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22대 대한민국 국회 국회정보길라잡이 국회의원검색
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ABSTRACT

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Nomenclature 8

1. 서론 15

1.1. 연구 동기 15

1.2. 연구 동향 16

1.3. 연구 개요 18

2. 충돌 해석을 위한 유한요소모델 19

2.1. 골프 공의 설계 19

2.2. 반발계수 20

2.3. 골프 클럽의 설계 21

2.4. 접촉 조건 22

3. 충돌 해석 32

3.1. 이론적인 충돌 계산 32

3.2. 유한요소해석 36

4. 여러 가지 충돌 해석 58

4.1. 마찰이 없을 경우 충돌 해석 58

4.2. 공의 강성에 따른 충돌 해석 59

4.3. 클럽 초기 속도, 로프트 각도를 변화시켰을 때 충돌 해석 61

4.4. 클럽이 공에 비스듬히 맞았을 경우 충돌 해석 62

4.5. 클럽의 무게중심에서 일정거리 떨어졌을 때 충돌 해석 64

5. 결론 82

참고문헌 85

부록 88

A.1. 궤적 운동 방정식 88

A.2. 항력, 양력, 항모멘트계수 89

A.3. 정면 충돌에서 공의 궤적, 회전 량 변화 및 최적화 91

A.4. 여러 가지 충돌의 궤적 계산 91

감사의 글 102

LIST OF TABLES

Table 2.1. Material property of golf ball and club head 25

Table 2.2. Mooney-Rivlin constants 25

Table 2.3. Coefficient of friction between club head and ball at impact 25

Table 3.1. Inconsistent results on contact forces at impact between ball and club head 43

Table 4.1. Velocities and spin rates of ball with club open angle(γ) varied 66

Table 4.2. Velocities and spin rates of ball for off-center hit with eccentricity (h) 66

Table A.1. Reference parameters at impact 93

Table A.2. Ball flight and trajectory 93

Table A.3. Effect of club head speed (V) on the ball flight 94

Table A.4. Effect of loft angles (Ψ) on ball flight 94

LIST OF FIGURES

Figure 2.1. Golf ball model 26

Figure 2.2. Bouncing of golf ball 27

Figure 2.3. Coefficient of restitution vs. ball impact speed 28

Figure 2.4. Club head model and coordinates: (a) top and (b) side views 29

Figure 2.5. Dynamics of ball and club head after impact for the ball contact line (a) above, (b) through and (c) below the club head mass center 30

Figure 2.6. Contact method by FEM 31

Figure 3.1. Vector of club and ball at impact 44

Figure 3.2. The realistic velocity of the moving frame 44

Figure 3.3. Golf club head and ball models: (a) overview and (b) cut-view 45

Figure 3.4. Ball and head velocity at impact: (a) launch angle and (b) ball and head velocity 46

Figure 3.5. Normal and tangential forces at impact 47

Figure 3.6. (a) Normal and tangential forces and (b) tangential force compared to Moriyama data 48

Figure 3.7. Normal and tangential forces during contact 49

Figure 3.8. Slip and roll of ball 54

Figure 3.9. Ball spin rate at impact: (a) method to compute spin rate and (b) ball spin rate compared to FEM result 55

Figure 3.10. Tangential force, tangential velocity and spin rate at impact 56

Figure 3.11. Effective radius of deformed ball at impact: (a) node plot at minimum radius and (b) radius vs. time 57

Figure 4.1. Normal and tangential forces: no friction 67

Figure 4.2. Tangential forces along the undeformed and deformed club faces: (a) deformed club faces and (b) tangential force vs. time 68

Figure 4.3. (a) Tangential forces and (b) spin rates for elastic club head with ball stiffness varied 69

Figure 4.4. (a) Tangential forces and (b) spin rates for rigid club head with ball stiffness varied 70

Figure 4.5. Ball velocity, launch angle, spin rate and compression factor for club initial velocity and loft angle varied 71

Figure 4.6. (a) Coordinates and (b) side spin rate for zero loft angle 72

Figure 4.7. Impact for open club face: (a) side and (b) top views 73

Figure 4.8. Normal (Fn) and tangential forces (Ft1, Ft2) for open club face with (a) 5 and (b) 15 degrees(이미지참조) 74

Figure 4.9. Tangential forces (Ft1, Ft2) with the club face open angle(γ) varied(이미지참조) 75

Figure 4.10. Ball spin rate components for the club face open angle γ=10° 76

Figure 4.11. Resultant spin axis with the club face open angle (γ) varied 77

Figure 4.12. (a) Coordinates and (b) tangential forces (Ft1, Ft2) for the off-center hit with eccentricity (h)(이미지참조) 78

Figure 4.13. Ball spin rate components for h= 10 mm 79

Figure 4.14. Gear effect 80

Figure 4.15. Spin rate axis vs. eccentricity (h) 81

Figure A.1. Coordinates for golf ball trajectory 95

Figure A.2. Dimples of golf ball 96

Figure A.3. Drag and lift coefficients of ball 96

Figure A.4. Ball trajectory 97

Figure A.5. Decrease of ball spin rate in flight 97

Figure A.6. Maximum ball distance (x) vs. upper blow angle (η) 98

Figure A.7. Ball trajectory vs. club head speed (V) 99

Figure A.8. Ball trajectory vs. loft angle (ψ) 99

Figure A.9. Ball trajectory vs. club open angle (γ) 100

Figure A.10. Ball trajectory vs. eccentricity (h) 101

초록보기

It is important to improve the initial launch conditions of golf ball at impact between golf club and ball to get a long flight distance. The flight distance is greatly influenced by the initial launch conditions such as ball speed, launch angle and back spin rate. It is also important to analyze the mechanism of ball spin to improve the initial conditions of golf ball. Back spin rate is created by the contact time and contact force.

Previous studies showed that the contact force is determined as the resultant force of the reaction forces normal and tangential to the club face at the contact point. The normal force causes the compression and restitution of ball, and the tangential force creates the spin. Especially, the tangential force is known to take either positive or negative values as the ball rolls and slides along the club face during impact. Moriyama (2004) conjectured that the positive and negative tangential forces create and reduce the back spin rate, respectively, without mentioning the mechanism of ball spin creation during impact. The mechanism of ball spin creation has not yet been discussed in detail in the literature.

In this paper, the influence of the contact force between golf club and ball is investigated to analyze the mechanism of impact. For this purpose, the contact force and the contact time at impact between golf club head and ball are computed using FEM and compared with previous results. In addition, we investigate the impact phenomenon between golf club head and ball by FEM and clarify the mechanism of ball spin creation accurately, particularly focusing on the effect of negative tangential force on ball spin rate.

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