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研究生: 林漢偉
Lin, Han-Wei
論文名稱: 胸膜表面之軟彈液動潤滑分析
Soft Elastohydrodynamic Lubrication Analysis of Pleural Surfaces
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: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 109
中文關鍵詞: 胸膜表面軟彈液動潤滑黏性剪切力橫向等向性摩擦係數分析
外文關鍵詞: pleural surfaces, soft EHL, viscous shear stress, transversely isotropic, coefficient of friction
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  • 於多數生物系統上彈液動潤滑機制能保護軟組織免於外部傷害或磨損,胸膜表面間的運動即為其中一種,胸膜表面間的運動受到呼吸運動或是外部環境影響而產生不同的潤滑機制,因此維持正常的胸膜表面運動備受關注。
    較少人針對胸膜的材料特性進行討論,為了更接近於生物軟組織的特性,本研究針對改變橫向等向性胸膜的各個材料特性及其他相關參數對潤滑結果的影響進行討論。藉由耦合雷諾方程式、線性彈性方程式和負載平衡方程式來進行求解,探討不同參數變化對軟彈液動潤滑結果的影響,同時加入流體黏性剪切力,計算胸膜表面間的摩擦係數。
    經模擬結果發現,對於生物軟組織或是楊氏係數較低的軟材料而言,黏性剪切力產生的影響非常顯著,不能將此效應忽略。相較於一般彈液動潤滑分析,軟彈液動潤滑分析會因材料產生大變形而使流體壓力分佈於出口區不會有壓力突起(pressure spike)的產生。對於摩擦係數而言,負載和速度對摩擦係數的相關性最高,黏度和軸向楊氏係數中等相關,而橫向楊氏係數、橫向蒲松比和軸向蒲松比則影響較小。透過本研究的分析結果,期望能做為日後呼吸學及胸腔方面相關症狀或疾病的重要參考依據。

    A soft elastohydrodynamic lubrication (EHL) model for a thin layer of fluid separating the transversely isotropic pleural surface from a rigid cylinder with an initial sinusoidal shape is presented. We consider the fluid viscous shear stress and discuss the fluid pressure, fluid thickness distribution, elastic deformation of pleura and coefficient of friction for various independent variables: Young’s modulus, Poisson’s ratio, viscosity, velocity and normal load. A finite element method (FEM) is utilized to solve the modified Reynolds equation, elasticity deformation equation and force balance equation simultaneously on a line contact soft EHL problem. The simulation results reveal that coefficient of friction is strongly dependent on normal load and velocity moderately dependent on the pleural viscosity and axial Young’s modulus, and weakly dependent on transverse Young’s modulus, transverse Poisson’s ratio and axial Poisson’s ratio. These characteristics are helpful to further investigate the biomechanical interactions between pleural surfaces with multilayer and viscoelastic properties.

    中文摘要 I 英文摘要 II 誌謝 IX 目錄 X 表目錄 XIII 圖目錄 XIV 符號總表 XVIII 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.2.1 彈液動模型 2 1.2.2 生物系統內彈液動潤滑問題 4 1.2.3 胸膜磨潤行為 5 1.2.4 胸膜組織的橫向等向性 7 1.2.5 胸膜液的特性 8 1.3 研究動機 9 1.4 本文架構 10 第二章 彈液動潤滑理論 17 2.1 Hertzian Contacts 17 2.2 液動潤滑理論 19 2.2.1 雷諾方程式 20 2.2.2 流體液膜厚度方程式 22 2.2.3 流體黏度與壓力之關係 23 2.2.4 流體密度與壓力之關係 24 2.2.5 Penalty method 24 2.3 彈性變形方程式 25 2.4 負載平衡方程式 32 2.5 摩擦力與摩擦係數 32 第三章 數值分析 39 3.1 有限元素法 39 3.1.1 Galerkin method 40 3.1.2 離散公式 41 3.1.3 Newton-Raphson method 42 3.2 模擬分析流程 44 第四章 結果與討論 47 4.1 網格獨立性測試 47 4.2 模擬方法驗證 49 4.3 Cavitation的影響 49 4.4 黏性剪切應力的影響 50 4.5 胸膜表面軟彈液動潤滑分析 51 4.5.1 橫向楊氏係數的影響 51 4.5.2 軸向楊氏係數的影響 53 4.5.3 橫向蒲松比的影響 55 4.5.4 軸向蒲松比的影響 56 4.5.5 滑動速度的影響 57 4.5.6 黏度的影響 58 4.6 摩擦係數分析 59 第五章 結論 95 第六章 未來展望 98 參考文獻 99 附錄A 負載平衡方程式推導 106 附錄B 胸膜軟組織之橫向等向性限制條件 107

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