臺灣博碩士論文加值系統

本文主要探討含人字形溝槽微型空氣軸承於極低間隙潤滑條件下的穩態、動態性能與穩定特性。對極低間隙下的氣態潤滑行為而言，稀薄氣體效應與表面調節係數的影響不容忽視，傳統潤滑方程式已然無法適用。透過壓力流率與剪切流率修正因子(Qp、Qc)，傳統的潤滑方程式將可進一步修正為含稀薄氣體效應潤滑方程式(The modified molecular gas lubriccation equation，MMGL equation)，解決極低間隙下的氣態潤滑問題。本研究內容共包含三個部份。

第一部分透過微擾線性化方法，將可推導MMGL方程式之零階與一階方程式，求解含人字形溝槽微型空氣軸承於極低間隙潤滑條件下之穩態、動態性能，探討不同人字形溝槽幾何設計、軸承運轉參數與稀薄氣體效應對軸承運轉特性帶來的影響。

第二部份經由軸承穩定性理論與軸承動態係數，將能求解臨界穩定情形下之臨界轉速與關鍵質量，進而定義軸承穩定性邊界，並針對不同的人字形溝槽幾何設計、軸承運轉參數與稀薄氣體效應進行分析，討論其對含人字形溝槽微型空氣軸承穩定性之影響。



第三部份則說明如何藉由軟體物件化概念，輔以區間分散法、循環誤差逼近法，與黃金分割法，完成軸承穩定性分析流程，增進軸承穩定性分析工作之運算效率。

In this thesis, the load capacity, dynamic characteristics (stiffness coefficients and damping coefficients), and the stability performance of a micro-gas bearings with herringbone-grooved under ultra-thin film lubrication are analyzed. In the analysis of ultra-thin gas film lubrication problems, effects of gas rarefaction and accommodation coefficients can not be ignored. Traditional lubricated equation could be revised by incorporating the Couette flow rate (Qc) and the Poiseuille flow rate (Qp), to change to the modified molecular gas lubrication (MMGL) equation. Therefore it could be used to solve the problems of narrow clearance and ultra-thin gas film. This thesis includes three parts.
In the first part, we could obtain the zeroth order and the first order MMGL equation through the linear MMGL equation that is linearized by perturbation method. Therefore, the static performance and dynamic characteristics on the micro-gas lubricated bearing with herringbone grooves under different geometry and gas rarefaction conditions can be analyzed and discussed.
In the second part, by the theory of stability, the instability threshold speed and the critical mass of the journal bearings can be calculated through dynamic coefficients to define the stability characteristics. Therefore, the stability performance on the micro-gas lubricated bearing with herringbone grooves under different geometry and gas rarefaction conditions can be analyzed and discussed.
Finally, the stability analysis procedure by the object oriented conceptions is proposed. In the analysis procedure, algorithms include the range-average, the cycle-error-approach and the golden section are applied. And the computational efficiency can be improved.

中文摘要 --------------------------------------------------------------------- i
英文摘要 --------------------------------------------------------------------- iii
誌謝 --------------------------------------------------------------------- v
目錄 --------------------------------------------------------------------- vi
表目錄 --------------------------------------------------------------------- ix
圖目錄 --------------------------------------------------------------------- x
符號說明 --------------------------------------------------------------------- xii
第一章 緒論--------------------------------------------------------------- 1
1.1 軸承種類--------------------------------------------------------- 1
1.2 高轉速∕微型化趨勢------------------------------------------ 2
1.3 軸承設計∕性能優化------------------------------------------ 6
1.3.1 靜壓軸承--------------------------------------------------------- 6
1.3.2 動壓軸承--------------------------------------------------------- 7
1.3.3 混壓軸承--------------------------------------------------------- 10
1.4 軸承性能∕穩定性分析--------------------------------------- 10
1.4.1 液態潤滑特性--------------------------------------------------- 10
1.4.2 氣態潤滑特性--------------------------------------------------- 11
1.5 基礎科學∕數值方法------------------------------------------ 12
1.5.1 液態軸承的限制------------------------------------------------ 13
1.5.2 氣態軸承的挑戰------------------------------------------------ 13
1.5.3 軸承性能數值分析--------------------------------------------- 14
1.6 研究動機------------------------------------------------------ 16
1.7 研究目的--------------------------------------------------------- 16
1.8 本文架構--------------------------------------------------------- 17
第二章 統御方程式------------------------------------------------------ 19
2.1 可壓縮雷諾方程式--------------------------------------------- 19
2.1.1 基本假設--------------------------------------------------------- 19
2.1.2 微分連續性方程式--------------------------------------------- 20
2.1.3 流體動量方程式------------------------------------------------ 21
2.1.4 那維爾─史托克方程式--------------------------------------- 21
2.2 稀薄氣體效應--------------------------------------------------- 22
2.2.1 滑移邊界條件--------------------------------------------------- 24
2.2.2 表面調節係數--------------------------------------------------- 29
2.3 修正型氣體分子潤滑方程式--------------------------------- 30
第三章 軸承運轉特性--------------------------------------------------- 32
3.1 軸承潤滑模式--------------------------------------------------- 32
3.1.1 基本膜厚方程式------------------------------------------------ 32
3.1.2 含人字形溝槽膜厚方程式------------------------------------ 33
3.2 微擾法------------------------------------------------------------ 35
3.2.1 統御方程式線性化--------------------------------------------- 36
3.2.2 穩態與動態方程式--------------------------------------------- 37
3.2.3 時頻轉換--------------------------------------------------------- 38
3.3 軸承氣膜模式化------------------------------------------------ 43
3.4 軸承穩定性理論------------------------------------------------ 45
3.4.1 臨界穩定門檻--------------------------------------------------- 45
3.4.2 穩定性邊界法則------------------------------------------------ 47
第四章 軸承穩定性分析流程------------------------------------------ 49
4.1 物件導向程式設計概念--------------------------------------- 49
4.2 有限元素方法物件化------------------------------------------ 50
4.2.1 軸承幾何與參數定義------------------------------------------ 51
4.3 最佳演算法則--------------------------------------------------- 52
4.3.1 區間分散求解法------------------------------------------------ 53
4.3.2 循環誤差逼近法------------------------------------------------ 53
4.3.3 黃金分割法------------------------------------------------------ 54
4.4 穩定性分析流程------------------------------------------------ 55
第五章 含人字形溝槽微型空氣軸承穩態與動態性能分析------ 57
5.1 統御方程式驗證------------------------------------------------ 59
5.2 人字形溝槽幾何特性分析------------------------------------ 59
5.2.1 人字形溝槽深度------------------------------------------------ 63
5.2.2 人字形溝槽寬度比--------------------------------------------- 63
5.3 軸承偏心效應--------------------------------------------------- 63
5.4 稀薄氣體效應--------------------------------------------------- 72
5.4.1 表面調節係數與軸承數--------------------------------------- 72
5.4.2 低軸承數之表面調節係數影響------------------------------ 76
5.4.3 高軸承數之表面調節係數影響------------------------------ 79
第六章 含人字形溝槽微型空氣軸承穩定性分析------------------ 83
6.1 穩定性理論驗證------------------------------------------------ 83
6.2 人字形溝槽幾何特性分析------------------------------------ 86
6.2.1 溝槽化設計與軸承穩定性------------------------------------ 86
6.2.2 溝槽深度與軸承穩定性--------------------------------------- 93
6.2.3 軸承表面溝槽數之影響--------------------------------------- 95
6.3 稀薄氣體效應--------------------------------------------------- 95
6.3.1 軸承間隙與反克努森數--------------------------------------- 96
6.3.2 表面調節係數--------------------------------------------------- 98
第七章 結論--------------------------------------------------------------- 103
參考文獻 --------------------------------------------------------------------- 106
作者簡介 --------------------------------------------------------------------- 111

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