
系統識別號 
U00261012201810130600 
論文名稱(中文) 
冷軋金屬材料表面形貌和光學性能理論分析和實驗檢驗 
論文名稱(英文) 
Theoretical Analyses and Experimental Inspections for Surface Topographs and Optical Properties of Metal Material after Cold Rolling 
校院名稱 
成功大學 
系所名稱(中) 
機械工程學系 
系所名稱(英) 
Department of Mechanical Engineering 
學年度 
107 
學期 
1 
出版年 
107 
研究生(中文) 
馬莫 
研究生(英文) 
Muhammad Arif Mahmood 
學號 
N16067038 
學位類別 
碩士 
語文別 
英文 
論文頁數 
187頁 
口試委員 
指導教授林仁輝 召集委員李榮顯 口試委員胡毓仁 口試委員李旺龍 口試委員洪政豪

中文關鍵字 
None

英文關鍵字 
3D WM fractal model
Deflection angle after rolling
Fractal dimensions
Periodic lengths of fractal surface
Optical properties in reflection
Fractal relation between roller and rolled surfaces
Hersey number
Phase transformations
Mechanical properties

學科別分類 

中文摘要 
None

英文摘要 
Cold rollings for the Al5182 aluminum alloy and CQ steel strips are carried out for the purpose of improving the reflected illuminance parameters and the reflection uniformity due to the uses of lubricants and the changes in operating conditions. A threedimensional (3D) fractal model is developed through the extension of the twodimensional (2D) WeierstrassMandelbrot (WM) model for the morphologies of rolled and roller surfaces. A numerical scheme is developed in this in this study for the morphologies of roller and rolled surfaces in order to determine the solutions of the periodic lengths, Lx and Ly, and fractal dimensions, Dx and Dy, in the x and y directions, which are the parameters existing in the 3D WM fractal model. This 3D fractal model in combination with the “TracePro” software is able to have the reflection light tracking simulations for the rolled surfaces with different deflection angles (θ) after rolling. The simulational reflection distribution fraction (RDF) for an incident angle of 20⁰ is obtained for Al 5182 to compare with that shown in the experimental one in order to prove the trustworthiness of this 3D fractal model. For Al 51825, an increase in θ of rolled specimen can reduce Dx and Dy slightly but increase Lx and Ly significantly; an increase in either Dx and Dy can elevate the maximum illuminance ((IL)max), but lower the minimum illuminance ((IL)min); the illuminance uniformity is reduced by increasing either Dx and Dy to be sufficiently large; Lx and Ly created in the specimens with a relatively smaller θ are shorter than those formed in the specimens with a relatively large θ; (IL)max is a value determined to be dependent on the θ value; however, (IL)min is always lowered by increasing either Lx or Ly, irrespective of the θ value; Increasing Dx, Dy, Lx and Ly can result in a reduction of the illuminance uniformity (Un); a specimen with a relatively larger θ can result in a higher uniformity; increasing the ((IL)max–(IL)min) value in the specimens with a small θ may result in a reduction of illuminance uniformity; increment in either of Lx, Ly or decline in either of Dx, Dy can increase the glossiness. For CQ steel, an increase in reduction ratio or fractal parameters, Dx, Dy Lx, and Ly of roller surface can result in higher Dx, Dy, Lx, and Ly values of rolled surfaces; decrease in Hersey number causes a minor decrease in Lx and Ly, but increases the Dx and Dy values of specimens; an increase in the Dx, Dy or a decrease in Lx, Ly can raise the (IL)max and lower the (IL)min of specimens; Un can be elevated by either decreasing Dx, Dy or increasing Lx, Ly of specimens; Un can be reduced by increasing the (IL)max or decreasing (IL)min; an increase in the reduction ratio of specimen causes a decrease in ferrite intensity and increase the austenite and cementite intensity which causes an increase in hardness (HRB) of rolled specimens. However, no significant correlation was found between reduction ratio and Young's modulus.

論文目次 
Abstract 1
Chapter 1  Introduction 3
1.1. Preface 3
1.2. Literature review 4
1.3. Research motive 8
1.4. Thesis writing methodology 10
Chapter 2  Basic Theories 12
2.1. Rolling 12
1. Lubricants 13
2. Reduction ratio 14
3. Rolling Speed 14
2.2. Surface Roughness 15
1. Form 15
2. Waviness 16
3. Roughness 16
4. Flaw 16
5. Lay of gringind mark 16
6. Section curve 17
2.2.1. Roughness measurement method 17
1. Sampling length 17
2. Evaluation length 18
3. Center line 18
2.2.2. Roughness parameters 18
1. Arithmetic avergae height (Ra) 18
2. Root mean square roughness (Rq) 19
3. Tenpoint height (Rz) 19
4. Skewness (Sk) 20
5. Kurtosis (Ku) 21
2.3. Fractal theory 21
2.3.1. Introduction 21
1. SelfSimilarity 22
2. SelfAffinity 22
3. Fractal dimension (D) 23
4. Autocorrelation 23
2.3.2. Two dimensional WeierstrassMadelbrot (WM) fractal model 23
2.3.3. Transfer of 2D to 3D WM model 26
2.3.4. Steps to calculate the fractal parameters of surface topographs 30
1. Step 1 31
2. Step 2 and 3 31
3. Step 4 32
4. Step 5 32
5. Step 6 33
6. Step 7 33
7. Step 8 33
2.4. Bspline curves and surfaces 34
2.5. Light properties 36
1. Luminous flux (Flux) 37
2. Luminous intensity 37
3. Illuminance 38
4. Gloss unit (GU) 38
5. Uniformity of illuminance 40
6. Bidirectional reflectance distribution function (BRDF) 40
2.6. Introduction to TracePro software 41
2.7. Ray trace setting 42
Chapter 3 – Experimental and Simulation Details 59
3.1. Main objective 59
3.2. Experimental apparatus for cold rolling 60
3.3. Sample preparation 61
1. First set of data (Al 5182) 62
2. Second set of data (Al 5182) 63
3. Third set of data (CQ steel) 63
3.4. Measuring instrument 64
3.4.1. 3D microfigure measuirng instrument 64
3.4.2. Imaging sphere for scatter and appearance measurement (ISSA) 65
3.4.3. AR 2000ex Rheometer 66
3.4.4. XRay diffractometer 67
3.4.5. Rockwell hardness tester 68
3.4.6. Micro/Nano tensile tester 69
3.5. Abaqus CAE software 69
3.6. Experimental methods and materials 70
Chapter 4 – Results and Discussions 87
4.1. Aluminum (Al 5182) (data set 01) 87
4.1.1. Surface simulations of specimens using 3D WM model 88
4.1.2. Comparison of skewness and kurtosis 89
4.1.3. Light tracking simulation results 89
4.1.4. Cold rolling simulations by Abaqus CAE software 96
4.2. Aluminum (Al 5182) (data set 02) 98
4.2.1. Surface simulations of specimens using 3D WM model 98
4.2.2. Light tracking simulations results 98
4.3. CQ steel (data set 03) 100
4.3.1. Surface simulations of specimens using 3D WM model 101
4.3.2. Light tracking simulations results 105
4.3.3. Metallographic analysis using XRD 111
4.3.4. Rockwell hardness testing 112
4.3.5. Micro/Nano tensile testing 113
Chapter 5 – Conclusion 185
5.1. Conclusion of Aluminum (Al 5182) data set 01 and 02 185
5.2. Conclusion of CQ steel data set 03 185
Chapter 6 – Future study 187

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