage trajectory of defect 10 measured by probe prototype Since defects 1 ~ 5 have the same diameter but different depths, the induce voltage trajectories are plotted and compared on the same figure as shown in Figure 6.24. The maximum 164

amplitude and phase versus defect depth are shown in Figure 6.25. The amplitudes increase as the depth increase proportionally, whereas the phases remain the same since these defects are located on the same positions of circumference. The figures of amplitude and phase versus depth defects 7~10 are also represented in Figure 6.27. The same conclusions can be drawn as that of defects 1~5. Note that the signal for the defect 10 is very weak because of small depth and diameter (depth 0.016 inch, diameter 0.06 inch, volume 4.52x10-3inch3) compared with other defects on the tube wall.

0.025 0.02

Defect 1 Defect 2 Defect 3 Defect 4 Defect 5

Imaginary part (V)

0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.02

-0.01

0 Real part (V)

0.01

0.02

Figure 6.24 Comparison of induced voltage trajectories of defect 1 ~ 5 measured by prototype probe

165

Amplitude (V)

0.015 0.01 0.005

Phase (degree)

0 0.02

0.025

0.03

0.035 0.04 Depth (inch)

0.045

0.05

0.025

0.03

0.035 0.04 Depth (inch)

0.045

0.05

150 100 50 0 0.02

Figure 6.25 Signals amplitude and phase versus depth for defect 2~5

3

x 10

-3

Defect 7 Defect 8 Defect 9 Defect 10

Imaginary part (V)

2 1 0 -1 -2 -3 -2

-1

0 Real part (V)

1

2 x 10

-3

Figure 6.26 Comparison of induced voltage trajectories of defect 7 ~ 10 measured by prototype probe 166

Amplitude (V)

30 20 10

Phase (degree)

0 0.015

0.02

0.025

0.03 0.035 Depth (inch)

0.04

0.045

0.02

0.025

0.03 0.035 Depth (inch)

0.04

0.045

150 100 50 0 0.015

Figure 6.27 Signals amplitude and phase versus depth for defect 7~9 The probe is excited at 150 kHz to detect defects 2 and 3. The real and imaginary parts of experimental signals are shown in Figure 6.28. Since the impedance of three phase windings increase with higher frequency excitation, the input currents are highly reduced. The output voltage for the pickup coil is much smaller than that of at the lower frequency 35 kHz.

167

Real part (V)

-0.8

-3

-1

-1.2

Imaginary part (V)

x 10

1.8

0 -3 x 10

50

100

0

50

100

150 Axial points

200

250

300

200

250

300

1.6 1.4 1.2

150 Axial points

Figure 6.28 Real and imaginary parts of experimental signal for defect 2 and 3 at 150 kHz As discussed in Chapter 5, if the defects are at the same location of circumference, the phases of the induce voltage trajectory are the same no matter the variation of defect depth. In order to validate the simulation, the probe is applied to detect defects of through wall holes of dimension 4×4 mm, which are located at 0, 45, 90, 135 and 180 degrees around the circumference of tube wall. Figure 6.29(b) and (d) show the phase shift in the induced voltage for different circumferential locations of the defect as predicted by simulation results, whereas the amplitude remains the same for the same depth of defects, as shown in Figure 6.29(c).

168

100% through hole

Probe prototype

(a)

(b) Figure 6.29 Induced voltage measurement in the bobbin coil for defects at different circumferential locations: (a) probe prototype, (b) induced voltage plot by real and imaginary parts, (b) amplitude vs. defect circumferential location, (c) phase vs. defect circumferential location

169

Figure 6.29 (cont’d)

(c)

(d)

6.6 Summary A prototype of rotating field eddy current probe is built in the lab to validate the simulation results obtained using finite element analysis. To operate the probe, a three phase excitation source is built. And a test bench with stepper motor, tube holder and data acquisition system is used for tube inspection. The output voltage in the pickup coil is directly proportional to the defect depths and the phase of induced voltage in the bobbin coil is related to the circumferential location of defects in the tube wall allowing both depth and location to be estimated from a single line scan data. The probe is easy to build with simple instrumentation and the single axial scan enables rapid inspection rates.

170

CHAPTER 7 DESIGN OF ENCIRCLING ROTATING EDDY CURRENT PROBE This chapter investigates the design of a RoFEC probe built with encircling excitation coils that is useful for inspecting cylindrical rods. The feasibility of the proposed approach is studied using finite element models and results are presented for non-magnetic and ferromagnetic tube inspection. 7.1 Introduction This chapter investigates the design of a rotating field eddy current probe with excitation coil encircling the external surface [14, 120]. The probe can be used for inspection of nonmagnetic and magnetic cylindrical samples with high operation speed. Axial magnetic field component which results from eddy current distribution around the defect is used for detecting the presence of defect in nonmagnetic sample. The flux leakage caused by defect is used for defect detection in ferromagnetic samples. Two dimensional and three dimensional finite element models are used to analyze the rotating field excitation and probe operation principles of defect detection for nonmagnetic and magnetic samples. Simulation results demonstrate the sensitivity of probe to volumetric, axial and circumferential oriented cracks in nonmagnetic and ferromagnetic tubes. This chapter is organized as following sections: section 7.2 presents how the probe generates a rotating magnetic field with three pairs of windings on the probe cross section plane. Section 7.3 describes finite element models for the simulation of RoFEC probe scan. Section 7.4 shows the simulation results of various defects in magnetic and nonmagnetic samples. 171

7.2 Operational Principles The encircling RoFEC probe generates a rotating magnetic field, using three pairs of identical coils wound on a toroid ferrite core and excited by three-phase balanced alternating current source, as shown in the schematic of Figure 7. 1 (a). The ferrite core concentrates the magnetic flux and magnifies the magnetic field flux density, as shown in Figure 7. 1 (b). The magnetic flux densities associated with three windings are shown in Figure 7. 2 (a), (b) and (c), when the phase A, B and C are 0°, -120° and -240° respectively. At a different time instant, the resultant magnetic flux density has constant amplitude and different orientations, as shown Figure 7. 3. As a function of time, the magnetic flux density scans circumference of the tube wall and rotates at the frequency of excitation current source, as shown in Figure 7. 3(a) ~ (e). The magnetic field is mainly radial and induces eddy currents in the tube wall which flow circularly around the radial axis. As the probe scan along the axial direction of the cylindrical sample, the probe is sensitive to the defects of all orientations in the sample. The defects in nonmagnetic samples disturb the eddy currents resulting in an axial component of magnetic field on the cross sectional plane. Defects in ferromagnetic samples lead the magnetic field flux leakage around the defect circumferential location. The response signal due to field/defects interaction can be picked up by an array of Giant Magneto-Resistance (GMR) sensors or a bobbin coil located circumferentially in the center plane of the excitation windings. The GMR sensor has unique sensitive axes and high sensitivity to static and alternating magnetic field. It measures the magnetic field aligned with the sensor axes. The bobbin pickup coil is sensitive to the change of 172

encircled flux by the coil. As shown in Figure 7. 1(a), the GMR array sensors with sensitive orientation along magnetic field variation directions are located circumferentially between the ferrite core and the outer surface of tube sample. The bobbin pickup coil can also be located encircling the tube sample to monitor or detect the flux change along tube axes.

A Z Y B C

X

(a) (b) Figure 7. 1 Rotating Field Eddy Current Probe: (a) 3D model, (b) Magnetic flux contour

173

A B’ B A’

By

Bx

(a)

(b) A B’

C’

C’

By Bx

C

C

BZ

B

A’ BZ

(c)

(d)

Figure 7. 2 Magnetic flux density due to three phase windings and total magnetic flux density

(a)

(b)

(c)

Figure 7. 3 Rotating magnetic field (clockwise) at different current excitation phase angle: (a) 0°, (b) 45°, (c) 90°, (d) 135°, (e) 180° 174

Figure 7.3 (cont’d)

(d)

(e)

7.3 Finite Element Simulation A three dimensional finite element model for the probe and cylinder geometry is developed using reduced vector potential Ar, V-Ar formulation[28]. The reduced vector potential formulation avoids modeling the excitation source. A nonmagnetic Inconel 600 hollow cylinder (OD/ID, 22.23/19.69 mm) is modeled using the encircling RoFEC. The tube wall has two different machined defects, namely, a rectangular hole and a circumferential notch The probe is excited by three phase current source with frequencies of 35, 150 and 300 kHz. The inner radius of the ferrite core is 19 mm, and the height and thickness are 4 mm. Three pairs of excitation windings are modeled as coils with 6 mm/10 mm in inner/outer diameter and 3 mm in height. The magnetic flux density induced by rotating fields is measured by an array of GMR sensors. A bobbin pickup probe is also sensitive to changes in axial flux. An induced voltage in the bobbin coil results from the defects in the tube wall. Note that for the ferromagnetic cylindrical samples, the reduced magnetic vector potential is not applicable, because the magnetic field generated by the excitation windings cannot be 175

calculated analytically by Biot-Savart law with the presence of ferromagnetic samples in the domain. Thus the traditional magnetic vector potential formulation is needed to simulate the probe scan. This would require re-meshing of the probe with ferrite core at each scan position. A two dimensional finite element model is presented in the following section for simulation of ferromagnetic sample with the encircling probe. Pickup sensor

(a) (b) Figure 7. 4 Finite element modeling of probe and tube: (a) 3D mesh, (b) top view of 3D mesh 7.4 Simulation Results 7.4.1 Nonmagnetic samples The Inconel 600 nonmagnetic tube with ID/OD 0.775”/0.875” is used as the cylindrical sample. The conductivity is 969,000 S/m, and relative permeability is 1. The bobbin pickup coil is in the center plane of the excitation windings of the probe. As the probe scans axially, induced voltage due to the axial flux change is measured from the coil terminal at each scan position. The measurements are voltage amplitude and phase with reference to the phase of the excitation 176

source, i.e. phase A. The finite element simulation results of induced voltage in bobbin pickup coil are shown in Figure 7. 1. The voltage is calculated as same as by equation (3.109), where A is the total magnetic vector potential and dl the segmentation of bobbin coil loop. These loops in the figures are plotted in complex plane with real and imaginary parts of voltage respectively. The phases of the signals are defined at scan positions where the amplitudes are maximum. Three different defects are simulated: (a) square hole: 2 mm x 2 mm, 100% depth of tube wall; (b) axial notch: 8 mm x 0.127 mm, 100% depth; (c) circumferential notch: 0.127 mm x 8 mm, 100% depth. With increasing frequency, the maximum amplitude of the induced voltage increase. Notice that the phases of the loops change with frequencies, which is due to the skin effect of eddy current reflecting on phases. In order to detect and discriminate defect types, an appropriate frequency should be chosen. The following study of the effect of defect depths on induced voltage amplitude and phase provide a clue for choosing the excitation frequency. 1

x 10

-4

8 square hole - 35 kHz square hole - 150 kHz square hole - 300 kHz

-4

axial notch - 35 kHz axial notch - 150 kHz axial notch - 300 kHz

6 4

Imaginary part (V)

0.5

Imaginary part (V)

x 10

0

-0.5

2 0 -2 -4 -6

-1 -1.5

-1

-0.5

0 0.5 Real part (V)

1

1.5 x 10

-4

-8 -2

-1

0 Real part (V)

1

2 x 10

-3

(a) (b) Figure 7. 5 Simulation results of Bobbin pickup signals from square hole, axial and circumferential notches at 35, 150, 300 kHz: (a) square hole, (b) axial notch, (c) circumferential notch

177

Figure 7.5 (cont’d) 2

x 10

-5

circ notch - 35 kHz circ notch - 150 kHz circ notch - 300 kHz

1.5

Imaginary part (V)

1 0.5 0 -0.5 -1 -1.5 -2 -2

-1

0 Real part(V)

1

2 x 10

-5

(c) Bobbin pickup signals of a square cross-section flat bottom hole defect are shown in Figure 7. 6. The amplitude and phase of the signals for different ID/OD depths 20%~100% at three frequencies, namely, 35, 150, and 300 kHz are shown in Figure 7. 2. It is seen that the phase does not change with defect depth at low frequency, however, phase angle changes at high frequency and is related to defect depth. Therefore, the defect at the same circumferential location results in the signals with the same phase but different amplitude. The reason for this is that when the excitation frequency is low, the eddy current penetration depth is much bigger than the tube wall thickness. So the bobbin pickup coil signal for different depths is changed in the signal magnitude only and the phase is invariant. With increase in excitation frequency, the penetration depth is similar to or smaller than tube wall thickness, so the phase of bobbin pickup coil signal is more dependent on the defect depth in the tube wall. Therefore, the low frequency signal can be used to locate the circumferential location of the defect using phase and determine depth using amplitude. The high frequency signal can be used to discriminate between ID and OD defects. 178

6

x 10

-5

x 10

-4

ID - 20% ID - 40% ID - 60% 100% OD - 20% OD - 40% OD - 60%

1

2

0 ID - 20% ID - 40% ID - 60% 100% OD - 20% OD - 40% OD - 60 %

-2

-4

-6

-6

-4

-2

0 2 Real part (V)

4

Imaginary part (V)

Imaginary part (V)

4

0

-1 -1

6 x 10

-5

(a)

0 Real part (V)

1 x 10

-4

(b) x 10

-4

Imaginary part (V)

1

0

-1

ID - 20% ID - 40% ID - 60% 100% OD - 20% OD - 40% OD - 60% -1

0 Real part (V)

1 x 10

-4

(c) Figure 7. 6 Signals for different depths square hole at different excitation frequency: (a) 35 kHz, (b) 150 kHz, (c) 300 kHz

179

1.8

x 10

1.6

Amplitude (V)

1.4 1.2 1

-4

35kHz_ID 35kHz_OD 150kHz_ID 150kHz_OD 300kHz_ID 300kHz_OD

0.8 0.6 0.4 0.2 0 20

40

60 Depth(%)

80

100

(a)

200 150

Phase (Degree)

100 35kHz_ID 35kHz_OD 150kHz_ID 150kHz_OD 300kHz_ID 300kHz_OD

50 0 -50 -100 -150 -200 20

40

60 Depth (%)

80

100

(b) Figure 7. 7 Phase and amplitude of different depths square hole at 35, 150 and 300 kHz: (a) amplitude, (b) phase The axial component of magnetic field, due to square hole (4 X 4mm), axial notches (8 mm x 0.5 mm) and circumferential notch (2 X 15.7 mm) of depth 100% TW, as the encircling probe scans axially on the outside, are shown in Figure 7. 8. Since the main source field has a rotating radial magnetic field, the axial component of magnetic field is generated only in the presence of defect. At defect-free position, the induced eddy currents generate radial field opposed to the source field. When a defect is present, the eddy current is disturbed and an axial magnetic field 180

component appears due to the eddy current re-distribution. From the 2D images, the profiles of those three different defects are easily determined and classified. The biggest challenge for this inspection technique is to fabricate large number of GMR sensor elements for the array with high resolution to cover the tube wall circumference.

Bz

x 10

-5

4

-10

3.5

Axial(mm)

-5

3 2.5

0

2 1.5

5

1 0.5

10 0

50

100

150 200 250 Circ.(degrees)

300

350

(a)

(b) -5

Bz

x 10

-15 3.5 -10

3 2.5

Axial(mm)

-5

2 0 1.5 5

1 0.5

10

0 15 0

50

100

150 200 Circ.(degrees)

250

300

350

(c)

(d)

Figure 7. 8 Axial magnetic flux density due to different defect with 100% depth measure by GMR sensors: square hole (a) 2D, (b) 3D, axial notch (c) 2D, (d) 3D, circumferential notch (e) 2D, (f) 3D. Note that black box indicate the defect size and location.

181

Figure 7.8 (cont’d)

Axial(mm)

Bz

-15

x 10 3.5

-10

3

-4

2.5

-5

2 0 1.5 5 1 10

0.5

15 0

100

200 Circ.(degrees)

300

0

(e)

(f)

7.4.2 Ferromagnetic Tube Sample In the case of ferromagnetic samples, the magnetic flux is concentrated in the ferromagnetic tube wall. The presence of defect disturbs induced eddy currents in tube wall and also results in flux leakage. Instead of receiving the magnetic field variation caused by eddy current, the flux leakage is picked up by the GMR array sensor for defect detection. A 2D axisymmetric finite element model is used for modeling the ferromagnetic cylindrical sample, where only the radial or tangential fields on the cross plane is of interest. The formulation for this model is based on traditional magnetic vector potential. The relative permeability for the ferrite core is chosen to be 2000. The conductivity of the ferromagnetic sample is 969,000 S/m and the relative permeability of sample is 100. The frequency of the three phase excitation current is varied from 60 Hz ~ 300 kHz. Two 100% through wall holes of cross-sectional area 1 mm x 1.27 mm are located at 0° and 180°, as shown in Figure 7. 9.

182

Figure 7. 9 2D model for encircling probe with ferrite core and ferromagnetic tube In the 2D simulation model, the three phase excitation current directions are out-of-plane, i.e., inward and outward of the x-y plane. The directions of magnetic field due to the current are in plane, i.e. radial or tangential directions. To get the axial magnetic field, a 3D model is required. For ferromagnetic tube samples, the magnetic flux density on the x-y plane is of importance for defect detection. The magnetic flux density around the tube wall is shown in Figure 7. 6. The excitation frequency for this setup is 60 Hz. When the relative permeability µr is equal to 1 (nonmagnetic tube), the magnetic flux density is close to sinusoidal waveform (rotating field) around circumference (including spatial harmonics which can be analyzed by the same way as the motor winding theorem) because of winding distribution. When µr increases from 1 to 1000, the magnetic flux density becomes less sinusoidal and approximates to a constant value and is uniformly distributed around the tube circumference. The magnetic flux inside the tube wall does not vary circumferentially when the field is rotating.

183

Magnetic Flux Density |B| (T)

Relative Permeability of Tube 0.5

µ↑

0.4

Mur = 1 Mur = 10

0.3

Mur = 20

0.2

Mur = 50

0.1

Mur = 100

0 0

100 200 300 400 Circ. Angular Position (Degree)

Mur = 200 Mur = 1000

Maximum Magnetic Flux Density(T)

(a) 0.5 0.4 0.3 0.2 0.1 0 0

200

400 600 Relative Permeability

800

1000

(b) Figure 7.10 GMR sensor signal for amplitude of magnetic flux density around circumference versus the relative permeability of the ferromagnetic tube sample: (a) magnetic flux density vs. circ. Angular position, (b) maximum magnetic flux density vs. relative permeability The magnetic flux density contours for the nonmagnetic and ferromagnetic tube samples are shown in Figure 7.10. The ferromagnetic tube serves to shield the magnetic flux and does not penetrate the tube wall. So the principles of defect detection for ferromagnetic and nonmagnetic samples are different. For the nonmagnetic tube sample, the radial rotating magnetic field goes 184

through tube wall and rotates in time. Eddy current is induced in the tube wall by the rotating field. The defect in the tube wall interrupts the induced eddy current, which results in the magnetic field variation. However, in a ferromagnetic tube, where µr is greater than 1, the magnetic flux is concentrated in the tube wall. The defect in the tube wall results in magnetic flux leakage which is used for defect detection. Compared with the magnetic field variation caused by eddy current disturbance, the flux leakage effect dominates the magnetic field variations due to defect. As shown in Figure 7.12, there are two peaks of magnetic flux density around the circumference because of flux leakage of two defects in the ferromagnetic tube wall at 90° and 270° in Figure 7.12 (a) and 45° and 225° in Figure 7.12 (b). The peaks are shifted circumferentially corresponding to locations of defects in the tube wall. So the two defects can be detected and located circumferentially by the probe. However, two defects in the nonmagnetic tube wall are not detected by the magnetic flux leakage because of low signal to noise ratio of magnetic flux density variation on the cross section plane caused by eddy current disturbance. As mentioned before, the axial component of magnetic field is useful for defect detection in nonmagnetic tube sample, because it is generated only at the location of defect.

185

(a)

(b)

Figure 7.11 Magnetic flux contour and flux density for (a) nonmagnetic and (b) ferromagnetic samples (µr = 100)

|B| (T)

0.6 0.4

Magnetic tube + defects

0.2

Nonmagnetic tube + defects

0 0

200 400 Circ. Angular Position (Degree) (a)

Figure 7.12 Nonmagnetic and ferromagnetic tube samples with two defects at circumference: (a) defects at 90° and 270°, (b) defects at 45° and 225°

186

|B| (T)

Figure 7.12 (cont’d) 0.5 0.4 0.3 0.2 0.1 0

Magnetic tube + defects Nonmagnetic tube + defects 0

100 200 300 400 Circ. Angular Position (Degree) (b)

Since the defect in the ferromagnetic tube samples is detectable due to magnetic flux leakage as shown in the simulation results in Figure 7. 13, the magnetic flux density signal is stronger with higher signal to noise ratio with a ferrite core in the probe than that without ferrite

Magnetic Flux Density |B|(T)

core (air core). So a ferrite core probe is recommended for ferromagnetic tube inspection. 0.5 AirCore + Nonmagnetic Tube AirCore + Magnetic Tube FerriteCore + Nonmagnetic Tube FerriteCore + Magnetic Tube

0.4 0.3 0.2 0.1 0 0

100 200 300 400 Circ. Angular Position(degree)

Figure 7. 13 Amplitude of magnetic flux density from GMR array from nonmagnetic/ferromagnetic tube with air/ferrite core with 100% defect A study of excitation frequency on flux leakage amplitude is studied using the 2D model.

187

Two defects (1mm x1.27mm) with 100% depth are introduced at 90° and 270° in the ferromagnetic tube wall. As the frequency increases from 60Hz to 300 kHz, the skin depth into the tube wall decreases and the radial component measured at the sensor array tends to be sinusoidal, and the two defect signals are not visible. The reason is that eddy current penetration depth decreases as excitation frequency increases. So the induced eddy current is concentrated on the tube wall surface at high frequency excitation. The magnetic field due to induced eddy current dominates the magnetic field compared with the field due to leakage flux density. So in order to detect the defects in ferromagnetic tube by leakage flux, low frequency is preferable to

Magnetic Flux Density |B|(T)

achieve high signal to noise ratio.

0.6 0.5 0.4 0.3 0.2 0.1 0

60 Hz 100 Hz 1000 Hz 5000 Hz 10 kHz 0

100 200 300 400 Circ. Angular Position (Degree)

35 kHz 150 kHz

(a) Figure 7. 14 Ferromagnetic tube with two defects (90° and 270°) at different frequencies (60 Hz ~ 300 kHz): (a) magnetic flux density vs. circ. Angular position, (b) maximum amplitude of magnetic flux density vs. frequency

188

Figure 7.14 (cont’d)

Magnetic Flux Density Amplitude (T)

0.6 0.5 0.4 0.3 0.2 0.1 0 0

100000

200000 Frequency

300000

400000

(b) 7.5 Summary The RoFEC probe with encircling excitation coils generates rotating magnetic field on the probe cross-sectional plane. The probe is sensitive to all orientation defects. It is capable of detecting a defect and determining its axial and circumferential locations with only single pass axial scan. Thus the probe has fast scan speed compared with conventional mechanical rotation probe. Two different pickup sensors, bobbin coil and GMR sensor are used to receive the magnetic field variations due to defects. For nonmagnetic samples, the axial component of magnetic field is measured and used for the defect detection, since the presence of a defect results in axial component associated with eddy current distribution in the vicinity of the defect. For ferromagnetic samples, the flux leakage phenomenon is used to detect and located defects. Simulation results show the encircling probe operation principles and feasibility for defect

189

detection. The future work for the encircling rotating field probe is the 3D modeling for the ferromagnetic samples. The ID/OD with different depth defects are going to be modeled and detected according to the magnetic flux leakage principles. In the 3D model, the axial component of magnetic flux leakage can also be investigated to characterize the defect.

190

CHAPTER 8 CONCLUSIONS AND FUTURE PLAN 8.1 Conclusions The main contributions of the thesis are as following: (1) Methods of modeling complex tube and defect geometries, such as shallow dents, real cracks, TTS and loose parts in an interactive manner. (2) Tube inspection challenges are studied and solved by simulation using differential bobbin, plus point and rotating pancake probes. (3) Validation of eddy current probe simulation results with industrial data base for bobbin, pancake and plus point eddy current probes. Detection principles of eddy current probes for complex geometries are explained by models and validated with experiment data. (4) Design of novel rotating field eddy current probe with finite element modeling and development of prototype of probe for the validation of simulation results from modeling. (5) Analysis of phase of bobbin pickup coil induced voltage for determining circumferential location of defect. (6) Model-based parametric studies for optimizing probe design (7) Design and simulation of encircling rotating field eddy current probe for cylindrical specimen inspection. (8) Analysis of fields in ferromagnetic and non-ferromagnetic test samples. (9) Parametric studies for optimization of encircling RoFEC probe design.

191

8.2 Future Plan Rotating field Probe The prototype probe using bobbin coil pick up has been modeled and validated using experimental measurements. An alternate design of the probe using a GMR pickup sensor array is planned for fabrication. The sensor array will be located in the center plane of the probe to pick up the axial component of magnetic field. Figure 8. 1 shows a schematic of the RoFEC probe integrated with an array of GMR sensors on the circumference of probe center. The controller, pre-amplifiers are placed together closed to the GMR array, which eliminate the transmission noise along the wires from probe to computer for the data acquisition. With the GMR array sensor, a 2D C-scan image of axial component of magnetic field resulted from defect in the tube wall will be available. Encircling RoFEC probe The encircling RoFEC probe has been simulated with 2D and 3D finite element models. To validate the simulation results, some probe prototype is needed to be built in the lab. With the development of 3D printing, it is easy to make the core for the three pairs of windings and the pickup coils. The excitation source, data acquisition and auto scan system is already built for inside tube RoFEC probe system. In order to build a prototype probe, additional parametric studies, such as coil height, width and excitation frequency, also need to be done using 2D and 3D models.

192

Figure 8. 1 RoFEC probe with GMR sensor array as pickup in the center

193

APPENDIX

194

APPENDIX SIMULATION SIGNALS VALIDATION OF EDDY CURRENT PROBES FOR TUBE INSPECTION A.1 Bobbin Probe Validation – Flat Bottom Hole The simulation results of three different bobbin probes from four different types of defects are compared with the experimental data from industry. The simulations are conducted with varied parameters, as shown in Table A.1. Table A. 1 Parameter of defects for the bobbin probe validation Type 610MR

Depth (%) 100 60

Diameter (inch) 0.067 0.109

Freq. (kHz)

OD (inch)

ID (inch)

THK (inch)

Material

270

0.75

0.668

0.041

Inconel 600

(a) Figure A. 1 610 MR bobbin probe experimental and simulation signals (60% depth defect) at 270 kHz: (a) Liz plot; (b) real plot; (c) imaginary plot.

195

Figure A.1 (cont’d)

(b)

(c)

196

(a)

(b) Figure A. 2 610 MR bobbin probe experimental and simulation signals (100% depth defect) at 270 kHz: (a) Liz plot; (b) real plot; (c) imaginary plot.

197

Figure A.2 (cont’d)

(c) A quantitative metric for comparing the experimental and simulation results are defined using the magnitude and phase information as:

 e  (1 

 e  a tan(

max{ Re2sim  Im 2sim } 2 2 max{ Reexpt  Imexpt }

) 100%

(A.1)

Imexpt Im sim 2 2 ) max{ Re2sim  Im2sim }  a tan( ) max{ Reexpt  Imexpt } (A.2) Resim Reexpt

The quantitative error analysis for the 610 MR probe simulation is summarized in Table A. 2. Table A. 2 Quantitative analysis of simulation and experimental signals for 610 MR probe Crack Depth (%) 100% 60%

Probe type

Magnitude error (%)

Phase error(º)

5.39

0.5

5.96

3.49

.610 Bobbin probe

A.2 Bobbin Probe Validation – 360 degrees Dent The three dimensional tube with a 360 degrees dent around the circumference is meshed as shown in Figure A. 3. The simulation parameters are listed in Table A. 3. The differential bobbin

198

probe inspection is simulated. The experimental and simulation results for the dent at frequencies 15, 100, 200 and 400 kHz are shown in Figure A. 4, Figure A. 5 and Figure A. 6 respectively. The quantitative error analysis of the model performance is listed in Table A. 4.

Tube Dent Bobbin

Table A. 3 Parameters settings for dent simulation ID OD Material 0.774" 0.874" Inconel 600 Axial Max. Depth Opening 0.001 0.75" ID OD Height Spacing Frequency (kHz) 0.6" 0.702" 0.06" 0.06" 15, 100, 200, 400

Figure A. 3 3D mesh for the tube with 360 degrees dent

199

Simulation 400kHz Experiment 400kHz

0.6

Imaginary part (V)

0.4 0.2 0 -0.2 -0.4 -0.6 -0.5

0 Real part (V)

0.5

(a)

Real part (V)

1 Simulation 400kHz Experiment 400kHz 0

Imaginary part (V)

-1 -20

-10

0 10 20 Axial location (mm)

30

40

0.1

0 Simulation 400kHz Experiment 400kHz -0.1 -20

-10

0 10 20 Axial location (mm)

30

40

(b) Figure A. 4 Comparison of simulation and experiment signals of 3D dent at 400 kHz: (a) impedance trajectory, (b) real and imaginary parts

200

0.6

Simulation 200kHz Experiment 100kHz

Imaginary part (V)

0.4 0.2 0 -0.2 -0.4 -0.6 -0.5

0 Real part (V)

0.5

(a)

Real part (V)

1 Simulation 200kHz Experiment 200kHz 0

Imaginary part (V)

-1 -20

-10

0 10 20 Axial location (mm)

30

40

0.1

0 Simulation 200kHz Experiment 200kHz -0.1 -20

-10

0 10 20 Axial location (mm)

30

40

(b) Figure A. 5 Comparison of simulation and experiment signals of 3D dent at 200 kHz: (a) impedance trajectory, (b) real and imaginary parts

201

Simulation 100kHz Experiment 100kHz

0.6 Imaginary part (V)

0.4 0.2 0 -0.2 -0.4 -0.6 -0.5

0 Real part (V)

0.5

(a)

Real part (V)

1 Simulation 100kHz Experiment 100kHz 0

Imaginary part (V)

-1 -20

-10

0

10 20 Axial location (mm)

30

40

0.2

0 Simulation 100kHz Experiment 100kHz -0.2 -20

-10

0

10 20 Axial location (mm)

30

40

(b) Figure A. 6 Comparison of simulation and experiment signals of 3D dent at 100 kHz: (a) impedance trajectory, (b) real and imaginary parts

202

Table A. 4 Quantitative analysis of simulation and experimental signals for 360 dent inspection Frequency (kHz)

Defect type

400 200

Magnitude error (%) 1.15

360 Dent

100

0.52 6.34

A.3 Bobbin Probe Validation - Spherical dent Bobbin probe – 0.610” is used in the simulation for dent detection. The experimental measurements and model predictions of probe impedance are plotted below in Figure A. 7 for four different frequencies (550, 400, 300, 130 kHz). The results show agreement between measurement and simulation.

(a) Figure A. 7 LIZ plot comparison of Bobbin probe impedance from experiment and simulation at five different excitation frequencies: (a) 550 kHz, (b) 400 kHz, (c) 300 kHz, (d), 130 kHz

203

Figure A.7 (cont’d)

(b)

(c)

(d)

204

Table A. 5 Quantitative analysis for simulation and experimental signals for spherical dent inspection Frequency (kHz)

Defect type

Magnitude error (%)

550

8.22

400

0.13

Spherical Dent

300

8.33

130

18.6

A.4 Plus Point Probe Validation - Real Crack A typical axial real crack profile obtained from metallurgic data and its FE mesh is shown in Figure A. 8(a) and (b). The tube wall outer diameter for this case is 0.688 inch, and thickness is 0.037 inch. The finite element simulation, results of real (horizontal) and imaginary (vertical) channels are compared with corresponding experimental signals in Figure A. 9 and Figure A. 10. 80

Radial depth (% TW)

70 60 50 40 30 20 10 0 -0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Axial location (inch)

(a) Figure A. 8 Free span axial real crack profile from EPRI Database: (a) Measured profile, (b) simulation model

205

Figure A.8 (cont’d)

(b)

(a)

(b) Figure A. 9 3D images of real channel from Plus Point probe: (a) experimental signal, (b) simulation signal

206

(a)

(b) Figure A. 10 3D images of imaginary channel from Plus Point probe: (a) experimental signal, (b) simulation signal Line scans across the center of image data of real and imaginary channels shown in Figures 4.40 and 4.41 are compared in Figure 4.42 and 4.43. The real and imaginary part line scans of the simulation signal are closer to the real crack profile measured, however the real and imaginary part of experimental signal are seen to contain significant amount of noise.

207

0.05

Amplitude(V)

0

-0.05

-0.1 simulation experiment -0.15

0

0.1

0.2

0.3 0.4 0.5 Axial distance(inches)

0.6

0.7

Figure A. 11 Line scan of real channel in the center of crack 0.25

Amplitude(V)

0.2

simulation experiment

0.15 0.1 0.05 0 -0.05 -0.1

0

0.1

0.2

0.3 0.4 0.5 Axial distance(inches)

0.6

0.7

Figure A. 12 Line scan of imaginary channel in the center of crack Similar simulation is conducted for another axial crack from the EPRI database. The tube outer diameter is 0.629 inch and thickness 0.039 inch. The material of the tube is Alloy 600.The profile and the models for the crack are shown in Figure A. 13(a) and (b). The Plus point probe works at excitation frequency of 300 kHz. The real and imaginary channels of the simulation and experimental signals are shown and compared in Figure A. 14 and Figure A. 15. The line scans of real and imaginary channels from experimental measurement and simulation results are compared as shown in Figure A. 16 and Figure A. 17. The mismatch seen is due to noise in the experimental data.

208

Radial depth (% TW)

50

40

30

20

10

0 -20

-15

-10

-5

0

5

10

15

20

Axial location (inch)

(a)

(b) Figure A. 13 Free span axial real crack profile from ETSS database (TMI1_91_55): (a) measured profile, (b) simulation model

209

(a)

(b) Figure A. 14 3D images of real channel from Plus Point probe: (a) experimental signal, (b) simulation signal

210

(a)

(b) Figure A. 15 3D images of imaginary channel from Plus Point probe: (a) experimental signal, (b) simulation signal 0.04

Amplitude(V)

0.02 0 -0.02 -0.04 -0.06 Simulation Experiment

-0.08 -0.1

6

6.5

7 7.5 Axial distance(inches)

8

8.5

Figure A. 16 Line scan of vertical channel in the center of crack

211

0.3 Simulation Experiment

Amplitude(V)

0.25 0.2 0.15 0.1 0.05 0 -0.05

6

6.5

7 7.5 Axial distance(inches)

8

8.5

Figure A. 17 Line scan of horizontal channel in the center of crack

212

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