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系統識別號 U0026-1308201814453500
論文名稱(中文) 含電雙層效應之水潤滑-彈液動潤滑分析
論文名稱(英文) EHL Analysis of Water Lubrication Problems-Consideration of Electric Double Layer Effect
校院名稱 成功大學
系所名稱(中) 材料科學及工程學系
系所名稱(英) Department of Materials Science and Engineering
學年度 106
學期 2
出版年 107
研究生(中文) 陳俊良
研究生(英文) Chun-Liang Chen
學號 N56051182
學位類別 碩士
語文別 中文
論文頁數 136頁
口試委員 指導教授-李旺龍
口試委員-朱力民
口試委員-洪廷甫
中文關鍵字 電雙層效應  非等向邊界滑移條件  雷諾方程式  彈液動潤滑理論  水潤滑 
英文關鍵字 electric double layer  Reynolds equation  anisotropic boundary slip condition  elastohydrodynamic lubrication  water lubrication 
學科別分類
中文摘要 近年來環保意識的抬頭,針對廢棄潤滑油所造成的汙染逐漸受到重視,其中一個解決辦法是尋求機油的潔淨替代品,其中若能以水溶液作為媒介流體來代替機油,則可以大幅降低對環境的污染。
水溶液本身的黏度表現不佳,但水溶液的離子特性有助於形成電雙層,而電雙層的存在則會為水流體提供電黏度的特性。傳統的電雙層現象模型解是在半無限幾何條件下推導而來,但在兩物體接觸的過程中,其間距逐漸縮小,也逐漸無法滿足推導過程中對半無限幾何的假設。因此,本篇研究致力於建立不受限於邊界電位與半無限幾何條件之電雙層模型,並將電黏度的效應與邊界滑移條件考慮其中,對傳統雷諾方程式執行進一步的修正,推導出適合用於接觸學上之修正型雷諾方程式。
研究結果發現電雙層效應越強,其引發的電黏度也隨之增強。邊界滑移條件的存在雖然會降低該方向的壓力黏度項,但對於該方向之電黏度卻有提升的效果。而在接觸區域內,水溶液流體視黏度由電黏度項主導,因此水流體的黏度表現有大幅提升的現象。但由於水流體本身黏度低落,即使考慮到電黏度的貢獻後,液膜厚度之尺度仍舊被壓在奈米級,接觸體之間具有更高的機會發生干涉,造成破壞。水流體仍不適合作為工業用油的替代品。但電雙層之電黏度效果顯著,未來可搜尋本身流體黏度較高且具有電雙層現象之對象再進行更進一步的研究。
英文摘要 The classical solution for electric double layer known as Debye-Hückel solution and nonlinear Poisson-Boltzmann solution is derived with the assumption of semi-infinite space. When it comes to contacting mechanics, two objects is getting close to each other. In this process, the assumption of semi-infinite space is gradually invalid. The classical solution of EDL is malfunctioned. In this research, we developed a numerical solution for EDL with ion conservation rule instead of semi-infinite space assumption. On the other hand, we modified the Reynolds equation with consideration of electro-viscosity induced by EDL and anisotropic boundary slip condition. In the end, the property of water solution as lubricant is analyzed in elastohydrodynamic lubrication theory by using finite element method to solve modified Reynolds equation.
As a result, it surprisingly shows that the electro-viscosity in water solution is quite effective and occurrence of slip condition is help to improve the electro-viscosity. One more issue needed to understand is that we assumed electrical conductivity is constant in this study. The electrical conductivity increases with the decrease of the film thickness. The increased conductivity weakens the electro-viscosity. The apparent viscosity of water solution is overestimated without consideration of variation of conductivity.
論文目次 目錄
摘要 i
Extended Abstract ii
誌謝 x
目錄 xi
表目錄 xv
圖目錄 xv
符號表 xix

第一章 緒論 1
1.1文獻回顧 2
1.1.1電雙層效應 2
1.1.2潤滑理論的發展 3
1.1.3彈液動潤滑理論 5
1.1.4考慮電雙層效應之潤滑理論 7
1.2研究動機 10
1.3研究目的 10
1.4本文架構 11

第二章 研究理論 13
2.1電雙層模型 14
2.1.1統御方程式 14
2.1.2離子守恆定律 15
2.1.3數值方法求解 20
2.2雷諾方程式 21
2.2.1基本假設 21
2.2.2動量守恆方程式 21
2.2.3奈維爾-史托克方程式 22
2.2.4質量守恆方程式 23
2.2.5雷諾方程式 23
2.3邊界滑移條件 28
2.3.1等向性邊界滑移條件 28
2.3.2非等向性邊界滑移條件 28
2.4修正型雷諾方程式 30
2.4.1修正型雷諾方程式 30
2.4.2空蝕效應 33
2.5彈液動潤滑理論 35
2.5.1參數等效方程式 35
2.5.2液膜厚度方程式 36
2.5.3流體黏度與壓力關係式 37
2.5.4流體密度與壓力關係式 38
2.5.5彈性變形方程式 38
2.5.6負載平衡方程式 40
2.5.7 von Mises降伏準則 40
2.5.8摩擦力與摩擦係數 41

第三章 研究方法 45
3.1有限元素法的離散與求解 45
3.1.1 Galerkin法 45
3.1.2離散公式 46
3.1.3運算法則 47
3.1.4補償函數法 48
3.2有限元素法物件化 52
3.3三次樣條插值法 53

第四章 結果與討論 55
4.1電雙層現象 55
4.1.1模型網格測試 55
4.1.2電雙層模型驗證 56
4.1.3邊界電位對電雙層的影響 56
4.1.4液膜膜厚對電雙層的影響 58
4.1.5溶液濃度對電雙層的影響 60
4.1.6電雙層模型的適用性與應用 61
4.2特例與驗證 71
4.2.1視黏度之效應 71
4.2.2視黏度之簡化 74
4.2.3修正型雷諾方程式驗證 76
4.2.4非等向滑移彈液動潤滑理論模組驗證 76
4.3彈液動潤滑性能 80
4.3.1電雙層參數設定 80
4.3.2彈液動潤滑模型網格測試 81
4.3.3電雙層強弱之影響 82
4.3.3負載對彈液動之效應 82
4.3.4邊界滑移對彈液動潤滑之效應 84
4.3.5平均滑動速度對彈液動性能效應 86
4.3.6水潤滑的性能表現 86

第五章 結論與展望 108
5.1結論 108
5.1.1電雙層現象之數值模型 108
5.1.2彈液動潤滑之表現 109
5.2未來展望 110

參考文獻 112
附錄一:德拜-休克耳近似解 118
附錄二:非線性帕松-波茲曼解 121
附錄三:三次樣條插值法之誤差 128
附錄四:電導率的變化 129
附錄五:電雙層資料庫 131


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