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Nomenclature 5

제1장 서론 14

1.1. 연구배경 및 동향 14

1.1.1. 정상상태 풀림 동역학(Steady-state Unwinding Dynamics) 14

1.1.2. 과도상태 풀림 동역학(Transient-state Unwinding Dynamics) 19

1.2. 연구 동기 및 목적 21

제2장 속도가 변하는 풀림계의 지배방정식 24

2.1. 확장 해밀턴 원리 24

2.2. 풀림역학의 에너지 26

2.3. 지배방정식의 유도 29

2.4. 유체 저항력 36

2.5. 속도가변 풀림계의 스칼라 방정식의 유도 39

제3장 과도상태 장력방정식 45

3.1. 과도상태 장력방정식의 필요성 45

3.2. 기존의 장력방정식 46

3.3. 속도가변 풀림계에서의 장력 방정식 48

제4장 속도가 변하는 풀림계의 수치해석 기법 52

4.1. 운동방정식의 공간차분화 52

4.2. 요소 행렬의 정리 57

4.3. 수치적분법 60

4.4. 제안된 장력방정식의 비교 61

4.5. 풀림 속도에 따른 과도상태 경계조건 66

4.5.1. 경계조건에 대한 고찰 66

4.5.2. 과도상태 경계에서의 이탈점 정의 67

제5장 실험적 연구 71

5.1. 풀림 시험 장비 제작 71

5.2. 고속카메라 촬영 영상의 이미지 처리 79

5.3. 속도 및 볼룬높이에 따른 풀림 거동 분석 84

5.4. 가속구간에서의 풀림 거동 분석 96

5.5. 접착 특성에 따른 거동 분석 99

5.5.1. 패키지 전체 접착제 도포 99

5.5.2. 패키지 부분 접착제 도포 102

제6장 속도가 변하는 풀림계 해석 및 적용 104

6.1. 수치해석 모델과 실험의 비교 검증 105

6.2. 속도 가변에 의한 풀림 거동 해석 108

6.3. 경계조건에 따른 풀림 거동 분석 113

6.3.1. 권선각에 따른 풀림 거동 분석 113

6.3.2. 볼룬높이의 영향 119

6.3.3. 초기 장력 변화에 따른 풀림 거동 분석 128

제7장 결론 134

참고문헌 137

Abstract 143

List of Tables

Table 4.1. Constants value of Newmark integration method 60

Table 4.2. Unwinding parameters for comparing tension equations 63

Table 5.1. Property of sewing cotton for unwinding experiment 84

Table 6.1. Property of unwinding fiber-optic cable for high speed conditions 109

Table 6.2. Property of unwinding cable for balloon height case study 115

Table 6.3. Winding angle cases of transient unwinding dynamic analysis 116

Table 6.4. Property of unwinding fiber-optic cable for balloon height case study 119

Table 6.5. Balloon height and velocity cases of transient unwinding dynamic... 119

Table 6.6. Tension and velocity cases of transient unwinding dynamic analysis 129

List of Figures

Fig. 1.1. Applications of low-speed unwinding dynamics 15

Fig. 1.2. Over-end unwinding from cylindrical package 16

Fig. 1.3. Illustration of balloon configuration in unwinding state 16

Fig. 1.4. Applications of high-speed unwinding dynamics 23

Fig. 2.1. Open and closed system for extended Hamilton's principle 25

Fig. 2.2. A schematic diagram on unwinding cables from cylindrical package 27

Fig. 2.3. Acceleration vectors in unwinding dynamics 34

Fig. 2.4. Illustration of the balloon configuration shapes 35

Fig. 2.5. Normal velocities of cable 37

Fig. 2.6. Drag coefficient of cylinder according to Reynolds number by Choo's... 38

Fig. 4.1. Unwinding velocity profile for comparing tension equations 63

Fig. 4.2. Unwinding configurations according to tension equations 64

Fig. 4.3. Unwinding configurations in polar and Cartesian coordinate according to... 64

Fig. 4.4. Tension profile at each tension equation model 65

Fig. 4.5. Tension profiles at lift-off and middle point by 'L.Model' & 'J.Model' 65

Fig. 4.6. Unwinding packages 66

Fig. 4.7. Lift off point on a cylindrical package surface 67

Fig. 4.8. Lift off point on a conical package surface 68

Fig. 4.9. Distance, Velocity, Acceleration of unwinding by using step function 70

Fig. 5.1. 3D CAD model of unwinding experiment device 71

Fig. 5.2. Unwinding experiment set 72

Fig. 5.3. High speed camera mounting device for adjustable position 73

Fig. 5.4. Guide eyelet moving table 74

Fig. 5.5. Notebook with controller for high speed camera and motor controller 74

Fig. 5.6. Unwinding speed control module 75

Fig. 5.7. Blow pipe to prevent cable entangling 76

Fig. 5.8. Compress tool for preventing cable slip from driving wheel and upper fly... 76

Fig. 5.9. Container for collecting unwound fiber 77

Fig. 5.10. Modification process of driving wheel for decreasing the motor load 77

Fig. 5.11. Grid point for image processing 78

Fig. 5.12. Location of lamp for capturing motion by using high speed camera 78

Fig. 5.13. An example of 'point tracking' by using TEMA 80

Fig. 5.14. Image processing for analyzing unwinding configuration without edge... 80

Fig. 5.15. Image processing for analyzing unwinding configuration with edge... 82

Fig. 5.16. Image processing by using pixel information 82

Fig. 5.17. Captured image by using high speed camera and post-processing image... 83

Fig. 5.18. Unwinding behaviors 86

Fig. 5.19. Unwinding behaviors 86

Fig. 5.20. Unwinding behaviors 87

Fig. 5.21. Unwinding behaviors 87

Fig. 5.22. Unwinding behaviors 88

Fig. 5.23. Unwinding behaviors 88

Fig. 5.24. Unwinding behaviors 89

Fig. 5.25. Unwinding behaviors 89

Fig. 5.26. Unwinding behaviors 90

Fig. 5.27. Unwinding behaviors 90

Fig. 5.28. Unwinding behaviors 91

Fig. 5.29. Unwinding behaviors 91

Fig. 5.30. Unwinding behaviors 92

Fig. 5.31. Unwinding behaviors 92

Fig. 5.32. Unwinding behaviors 93

Fig. 5.33. Unwinding behaviors 93

Fig. 5.34. Number of balloon according to unwinding... 94

Fig. 5.35. Bar graph of balloon radius according to... 94

Fig. 5.36. Mesh plot of balloon radius according to unwinding velocity and balloon height 95

Fig. 5.37. Unwinding velocity profile in acceleration condition 97

Fig. 5.38. Balloon configuration according to acceleration conditions 97

Fig. 5.39. Balloon configuration at 2.1sec and 9.88㎧ 98

Fig. 5.40. Unwinding velocity profile in adhesion condition 100

Fig. 5.41. Balloon configuration according to adhesion conditions 100

Fig. 5.42. Balloon configuration at 2.5sec and 9.95 ㎧ in adhesion condition 101

Fig. 5.43. A part of the adhesive area 102

Fig. 5.44. Balloon configuration in case of a part of adhesive area 103

Fig. 6.1. Captured image and comparison unwinding 106

Fig. 6.2. Captured image and comparison unwinding 106

Fig. 6.3. Captured image and comparison unwinding 107

Fig. 6.4. Captured image and comparison unwinding 107

Fig. 6.5. Unwinding velocity profile length, velocity and acceleration 109

Fig. 6.6. Unwinding motion for unwinding velocity change 110

Fig. 6.7. Tension profiles according to velocity change 111

Fig. 6.8. 3D unwinding configuration at maximum tension condition 112

Fig. 6.9. 2D unwinding configuration at maximum tension condition 112

Fig. 6.10. Tension profile according to balloon height at maximum tension condition 112

Fig. 6.11. Illustration of winding angle for over-end unwinding 114

Fig. 6.12. Experimental results by Godawat 116

Fig. 6.13. Unwinding motion of winding angle CASE01 117

Fig. 6.14. Tension profiles for winding angle CASE01 118

Fig. 6.15. Tension profiles for winding angle CASE02 118

Fig. 6.16. Tension profiles for winding angle CASE03 118

Fig. 6.17. Unwinding velocity profile for case study of balloon height 120

Fig. 6.18. Unwinding behaviors for HB CASE01 122

Fig. 6.19. Unwinding behaviors for HB CASE02 123

Fig. 6.20. Unwinding behaviors for HB CASE03 124

Fig. 6.21. Unwinding behaviors for HB CASE04 125

Fig. 6.22. Tension profiles for HB CASE01 126

Fig. 6.23. Tension profiles for HB CASE02 126

Fig. 6.24. Tension profiles for HB CASE03 127

Fig. 6.25. Tension profiles for HB CASE04 127

Fig. 6.26. Unwinding velocity profile for case study of tension 129

Fig. 6.27. Unwinding behaviors for tension CASE01 130

Fig. 6.28. Unwinding behaviors for tension CASE02 131

Fig. 6.29. Unwinding behaviors for tension CASE03 132

Fig. 6.30. Tension profiles for tension CASE01 133

Fig. 6.31. Tension profiles for tension CASE02 133

Fig. 6.32. Tension profiles for tension CASE03 133

초록보기

 Steady-state unwinding systems had been studied during the past 50 years. Unwinding dynamics during a transient state had also been studied for military and electric fiber manufacturing applications. In this study, time-varying velocity conditions are considered for a transient unwinding dynamic system, including a time-varying velocity and transient tension equation.

Extended Hamilton's principles and the kinetic and potential energy are first used to derive the governing equations. The material derivative is then considered for the time-varying unwringing velocity. The transient tension equation is derived by utilizing the governing equations and inextensible conditions of the applied cable. Numerical methods, such as the finite difference method and Newmark integration algorithm, are suggested for a dynamic analysis of the unwinding behaviors for a time-varying unwinding velocity.

Private test equipment for an unwinding analysis was developed including a test zig, tables, an rpm controller, a high-speed camera, and a blow pipe for preventing entanglements. An experimental study was also carried out on the time-varying unwinding motion using the equipment applied to the unwinding tests. In addition, to validate the derived equations, unwinding behaviors at several unwinding velocities were analyzed by comparing experimental results and simulation results. In particular, tests on the effects of the adhesive conditions were carried out based on experimental research. In addition, the effects of the unwinding velocity, pitch angle, and tension were analyzed using a numerical simulation. Through this research, transient behaviors such as single to double, and multiple balloons were studied using the transient tension equation. The effects of several boundary conditions such as the winding angle, balloon height and tension were also examined.

In conclusion, transient-state unwinding dynamic equations were established, including time-varying unwinding velocity and transient-tension equations, which can be applied to the textile industry and military field.

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