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研究生： 陳芝宇
Chen, Chih-Yu
論文名稱： 三維有限長度線接觸軟彈液動潤滑分析
Analysis of Three-Dimensional Soft Elastohydrodynamic Lubrication in Finite Line Contact
指導教授： 李旺龍
Li, Wang-Long
學位類別： 碩士
Master
系所名稱： 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年： 2019
畢業學年度： 107
語文別： 中文
論文頁數： 119
中文關鍵詞： 軟彈液動潤滑理論 、有限長度線接觸 、雷諾方程式 、邊界負載效應
外文關鍵詞： Elastohydrodynamic lubrication(EHL), finite length line contact, Reynolds equation, edge effect
相關次數： 點閱：113  下載：5 
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    • 在機械元件相互運作時，表面接觸區若為直接接觸，則會因為直接摩擦而造成損耗，若加入適當的潤滑液則能夠降低磨損之程度，因此磨潤學(tribology)理論在這之中扮演著非常重要的角色，其包括了元件運作時的摩擦(friction)、磨耗(wear)及潤滑(lubrication)等現象。
    根據潤滑液的特性，潤滑液在不同條件下會出現不同的潤滑機制，可以分為邊界潤滑(boundary lubrication)、混合潤滑(mixed lubrication)及全油膜潤滑(full-film lubrication)。全油膜潤滑又包含了液動潤滑(hydrodynamic lubrication)及彈液動潤滑(elastohydrodynamic lubrication)，近年來越來越多學者研究液動壓力相對更低的軟彈液動潤滑(soft-elastohydrodynamic lubrication)，軟彈液動潤滑常見於很多彈性體或者生物體的接觸，其潤滑問題即是兩接觸物體中，其中一個或者是兩者的材料是柔軟的，會使得彈性變形變得很顯著。彈液動潤滑機制主要是發生在非共形接觸(non-conformal)之機械元件中，以往較多研究了無限長線接觸彈液動潤滑，然而現實中並不存在，因此後續有人研究了有限長度線接觸彈液動潤滑，並針對其應力集中問題做了幾何外形的修正，以改善邊緣效應(edge effect)的現象。
    本研究對於有限長度線接觸進行軟彈液動潤滑分析，因考慮了有限長度對於圓柱滾軸邊緣的影響，因此採用三維模型進行模擬，並探討了未修飾圓柱外形的壓力、膜厚、變形量等分佈，並將其與考慮了圓角(round corner)後的圓柱滾軸做比較，觀察兩者應力集中之現象，接著討論了不同圓柱半徑對於壓力、膜厚及變形量分佈的影響，再討論了不同的圓柱滾動速度、不同施加負載及不同基材楊氏係數的影響。

    In this study, soft-EHL is analyzed with finite length line contact. Due to the consideration of the effect of finite length on the cylindrical roller edge, a three-dimensional model is used for simulation. The distribution of pressure, film thickness and deformation of unmodified cylindrical shape is also discussed, and compare it to the cylindrical roller after considering the round corner to observe the phenomenon of stress concentration between these two. Then the effects of different cylindrical radii on the distribution of pressure, film thickness and deformation are discussed.

    目錄 摘要 i Extended Abstract ii 誌謝 xvi 目錄 xvii 表目錄 xx 圖目錄 xxi 符號表 xxiv 第一章 緒論 1 1.1文獻回顧 2 1.1.1軟彈液動潤滑 2 1.1.2有限長度線接觸潤滑 5 1.2研究動機 8 1.3研究目的 8 1.4本文架構 8 第二章 研究理論 11 2.1接觸力學理論 11 2.2雷諾方程式 12 2.2.1基本假設 12 2.2.2質量守恆定律 13 2.2.3動量守恆定律 15 2.2.4奈維爾-史托克方程式 18 2.2.5雷諾方程式 18 2.3彈液動潤滑理論 24 2.3.1模型幾何形狀 25 2.3.2流體液膜厚度方程式 26 2.3.3 流體黏度與壓力之關係 27 2.3.4 流體密度與壓力之關係 28 2.3.5 空蝕現象 28 2.4負載平衡方程式 31 2.5有限變形本構方程式 31 2.6 Von Mises降伏準則 35 第三章 數值分析 36 3.1 有限元素分析法之離散與求解 36 3.1.1蓋勒肯法(Galerkin method) 36 3.1.2離散公式 37 3.1.3運算法則 38 3.1.4補償函數法 41 3.2模擬分析流程 42 3.3有限元素法物件化 43 第四章 結果與討論 44 4.1模型網格測試 44 4.2軟彈液動模型驗證 47 4.3有無圓角之圓柱外形軟彈液動潤滑分析 48 4.3.1 沒有考慮圓角之圓柱外形 48 4.3.2帶有圓角之圓柱外形 50 4.3.3比較不考慮圓角半徑及考慮圓角半徑之影響 51 4.4不同圓角半徑之影響 62 4.5不同圓柱滾動速度之影響 64 4.6不同負載之影響 72 4.7不同基材楊氏係數之影響 77 第五章 結論與展望 82 5.1結論 82 5.1.1 有無圓角之圓柱外形對於軟彈液動的潤滑分析 82 5.1.2 有圓角之圓柱外形改變不同圓角半徑之影響 82 5.1.3 有圓角之圓柱外形改變不同速度之影響 83 5.1.4 有圓角之圓柱外形改變不同負載之影響 83 5.1.5 有圓角之圓柱外形改變不同基材楊氏係數之影響 83 文獻 1 表目錄 表4-1 網格測試使用之參數表 45 表4-2 軟彈液動潤滑模型之網格分析 46 表4-3 軟彈液動潤滑模型驗證使用之參數表 47 表4-4 軟彈液動潤滑模擬使用之參數表 54 表4-5 不同速度之軟彈液動潤滑分析參數表 66 表4-6 不同負載之軟彈液動潤滑分析使用參數 73 表4-7 不同基材楊氏係數對於軟彈液動潤滑分析的影響 78   圖目錄 圖1-1 斯特里貝克曲線示意圖 7 圖1-2 本篇研究架構流程 10 圖2-1 微小立方體上 軸向的質量流入及流出的流率 23 圖2-2 作用在微小立方體 軸向上之表面力 23 圖2-3 線接觸模型立體示意圖 30 圖2-4 考量圓角之圓柱示意圖 30 圖2-5 軟彈液動潤滑模型之區域參數示意圖 34 圖3-1 牛頓法示意圖 41 圖3-2 數值方法求解軟彈液動潤滑流程之示意圖 42 圖3-3 軟體物件化之示意圖 43 圖4-1 模型上視示意圖 44 圖4-2 軟彈液動壓力及膜厚分佈驗證圖 48 圖4-3 不考慮圓角之壓力立體分佈圖 54 圖4-4 不考慮圓角之膜厚立體分佈圖 55 圖4-5 不考慮圓角之變形量立體分佈圖 55 圖4-6 不考慮圓角之von Mises應力分佈圖 56 圖4-7 考慮圓角之壓力立體分佈圖 56 圖4-8 考慮圓角之膜厚立體分佈圖 57 圖4-9 考慮圓角之變形量立體分佈圖 57 圖4-10 考慮圓角之von Mises應力分佈圖 58 圖4-11 不同y軸位置上之x軸示意圖 58 圖4-12 在y = 0時之x軸上，不考慮圓角及考慮圓角之壓力與膜厚分佈之比較 59 圖4-13 在y = -13.96 mm時之x軸上，不考慮圓角及考慮圓角之壓力與膜厚分佈之比較 59 圖4-14 在y = -14.48 mm時之x軸上，不考慮圓角及考慮圓角之壓力與膜厚分佈之比較 60 圖4-15 在y = 0 mm、y = -13.96 mm及y = -14.48 mm時之x軸上，不考慮圓角及考慮圓角之變形量分佈之比較 60 圖4-16 在x = 0 mm時之y軸上，不考慮圓角及考慮圓角的圓柱外形之壓力與膜厚分佈之比較 61 圖4-17 在x = 0 mm時之y軸上，不考慮圓角及考慮圓角之變形量分佈之比較 61 圖4-18 不同圓角半徑對壓力、膜厚及變形量分佈之影響 63 圖4-19 在y = 0 mm時之x軸上，圓柱速度 為1m/s, 1.5m/s, 2m/s時之壓力及膜厚分佈 66 圖4-20 在y = 0 mm時之x軸上，圓柱速度 為1m/s, 1.5m/s, 2m/s時之變形量分佈 67 圖4-21 在y = -14.30 mm時之x軸上，圓柱速度 為1m/s, 1.5m/s, 2m/s時之壓力及膜厚分佈 67 圖4-22 在y = -14.87 mm時之x軸上，圓柱速度 為1m/s, 1.5m/s, 2m/s時之變形量分佈 68 圖4-23 在x = 0 mm時之y軸方向，圓柱速度 為1m/s, 1.5m/s, 2m/s時之壓力及膜厚分佈 68 圖4-24 在x = 0 mm時之y軸方向，圓柱速度 為1m/s, 1.5m/s, 2m/s時之變形量分佈 69 圖4-25 不同圓柱滾動速度之壓力分佈圖(a) = 1m/s, (b) = 1.5m/s, (c) = 2m/s 69 圖4-26 不同圓柱滾動速度之膜厚分佈圖(a) = 1m/s, (b) = 1.5m/s, (c) = 2m/s 70 圖4-27 不同圓柱滾動速度之變形量分佈圖(a) = 1m/s, (b) = 1.5m/s, (c) = 2m/s 70 圖4-28 不同圓柱滾動速度之von Mises應力分佈圖(a) = 1m/s, (b) = 1.5m/s,(c) = 2m/s 71 圖4-29 在y = 0 mm時之x軸上，不同負載之壓力及膜厚分佈圖 74 圖4-30 在y = 0 mm時之x軸上，不同負載之變形量分佈圖 74 圖4-31 在y = -14.30 mm時之x軸上，不同負載之壓力及膜厚分佈圖 75 圖4-32 在y = -14.30 mm時之x軸上，不同負載之變形量分佈圖 75 圖4-33 在x = 0 mm時之y軸上，不同負載之壓力及膜厚分佈圖 76 圖4-34 在x = 0 mm時之y軸上，不同負載之變形量分佈圖 76 圖4-35 在y = 0 mm時之x軸上，不同基材楊氏係數之壓力及膜厚分佈圖 79 圖4-36 在y = 0 mm時之x軸上，不同基材楊氏係數之變形量分佈圖 79 圖4-37 在y = -13.10 mm時之x軸上，不同基材楊氏係數之壓力及膜厚分佈圖 80 圖4-38 在y = -13.10 mm時之x軸上，不同基材楊氏係數之變形量分佈圖 80 圖4-39 在y軸上，不同基材楊氏係數之壓力及膜厚分佈圖 81 圖4-40 在y軸上，不同基材楊氏係數之變形量分佈圖 81

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