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Title Page

Abstracts

Contents

CHAPTER 1. Introduction 15

1.1. Motivation 15

1.2. Objectives and scope 18

1.3. Organization of this thesis 19

CHAPTER 2. Magnetic levitation technology 21

2.1. 6-DOF planar motor 21

2.2. Maglev stage using coarse-fine configuration (dual-servo) 24

2.3. Linear active magnetic bearing 27

CHAPTER 3. Design of linear active magnetic bearing 31

3.1. Design consideration 31

3.2. Gravity compensation mechanism 33

3.3. Halbach linear active magnetic bearing 37

3.4. Modeling of magnetic system 40

3.4.1. Analytical model 41

3.4.2. Transformation and superposition of magnetic field 45

3.4.3. Calculation of force and moment 46

3.4.4. Lorentz force modeling 47

3.4.5. Verification of HLAMB model 48

3.5. Force distribution 49

3.6. Remarks 52

CHAPTER 4. Design optimization of HLAMB 55

4.1. Parametric analysis 55

4.1.1. Gap 56

4.1.2. Halbach ratio 56

4.1.3. Width of Halbach magnet array 57

4.1.4. Thickness of Halbach magnet array 57

4.1.5. Assembling tolerance 57

4.2. Design optimization 61

4.2.1. Cost function and constraints 62

4.2.2. Design results 63

4.3. Prototype 69

CHAPTER 5. Design and control of 6-DOF dual-servo stage 75

5.1. Design of dual-servo stage 75

5.1.1. Design of the coarse stage 75

5.1.2. Design of the fine stage 77

5.1.3. System integration 79

5.2. System modeling and control strategy 80

CHAPTER 6. Experimental results 87

6.1. Manufactured 6-DOF dual-servo stage 87

6.2. Six degrees-of-freedom control 90

6.2.1. Experimental setup 90

6.2.2. Levitation process 91

6.2.3. Basic performances: in-position stability and minimum resolution 92

6.2.4. Dynamic performances 96

CHAPTER 7. Conclusions 101

Summary (요약문) 104

Bibliography 107

Acknowledgement(감사의 글) 111

Curriculum vitae 113

LIST OF TABLES

Table 2.1. Target specifications(내용없음) 21

Table 3.1. Modeling methods of electromagnetic system 40

Table 3.2. Analytical model verification using 3D FEM analysis 48

Table 3.3. Comparison of the original cases and the modified case 53

Table 4.1. Optimization results and final design parameters 66

Table 5.1. Specifications of voice coil motor 77

Table 6.1. In-position stability 93

LIST OF FIGURES

Fig. 1.1. Lithography exposure tool potential solutions (ITRS report, 2006) 17

Fig. 1.2. Feedback control of wafer stepper 17

Fig. 1.3. Dual-servo system using 6-DOF magnetically levitated fine stage 19

Fig. 2.1. Principle of Halbach magnet array 22

Fig. 2.2. Magnetically levitated planar motor using Halbach magnet array (Kim, 1998) 22

Fig. 2.3. Planar maglev (Philips applied technologies, 2006) 23

Fig. 2.4. Planar active magnetic bearing (Molenaar, 2000) 24

Fig. 2.5. Maglev wafer stage (a) coarse and maglev fine stage (b) maglev fine stage (Williams, 1997) 25

Fig. 2.6. Wafer stage with magnetic levitation (Nikon, 2004) 26

Fig. 2.7. XY stage apparatus (Canon, 2003) 26

Fig. 3.1. Zero-stiffness bearing using permanent magnets (Nijsse, 2001) 28

Fig. 3.2. A set of permanent magnets for levitation (Choi, 2005) 28

Fig. 3.3. Multipole array magnetic spring (Robertson, 2006) 29

Fig. 3.4. Magnetic gravity compensator (Hol, 2006) 30

Fig. 3.5. Conventional gravity compensator 34

Fig. 3.6. Contour plot of magnetic flux density of the conventional gravity compensator 35

Fig. 3.7. Proposed gravity compensator 36

Fig. 3.8. Contour plot of magnetic flux density of the proposed gravity compensator 36

Fig. 3.9. Lorentz coil implementation (a) moving coil type (b) moving magnet type 37

Fig. 3.10. Symmetric Lorentz coils in HLAMB 39

Fig. 3.11. Halbach linear active magnetic bearing (HLAMB) 39

Fig. 3.12. Surface current model of a block magnet 41

Fig. 3.13. Magnetic field by (a) FEA model (b) analytical model 44

Fig. 3.14. Coordinate transformation of magnetic field 46

Fig. 3.15. Effective volume for calculation of Lorentz force (Part of HLAMB) 47

Fig. 3.16. Static force distribution of the conventional gravity compensator (a) Z force (b) Y force (c) Torque about x-axis 50

Fig. 3.17. Static force distribution of the proposed HLAMB (a) Z force (b) Y force (c) Torque about x-axis 51

Fig. 3.18. Modification of Halbach magnet array in the HLAMB 53

Fig. 3.19. Static force distribution of the modified HLAMB (a) Z force (b) Y force (c) torque about x-axis 54

Fig. 4.1. Parametric model for design of HLAMB 56

Fig. 4.2. Force characteristics of HLAMB with regard to gap 58

Fig. 4.3. Force characteristics of HLAMB with regard to Halbach ratio 58

Fig. 4.4. Force characteristics of HLAMB with regard to width of Halbach magnet array 59

Fig. 4.5. Force characteristics of HLAMB with regard to thickness of Halbach magnet array 59

Fig. 4.6. Z-directional static force of HLAMB with regard to assembling tolerance 60

Fig. 4.7. Convergence of design parameters 64

Fig. 4.8. Convergence of cost function 64

Fig. 4.9. Global minimum verification 65

Fig. 4.10. Static force distribution of the finally designed HLAMB (a) Z force (b) Y farce (c)torque about x axis 67

Fig. 4.11. Dynamic force distribution of the finally designed HLAMB (a) Z force (b) Y force (c)torque about x axis 68

Fig. 4.12. Exploded view of prototype of HLAMB 69

Fig. 4.13. Fabricated mover (top) and stator (bottom) 70

Fig. 4.14. Test setup for the prototype of HLAMB 71

Fig. 4.15. Static force distribution of the prototype (a) Z force (b) Y force (c) torque about x axis 72

Fig. 4.16. Dynamic force distribution of the prototype (a) Z force (b) Y force (c) torque about x axis 73

Fig. 4.17. Current vs. dynamic Z force 74

Fig. 5.1. Coarse stage 76

Fig. 5.2. Voice coil motor (a) stator (b) mover 78

Fig. 5.3. Layout of the fine stage (exploded view) 79

Fig. 5.4. 3D modeling of the total system 80

Fig. 5.5. Rigid body model of the fine stage 81

Fig. 5.6. Sensor locations 82

Fig. 5.7. Control block diagram for the fine stage 84

Fig. 5.8. Dual-servo model 85

Fig. 5.9. Dual-servo control strategy 85

Fig. 5.10. High-level control block diagram 86

Fig. 6.1. Picture of the 6-DOF dual-servo stage 88

Fig. 6.2. Picture of the maglev fine stage 89

Fig. 6.3. Hardware components of the control system 90

Fig. 6.4. Flow chart of levitation process 91

Fig. 6.5. Levitation process 92

Fig. 6.6. In-position stability 93

Fig. 6.7. Current inputs of four HLAMBs 94

Fig. 6.8. Minimum resolution test (a) x-axis (b) y-axis 95

Fig. 6.9. 10um step response in x-axis 96

Fig. 6.10. 25㎜ step and settle 97

Fig. 6.11. Scan trajectory and tracking errors 98

Fig. 6.12. Mean tracking error for 10㎜/sec scan 99

Fig. 6.13. Jitter(RMS error) for 10㎜/sec scan 99

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