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title page
Contents
Nomenclature 13
(Abstract) 15
Chapter 1. Introduction 17
Chapter 2. Simulation of induction heating by the movement of heating planes 20
2.1. Introduction 20
2.2. Analysis of induction heating by calculating 2-d electro-magnetic field 21
2.2.1. Analysis of electro-magnetic field 21
2.2.2. Analysis of temperature distribution 25
2.3. Modeling of induction heating by the movement of heating planes 30
2.4. Results and discussions 31
2.5. Conclusions 33
Chapter 3. Analysis of induction heating using moving coordinate 55
3.1. Introduction 55
3.2. Finite element formulations 56
3.2.1. Analysis of electro-magnetic field 56
3.2.2. Analysis of heat transfer for moving heat source 57
3.3. Results and discussions 59
3.4. Conclusions 60
3.5. The results of comparison of two methods 61
Chapter 4. Angular deformations by induction heating 74
4.1. Introduction 74
4.2. Analysis of angular deformations by induction heating 75
4.3. Plate deformations in line heating process 76
4.4. Results and discussions 80
Chapter 5. Conclusions 97
References 99
Appendix 103
(초록) 104
Fig. 2.1. Schematic diagram of induction heating process and half coil shape 34
Fig. 2.2. Simulation procedure flow chart 35
Fig. 2.3. Schematic half diagram and boundary conditions for FEM 36
Fig. 2.4. Solution domains and mesh generations for 2-d electro-magnetic analysis 37
Fig. 2.5. Modeling of moving heat source using movement of heating planes 38
Fig. 2.6. Schematic half diagram for experiment 39
Fig. 2.7. Isolines of magnetic vector potential at initial state (wb/m) 40
Fig. 2.8. Distribution of the magnetic vector potential at initial state 41
Fig. 2.9. Distribution of the magnetic vector potential for 1st(이미지참조) plane 41
Fig. 2.10. Distribution of the magnetic vector potential for 10th(이미지참조) plane 42
Fig. 2.11. Distribution of the magnetic vector potential for 11th(이미지참조) plane 42
Fig. 2.12. Distribution of the magnetic vector potential for 15th(이미지참조) plane 43
Fig. 2.13. Distribution of the magnetic vector potential for 17th(이미지참조) plane 43
Fig. 2.14. Distribution of the magnetic vector potential for 21th(이미지참조) plane 44
Fig. 2.15. Heat generation for 1st(이미지참조) plane (behind) 45
Fig. 2.16. Heat generation for 10th(이미지참조) plane 45
Fig. 2.17. Heat generation for 11th(이미지참조) plane 46
Fig. 2.18. Heat generation for 15th(이미지참조) plane 46
Fig. 2.19. Heat generation for 17th(이미지참조) plane 47
Fig. 2.20. Heat generation for 21st(이미지참조) plane 47
Fig. 2.21. Maximum heat generation according to plane 48
Fig. 2.22. Three dimensional half model of the steel plate for FEM 49
Fig. 2.23. Temperature history at bottom center of steel plate at 50 kHz 50
Fig. 2.24. Shapes of experimental and calculated heat affected zones 51
Fig. 2.25. Temperature distribution for induction heating (frequency=50 kHz, time=20 sec) 52
Fig. 2.26. Temperature distribution for induction heating (frequency=50 kHz, time=20 sec) 52
Fig. 2.27. Maximum temperature according to frequency 53
Fig. 2.28. Temperature distribution along the direction of depth according to frequency 54
Fig. 3.1. Boundary conditions for FEM in moving coordinate system 63
Fig. 3.2. Three dimensional half model for FEM 64
Fig. 3.3. Isolines of magnetic vector potential for three dimensional analysis at center of coil (wb/m) 65
Fig. 3.4. Temperature history at bottom center of steel plate (frequency=50 kHz, velocity=6 mm/s, current=800 A) 66
Fig. 3.5. Shapes of experimental and calculated heat affected zones 67
Fig. 3.6. Three dimensional temperature distribution for quasi-stationary state at upper surface of steel plate (y=6 mm, frequency=50 kHz, velocity=6 mm/s, current=800 A) 68
Fig. 3.7. Maximum temperature and width of the heat affected zone according to current and velocity (frequency=50 kHz) 69
Fig. 3.8. Maximum temperature according to frequency (velocity=6 mm/s, current=800 A) 70
Fig. 3.9. Temperature plot from the maximum temperature of the surface in the direction of depth according to frequency (velocity=6mm/s, current=800 A) 71
Fig. 3.10. Magnetic vector potential at initial state for two methods 72
Fig. 3.11. Temperature history at bottom center of steel plate for two methods 73
Fig. 4.1. Schematic diagram of coil shape 82
Fig. 4.2. Three dimensional mesh generation 83
Fig. 4.3. Heat generation at 1st(이미지참조) step 84
Fig. 4.4. Heat generation at 2nd(이미지참조) step 84
Fig. 4.5. Heat generation at quasi-stationary state 85
Fig. 4.6. Shapes of experimental and calculated heat affected zones 86
Fig. 4.7. Temperature distribution for induction heating 86
Fig. 4.8. (a) model of plastic region, (b) model of elastic region 87
Fig. 4.9. Infinite plate containing a cuboidal inclusion with an eigenstrain 87
Fig. 4.10. Eigenstrain in one lamina 88
Fig. 4.11. Approximation of plastic region 88
Fig. 4.12. Schematic diagram of heating line 89
Fig. 4.13. Contour of vertical displacement in line heating 90
Fig. 4.14. Deformed shape of vertical displacement in line heating 91
Fig. 4.15. Contour and deformed shape of vertical displacement in line heating 92
Fig. 4.16. Vertical displacement of the plate at y=-50 mm 93
Fig. 4.17. Vertical displacement of the plate at y=50 mm 94
Fig. 4.18. Vertical displacement of the half plate at y=-50mm 95
Fig. 4.19. Vertical displacement of the half plate at y=50 mm 96
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