本研究以碎形理論與粗糙度分析鋁合金Al5182在不同潤滑劑黏度、軋延速度以及裁減率條件下的軋延表面，欲透過此理論找出表面特徵與光反射性質之間的關係。本研究修正Majumdar-Tien方程式(M-T方程式)將各種軋延表面的碎形特徵參數進行軋延表面結構函數之建構，使此數學模型能描述真實軋延試件含粗糙度之表面形貌。再進一步以TracePro光線追跡軟體模擬各軋延條件下的碎形曲面經光反射後的照度(Illuminance)，得出光反射分布(Reflection distribution)曲線。將分布曲線與利用散射量測儀量測軋延試片的結果相互比較並驗證了此數學模型之可信度。研究中發現到相較於軋延速度與試件厚度裁減率，潤滑黏度更能夠有效改變金屬軋延表面形貌。使用黏度低的潤滑劑所產生的試件表面會在軋延方向產生較大的週期長度(Period length)，並發現在平行以及垂直軋延兩方向的週期長度(Lx與Ly)比值(Lx/Ly)越大，光反射光線分布越均勻。此外，使用黏度低的潤滑劑也會使表面粗糙度中的陡峭度(Kurtosis)降低，更從中得知陡峭度越低，光反射分布曲線中的最大值會越大。而觀察碎形參數得知軋延方向的週期長度(Lx)或兩方向週期長度比值(Lx/Ly)越大，光反射分布曲線最大值也會隨之提高，因此表面光亮程度較高。而同道次下，裁減率越大，反射分布曲線最大值也會增大；但軋延速度對此最大值來說較無單向性的影響。實驗結果發現，碎形雖可以模擬試件表面粗度和形貌，但尚無法模擬軋延表面上存在的缺陷，而且建構碎形面時的解析度尚不足以完美模擬真實表面，再加上實驗與TracePro軟體兩結果的差異，都是造成模擬與實驗之間誤差的原因。藉由本研究得知，使用M-T方程式與光線追跡分析照度，能夠有效模擬出光線集中程度的趨勢，藉此判定影響軋延表面光澤的主要因素。

In this study, the surfaces of aluminum 5182 alloy (Al5182) rolling specimens with fractal behavior in roughness were analyzed. There are three variables including the viscosity of lubricant, rolling speed and the reduction ratio in this study. The attempt to find the relationship between the fractal characteristics and reflection behavior of surface was made. The rolling surface structure function can be constructed by Majumdar-Tien (M-T) function and the reflection distribution of a surface is simulated with TracePro. Moreover, the reflection distribution of a real surface is measured by imaging sphere for scatter and appearance measurement (IS-SA). The results show that the viscosity of the lubricant is the most important factor for changing the morphology. With the lubricant of the lower viscosity, there is the longer period length in the rolling direction (Lx) and the lower kurtosis on rolling surfaces. Additionally, the bigger ratio of the period lengths in the parallel and perpendicular rolling directions (Lx/Ly) is, the less uniformity of surface is. Furthermore, it showed the trend that the maximum value of reflection distribution increases as the kurtosis decreases. The trend also shows that the bigger Lx or Lx/Ly is, the larger maximum value of reflection distribution is. There are some reasons for the difference in the results between simulations and experiments including the flaws on the surface, the resolution of fractal surfaces and different solutions between IS-SA and TracePro. However, it is still reliable on the results of simulation of the concentration of reflection with M-T function and finding the factors which affect the glossiness of the surfaces.

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