臺灣博碩士論文加值系統

非等向性滑移邊界條件在微觀情況下是不可忽視的因素之一，它將會改變表面的潤滑行為。在考慮非剛體情況下，材料的彈性變形量亦是重要的考慮因素，它將會影響到膜厚的部分。
本文中提出了含非等向性滑移邊界條件與彈性變形量的潤滑理論。利用具有正交滑移長度 之Navier滑移邊界條件以及流量因子法 來修正傳統的Reynolds方程式。並且在膜厚方程式中考慮彈性變形量 。
透過有限元素法求解穩態頸軸承之液動問題，得到不同變因（負載、滑移長度）之下的軸承性能結果（偏心比、膜厚分佈、壓力分佈、彈性變形量、姿態角、摩擦力矩、摩擦係數、空蝕區、流量修正因子、無因次剪切力）。與傳統求解頸軸承液動問題不同之處在於，本文是給定負載與負載方向求偏心比與姿態角。另外，本文有進行座標軸轉換，以配合真實工作環境。
最終結果表明，考慮彈性變形量後，會使偏心比增加、膜厚增加、空蝕區縮小。考慮非等向性滑移邊界條件後，會使偏心比增加。 方向滑移造成摩擦力矩減少； 方向滑移造成摩擦力矩增加。 方向滑移會降低彈性變形量； 方向滑移會增加彈性變形量。

An anisotropic slip boundary condition which will change the lubrication behavior of the surface is one of the factors that cannot be ignored at the microscopic scale. Considering the rigid body, the elastic deformation of the material is also an important factor that affects the distribution of the film thickness.
In this study, the lubrication theory with anisotropic slip boundary conditions and elastic deformation is proposed. The traditional Reynolds equation is modified using Navier slip boundary conditions with orthogonal slip length and flow factor method. Additionally, elastic deformation is considered in the film thickness equation.
The finite element method (FEM) is used to solve the hydrodynamic problem of journal bearings in asteady state. We can get the bearing performances (eccentricity ratio, film thickness distribution, film pressure distribution, elastic deformation, attitude angle, friction torque, coefficient of friction, cavitation area, and flow rate correctors) under the different variables (load, and slip length). The difference from the traditional models of the journal bearing hydrodynamic problem is that this study is solving the eccentricity ratio and attitude angle for a given load and load direction. In addition, this study has done coordinate transformation to cooperate with the real working environment.
The final result shows that considering the elastic deformation, the eccentricity ratio will increase, the film thickness will increase, and the cavitation zone will reduce. Considering the anisotropic slip boundary condition, the eccentricity ratio will increase. Slip in the x direction causes a reduction in the friction torque; slip in the y direction causes an increase in the friction torque. Slip in the x direction will reduce the elastic deformation; slip in the y direction will increase the elastic deformation.

目錄
致謝----------------------------------------------------------------------------------------------i
中文摘要---------------------------------------------------------------------------------------ii
Extend Abstract-------------------------------------------------------------------------------iii
目錄---------------------------------------------------------------------------------------------v
表目綠-----------------------------------------------------------------------------------------vii
圖目錄------------------------------------------------------------------------------------------ix
符號表----------------------------------------------------------------------------------------xiii
第一章 緒論-----------------------------------------------------------------------------------1
1.1 前言-----------------------------------------------------------------------------------1
1.2 文獻回顧-----------------------------------------------------------------------------2
1.2.1 潤滑邊界條件的發展------------------------------------------------------2
1.2.2 等向性滑移邊界條件------------------------------------------------------3
1.2.3 非等向性滑移邊界條件---------------------------------------------------4
1.2.4 彈性變形量------------------------------------------------------------------5
1.3 研究動機與目的--------------------------------------------------------------------6
1.4 本文內容架構-----------------------------------------------------------------------7
第二章 研究理論-----------------------------------------------------------------------------9
2.1 Reynolds方程式-------------------------------------------------------------------- 9
2.1.1 微分連續方程式----------------------------------------------------------10
2.1.2 動量守恆方程式----------------------------------------------------------11
2.1.3 Navier-Stokes方程式-----------------------------------------------------13
2.1.4 Reynolds方程式-----------------------------------------------------------14
2.2 非等向性滑移邊界條件---------------------------------------------------------16
2.3 修正型Reynolds方程式--------------------------------------------------------19
2.4 空蝕效應---------------------------------------------------------------------------23
2.5 膜厚方程式------------------------------------------------------------------------24
2.6 負載方程式------------------------------------------------------------------------26
2.7 座標軸轉換------------------------------------------------------------------------28
2.8 摩擦力矩與摩擦係數------------------------------------------------------------29
2.9 線彈性方程式---------------------------------------------------------------------30
第三章 數值方法---------------------------------------------------------------------------32
3.1 有限元素法------------------------------------------------------------------------32
3.1.1 Galerkin法------------------------------------------------------------------33
3.1.2 離散公式-------------------------------------------------------------------34
3.1.3 Newton-Raphson法--------------------------------------------------------38
3.2 模型計算流程和網格測試------------------------------------------------------41
第四章 模擬結果與分析------------------------------------------------------------------43
4.1 襯套材料選用---------------------------------------------------------------------43
4.2 模型驗證---------------------------------------------------------------------------44
4.2.1 不含彈性變形量之模型驗證-------------------------------------------44
4.2.2 含彈性變形量之模型驗證----------------------------------------------46
4.3 無滑移條件下不同軸承長度之軸承性能分析------------------------------47
4.3.1 彈性變形量對軸承偏心比的影響-------------------------------------47
4.3.2 彈性變形量對軸承最小膜厚和姿態角的影響----------------------50
4.3.3 彈性變形量對軸承膜厚分佈和壓力分佈的影響-------------------52
4.3.4 彈性變形量對軸心位置、膜厚分佈、彈性變形量、空蝕區的影響
------------------------------------------------------------------------------58
4.3.5 彈性變形量對軸承摩擦力矩和摩擦係數的影響-------------------66
4.4 非等向性滑移邊界條件下之軸承性能分析---------------------------------71
4.4.1 非等向性滑移邊界條件對軸承偏心比的影響----------------------73
4.4.2 流量修正因子對軸承偏心比的影響----------------------------------79
4.4.3 非等向性滑移邊界條件對軸承摩擦力矩的影響-------------------87
4.4.4 非等向性滑移邊界條件對軸承彈性變形量的影響----------------92
第五章 結論---------------------------------------------------------------------------------94 
表目錄
表3-1 網格測試表--------------------------------------------------------------------------42
表4-1 Brewe [61]的操作條件表----------------------------------------------------------45
表4-2 Gong等人[55]的操作條件表------------------------------------------------------46
表4-3 本文所使用的操作條件表--------------------------------------------------------48
表4-4 本文所使用之Case表-------------------------------------------------------------50
表4-5 Case Ⅰ-1, 2, 3, 4的最大彈性變形量和姿態角表-----------------------------51
表4-6 Case Ⅱ-1, 2, 3, 4的最大彈性變形量和姿態角表-----------------------------51
表4-7 Case Ⅲ-1, 2, 3, 4的最大彈性變形量和姿態角表-----------------------------51
表4-8 Case Ⅰ-1, 2, 3, 4的摩擦力矩和摩擦係數表-----------------------------------67
表4-9 Case Ⅱ-1, 2, 3, 4的摩擦力矩和摩擦係數表-----------------------------------67
表4-10 Case Ⅲ-1, 2, 3, 4的摩擦力矩和摩擦係數表---------------------------------67表4-11 不同滑移長度之修正因子 表----------------------------------72
表4-12 細長比對偏心比的影響表-------------------------------------------------------79
表4-13 壓力流和剪切流流量因子對偏心比的影響表-------------------------------86
表4-14 細長比對摩擦力矩的影響表----------------------------------------------------91
 
圖目錄
圖1-1 研究架構流程圖----------------------------------------------------------------------8
圖2-1 連續方程式中之微控制容積之座標軸與各體積流率示意圖--------------12
圖2-2 動量方程式中微控制容積之座標軸示意圖-----------------------------------12
圖2-3 無滑移/滑移與滑移長度示意圖-------------------------------------------------18
圖2-4 非等向滑移示意圖-----------------------------------------------------------------18
圖2-5 空蝕現象示意圖--------------------------------------------------------------------24
圖2-6 軸承偏心時之潤滑型態示意圖--------------------------------------------------26
圖2-7 穩態負載說明圖--------------------------------------------------------------------28
圖2-8 座標軸轉換示意圖-----------------------------------------------------------------29
圖3-1 二維潤滑接觸區域 圖----------------------------------------------------------37
圖3-2 三維彈性變形區域 圖----------------------------------------------------------37
圖3-3 Newton-Raphson法示意圖--------------------------------------------------------40
圖3-4 模型計算流程圖--------------------------------------------------------------------41
圖4-1 不含彈性變形量之模型驗證圖--------------------------------------------------45
圖4-2 含彈性變形量之模型驗證圖-----------------------------------------------------47
圖4-3 短軸承之不同負載下偏心比的變化圖-----------------------------------------48
圖4-4 方軸承之不同負載下偏心比的變化圖-----------------------------------------49
圖4-5 長軸承之不同負載下偏心比的變化圖-----------------------------------------49
圖4-6 Case Ⅰ-1的膜厚與壓力分佈圖--------------------------------------------------52
圖4-7 Case Ⅰ-2的膜厚與壓力分佈圖--------------------------------------------------53
圖4-8 Case Ⅰ-3的膜厚與壓力分佈圖--------------------------------------------------53
圖4-9 Case Ⅰ-4的膜厚與壓力分佈圖--------------------------------------------------54
圖4-10 Case Ⅱ-1的膜厚與壓力分佈圖------------------------------------------------54
圖4-11 Case Ⅱ-2的膜厚與壓力分佈圖------------------------------------------------55
圖4-12 Case Ⅱ-3的膜厚與壓力分佈圖------------------------------------------------55
圖4-13 Case Ⅱ-4的膜厚與壓力分佈圖------------------------------------------------56
圖4-14 Case Ⅲ-1的膜厚與壓力分佈圖------------------------------------------------56
圖4-15 Case Ⅲ-2的膜厚與壓力分佈圖------------------------------------------------57
圖4-16 Case Ⅲ-3的膜厚與壓力分佈圖------------------------------------------------57
圖4-17 Case Ⅲ-4的膜厚與壓力分佈圖------------------------------------------------58
圖4-18 極座標示意圖----------------------------------------------------------------------59
圖4-19 Case Ⅰ-1的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------60
圖4-20 Case Ⅰ-2的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------61
圖4-21 Case Ⅰ-3的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------61
圖4-22 Case Ⅰ-4的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------62
圖4-23 Case Ⅱ-1的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------62
圖4-24 Case Ⅱ-2的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------63
圖4-25 Case Ⅱ-3的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------63
圖4-26 Case Ⅱ-4的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------64
圖4-27 Case Ⅲ-1的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------64
圖4-28 Case Ⅲ-2的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------65
圖4-29 Case Ⅲ-3的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------65
圖4-30 Case Ⅲ-4的軸心位置、膜厚分佈、彈性變形量、空蝕區圖-----------------66
圖4-31不含彈性變形量之Case Ⅰ-1, 2 , 3, 4的膜厚與壓力分佈圖--------------68
圖4-32含彈性變形量之Case Ⅰ-1, 2 , 3, 4的膜厚與壓力分佈圖-----------------68
圖4-33 不含彈性變形量之Case Ⅱ-1, 2 , 3, 4的膜厚與壓力分佈圖-------------69
圖4-34 含彈性變形量之Case Ⅱ-1, 2 , 3, 4的膜厚與壓力分佈圖----------------69
圖4-35 不含彈性變形量之Case Ⅲ-1, 2 , 3, 4的膜厚與壓力分佈圖-------------70
圖4-36 含彈性變形量之Case Ⅲ-1, 2 , 3, 4的膜厚與壓力分佈圖----------------70
圖4-37 不含彈性變形量短軸承Case A, B, E之不同滑移長度下偏心比圖-----74
圖4-38 不含彈性變形量短軸承Case C, D, F, G之不同滑移長度下偏心比圖--75
圖4-39 不含彈性變形量方軸承之不同滑移長度下偏心比圖----------------------75
圖4-40 不含彈性變形量長軸承之不同滑移長度下偏心比圖----------------------76
圖4-41 含彈性變形量短軸承Case A, B, E之不同滑移長度下偏心比圖--------76
圖4-42 含彈性變形量短軸承Case C, D, F, G之不同滑移長度下偏心比圖-----77
圖4-43 含彈性變形量方軸承之不同滑移長度下偏心比圖-------------------------77
圖4-44 含彈性變形量長軸承之不同滑移長度下偏心比圖-------------------------78
圖4-45 含彈性變形量短軸承之增加無因次滑移長度對 的影響圖-----------81
圖4-46 含彈性變形量短軸承之增加無因次滑移長度對 的影響圖-----------82
圖4-47 含彈性變形量短軸承之增加無因次滑移長度對 的影響圖-----------82
圖4-48 含彈性變形量方軸承之增加無因次滑移長度對 的影響圖-----------83
圖4-49 含彈性變形量方軸承之增加無因次滑移長度對 的影響圖-----------83
圖4-50 含彈性變形量方軸承之增加無因次滑移長度對 的影響圖-----------84
圖4-51 含彈性變形量長軸承之增加無因次滑移長度對 的影響圖-----------84
圖4-52 含彈性變形量長軸承之增加無因次滑移長度對 的影響圖-----------85
圖4-53 含彈性變形量長軸承之增加無因次滑移長度對 的影響圖-----------85
圖4-54 短軸承Case A, C, F之不同滑移長度下摩擦力矩圖------------------------88
圖4-55 短軸承Case B, D, E, G之不同滑移長度下摩擦力矩圖--------------------88
圖4-56 方軸承Case A, C, F之不同滑移長度下摩擦力矩圖------------------------89
圖4-57 方軸承Case B, D, E, G之不同滑移長度下摩擦力矩圖--------------------89
圖4-58 長軸承Case A, C, F之不同滑移長度下摩擦力矩圖------------------------90
圖4-59 長軸承Case B, D, E, G之不同滑移長度下摩擦力矩圖--------------------90
圖4-60 短軸承之不同滑移長度下彈性變形量的變化圖----------------------------92
圖4-61 方軸承之不同滑移長度下彈性變形量的變化圖----------------------------92
圖4-62 長軸承之不同滑移長度下彈性變形量的變化圖----------------------------93

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