由於現今製程技術越趨成熟，精密度很高的規則性微結構(regular micro structures)並不難被製造出來。當直接分析含表面粗糙度(surface roughness)的流體動力學問題時，必需建立非常緻密的網格，此舉將會耗費相當多的時間和記憶體，甚至緻密到連網格都無法被建立起來。因此近年來一些平均化結構幾何的方法也就應運而生。
流量因子(flow factor)和均質法(homogenization)是兩個在磨潤領域最著名的方法。其中流量因子法因為可以處理隨機分布的表面粗糙度而得名。相較於流量因子法，均質法因為較合理的邊界條件假設，所以具備較為嚴謹地理論基礎，也因而可以得到較可靠的答案。為了使均質法更容易地被使用，本文運用曲線擬合的技術(curve fitting techniques)修改了原本的均質化雷諾方程式，使得求解的過程能夠顯著地簡化，當膜厚產生變化時，由於擬合公式已經將離散的值近似出連續的方程式，無須一再求解新的均質法係數。這也是首度有人將曲線擬合技術應用在均質法中。同時，關於負載和一些參數之間的討論，像是表面紋理的方向性(orientation)，長短軸比(aspect ratio)和密度(density)皆包含於本文中。

With the development of the micro-machining process technology, manufacturing regular micro structures on surface with a high precision is feasible. While analyzing hydrodynamic lubrication effects induced by surface roughness, it requires enormous calculation time and tremendous memory space, in order to build extremely dense meshes. In some worse situations, the meshes cannot even be built. To solve the problem, averaging techniques have been developed recently.
Flow factor and homogenization are the most famous averaging techniques in Tribology. Flow factor used to be a well-known method because of its characteristic to deal with random surface that cannot be dealt by homogenization. Compared to the flow factor, homogenization is based on much rigorous theories mainly deduced from reasonable boundary setting. Thus, homogenization is much more reliable than flow factor. In order to make homogenization easier to use, this paper modified the original homogenized Reynolds Equation by using curve fitting techniques and Mohr’s circle theory, which simplifies the solution process significantly. It should be noted that this is the first time curve fitting techniques have been used in homogenization. Also, some discussions about the relationship between load and several parameters of texture such as orientation, aspect ratio and density are included in this article.

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