本論文分析非接觸螺旋溝槽機械軸封中的轉子和靜子之間液膜潤滑。考慮非等向滑移及流變效應，推導出修正型雷諾方程式，透過有限元素法求解不同變因：流變指數、滑移長度與方向、膜厚、轉速、溝槽深度下的負載、洩漏量及摩擦扭矩等的軸封性能。並使用線性微擾法將修正型雷諾方程式線性化，從零階穩態方程式中求解動態方程式，再求解一階動態方程式，分別求解各個一階壓力，算出軸封穩態的動態係數。
結果表示，在軸封中有滑移現象，會使整體軸封負載下降、洩漏率上升、摩擦扭矩下降。在不一樣方向滑移時，會受到壓力流率及剪切流率修正因子影響。流動特性指數在低於0.9以下後，開始對軸封性能沒有太大的改變，高於1.05以上後軸封性能變化就會很大。滑移對於洩漏率來說影響最大，壓力需要上升來減少洩漏率。剛性係數的成長趨勢跟負載的成長趨勢一樣，阻尼係數的成長趨勢跟摩擦扭矩的成長趨勢一樣。

This paper analyzed the liquid film lubrication between the rotor and the stator in the non-contact spiral groove mechanical seal. Considering the anisotropic slip and rheological effects, the modified Reynolds equation is derived, and the finite element method is used to solve the seal performance of load, leakage and friction torque under different variables(groove depth; slip direction and length; film thickness; rotating speed; flow behaviour index). The linear perturbed method is used to linearize the modified Reynolds equation, and the dynamic equation is solved from the zero-order steady-state equation, and then the dynamic coefficient of the shaft seal steady state is calculated.
As a result, there is a slip phenomenon in the shaft seal, which causes the overall shaft seal load to decrease, the leak rate to increase, and the friction torque to decrease. When slipping in different directions, it is affected by the Poiseuille flow and Couette flow correction factor. After flow behaviour index is less than 0.9, the seal performance does not change much, and the seal performance changes greatly when it is higher than 1.05. Slip had the greatest impact on the leakage rate and the pressure needed to rise to reduce the leakage rate. The stiffness coefficient is the same as the load growth trend, and the damping coefficient is the same as the friction torque growth trend.

摘要 i
英文摘要 ii
致謝 iii
目錄 iv
圖目錄 vii
表目錄 xii
符號說明 xiii
第一章 緒論 1
1.2文獻回顧 2
1.2.1機械軸封發展 4
1.2.2非等向滑移邊界條件 6
1.2.3流變效應 7
1.2.4穩定性 7
1.3研究動機 8
1.4論文架構 8
第二章 研究理論 11
2.1雷諾方程式(Reynolds equation) 11
2.1.1基本假設 11
2.1.2質量守恆方程式(微分連續方程式) 12
2.1.3 動量守恆方程式 12
2.1.4 奈維爾-史托克方程式(Naiver-Stokes equation) 14
2.1.5雷諾方程式 15
2.2滑移邊界條件 17
2.3修正型雷諾方程式 19
2.3.1含流變效應與非等向滑移之雷諾方程式 20
2.4空蝕效應 26
2.5軸封性能 27
2.5.1負載 27
2.5.2洩漏率 28
2.5.3摩擦扭矩 29
2.6方程式線性化 31
2.6.1線性微擾法 31
2.6.2軸封動態係數 36
第三章 數值分析 39
3.1有限元素法簡介 39
3.2有限元素法離散化 39
3.3軸封分析幾何形狀和操作參數 41
第四章 結果與討論 45
4.1控制方程式驗證 45
4.2非等向滑移之軸封性能分析 48
4.3流變效應之軸封性能分析 60
4.4非等向滑移及流變效應之軸封性能分析 70
4.5動態軸封性能分析 80
第五章 結論與未來展望 95
5.1結論 95
5.2未來展望 96
參考文獻 97
附錄 102

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