系統識別號 U0026-2108201315541500
論文名稱(中文) 含刻紋表面之液動潤滑問題均質化
論文名稱(英文) Homogenization of Hydrodynamic Lubrication Problems with Textured Surfaces
校院名稱 成功大學
系所名稱(中) 材料科學及工程學系碩博士班
系所名稱(英) Department of Materials Science and Engineering
學年度 101
學期 2
出版年 102
研究生(中文) 張子峻
研究生(英文) Tzu-Chun Chang
學號 n56001496
學位類別 碩士
語文別 中文
論文頁數 124頁
口試委員 指導教授-李旺龍
中文關鍵字 均質法  表面纹理  液動潤滑  曲線擬合 
英文關鍵字 homogenization  textured surface  hydrodynamic lubrication  curve fitting 
中文摘要 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。
英文摘要 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.
論文目次 目錄
摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VII
表目錄 XI
符號表 XIII
第 1 章 緒論 1
1-1 文獻回顧 1
1-2 研究動機與目的 4
1-3 本文架構 5
第 2 章 理論基礎 8
2-1 納維-斯托克斯方程式(Navier-Stokes equations) 8
2-1-1 連續方程式(continuity equation) 8
2-1-2 動量方程式(momentum equations) 10
2-1-3 納維-斯托克斯方程式(Navier-Stokes equations) 11
2-2 雷諾方程式(Reynolds equation ) 13
2-3 均質化雷諾方程式 (homogenized Reynolds equation) 15
2-4 旋轉公式 23
2-5 曲線擬合(curve fitting) 24
2-5-1 幾何參數 24
2-5-2 曲線擬合(curve fitting) 26
2-6 計算流程圖 33
第 3 章 表面圖樣 35
3-1 表面圖樣種類(pattern types) 35
3-1-1 正弦波 35
3-1-2 圓柱正位 36
3-1-3 圓柱錯位 37
3-1-4 橢圓 37
3-2 網格獨立測試(grid independent test) 38
3-2-1 局部尺度(local scale) 38
3-2-2 全域尺度(global scale) 39
3-3 驗證 40
第 4 章 結果與討論 59
4-1 均質法係數和壓力關係 59
4-2 表面圖樣高度與膜厚比值 61
4-3 表面圖樣疏密程度 62
4-4 表面圖樣長短軸比 64
4-5 滑塊軸承的長寬比 65
4-6 影響負載的其他因素 66
4-7 均質法適用範圍 67
第 5 章 結論 88
第 6 章 未來展望 93
參考文獻 1
附錄 A 與 關係式推導 6
附錄 B 圓柱正位公式 10
附錄 C 圓柱錯位公式 22
附錄 D 橢圓公式 31
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