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研究生:蔡德輝
研究生(外文):Te-Hui Tsai
論文名稱:空氣靜壓軸承主軸系統穩定性之氣腔體積效應
論文名稱(外文):The Volume Effect of Air Recess in Stability of Rotor-aerostatic Bearing System
指導教授:康淵康淵引用關係
指導教授(外文):Yuan Kang
口試日期:2011-01-25
學位類別:博士
校院名稱:中原大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:91
中文關鍵詞:穩定性門檻臨界慣性力氣體靜壓軸承臨界漩振比
外文關鍵詞:Stability thresholdWhirl ratioCritical inertial forceAerostatic bearing
DOI:10.6840/cycu201101014
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摘要
本研究探討由氣靜壓軸承所支撐的剛性主軸之靜態和動態特性及穩定性。其氣體通過雙排小孔或環面節流之軸承間隙且為絕熱過程。軸承間隙內的氣體薄膜遵循雷諾方程式,並耦合由主軸旋轉所形成的邊界效應及由軸頸振動所造成的擠壓效應。使用有限差分法求解雷諾方程式,然後用數值積分的方法求出氣體薄膜的靜態和動態特性。轉子軸承系統的運動方程式由微擾法及特徵解法得到臨界慣性力及臨界漩振比的穩定性門檻。增加氣腔的體積可以增加軸承承載能力及剛性,但所伴隨的問題是系統漩振不穩定的現象發生。最後,分析氣腔的體積比對軸承動態性能的影響,以作為氣體軸承設計之參考。
Abstract
This paper studies static and dynamic characteristics of a rigid spindle supported by aerostatic bearings. The air passes through the double-row hole entries, which consist of orifices restrictors, into the bearing clearance. The process is adiabatic. The air film in this bearing clearance is governed by Reynolds equation, coupling both wedge effect due to spindle rotation and squeezed effect due to journal oscillation. The -method is used to analyze Reynolds equation, solved by the finite difference method and numerical integration, and then yields static and dynamic characteristics of air film. The motion equation of the rotor-bearing system is obtained by perturbation method. The eigensolution method is used to determine the stability threshold including critical inertial force and critical whirl ratio. Various eccentricities, rotor speeds, and restriction parameters are taken into considerations. To increase volume ratio of air recess can get higher loading capacity and stiffness, but it will occur the instability of pneumatic hammer. The research gives the volume effect of air recess in stability of rotor-aerostatic bearing system.
目錄
摘要……………………………………………………………………………………I
Abstract……………………………………………………………………………….II
誌謝………………………………………………………………………………….III
目錄………………………………………………………………………………….IV
圖目錄………………………………………………………………………………VII
表目錄……………………………………………………………………………….IX
符號說明……………………………………………………………………………..X
第一章 緒論………………………………………………………………………….1
1.1 研究背景……………………………………………………………………1
1.2 文獻回顧……………………………………………………………………2
1.3 研究內容……………………………………………………………………7
第二章 理論推導…………………………………………………………………….8
2.1空氣靜壓軸承潤滑方程式的推導…………………………………………..8
2.2本研究所使用的氣體軸承及節流器之型式………………………………10
2.2.1氣體頸軸承型式…………………………………………………….10
2.2.2 節流器之型式………………………………………………………12
2.3流量平衡方程式……………………………………………………………12
2.3.1孔口節流器的流量平衡方程式……………………………………..12
2.3.2氣腔的流量平衡方程式……………………………………………..16
2.4微擾化分析…………………………………………………………………20
2.4.1雷諾方程式的微擾化………………………………………………..20
2.4.2孔口節流器的流量平衡方程式的微擾化…………………………..22
2.4.3氣腔流量平衡方程式的微擾化……………………………………..23
第三章 空氣靜壓軸承系統的性能分析…………………………………………..29
3.1靜態承載能力及靜態偏位角………………………………………………29
3.2剛度係數及阻尼係數………………………………………………………30
3.3轉子之運動方程式…………………………………………………………32
3.4穩定性分析…………………………………………………………………33
3.5漩振頻率……………………………………………………………………34
第四章 介紹數值方法……………………………………………………………...37
4.1求解方法……………………………………………………………………37
4.2雷諾方程式之離散化………………………………………………………40
4.3氣腔流量平衡方程式之離散化……………………………………………41
4.4 S.O.R. 方法………………………………………………………………..52
第五章 結果與討論………………………………………………………………...53
第六章 結論與未來展望…………………………………………………………...67
6.1 研究結論…………………………………………………………………..67
6.2 未來研究方向……………………………………………………………..67
參考文獻…………………………………………………………………………….69
個人資料…………………………………………………………………………….78
論文發表…………………………………………………………………………….79

圖目錄
圖2-1 平面軸頸與軸承之橫截面示意圖…………………………………………...9
圖2-2 氣體軸承示意圖(a)結構圖 (b)主軸中心擾動軌跡………………………..11
圖2-3 孔口節流器………………………………………………………………….12
圖2-4 從氣腔流出之流量 的積分路徑………………………………………….18
圖3-1 轉子-軸承系統圖……………………………………………………………33
圖4-1 數值計算區域……………………………………………………………….37
圖4-2 數值計算流程圖…………………………………………………………….39
圖5-1 六個供氣孔軸承型式的構造……………………………………………….53
圖5-2 空氣軸承沿周向表面通過孔口節流器在 及 時的壓力分布(左欄為 ,右欄為 )……………………………………………...55
圖5-3 軸承的承載能力( )與其相關的偏位角( )在 及 時隨節流參數( )變化之分布………………………………………………………….56
圖5-4 軸承的承載能力( )與其相關的偏位角( )在 及 時隨偏心率( )變化之分布……………………………………………………………..56
圖5-5軸承的剛度係數( )及阻尼係數( )隨漩振比( )變化之分布, , , 及 ……………………………………………………...58
圖5-6 軸承的(a)剛度係數( ) (b)阻尼係數( ) (c)臨界慣性力( )及漩振比的平方( )隨漩振比( )變化之分布, , , 及 ………60
圖5-7 軸承的臨界慣性力( )及漩振比( )在 及 時隨節流參數( )變化之分布………………………………………………………………….61
圖5-8 軸承的臨界慣性力( )及漩振比( )隨偏心率( )變化之分布(a) (b) (c) …………………………………………………………..61
圖5-9 節流參數( )與供壓比( )的相對關係…………………………………..63
圖5-10臨界慣性力( )在 , 及 時與速度參數( )的關係………………………………………………………………………….…64
圖5-11臨界慣性力( )在 , 及 時與供壓比( )的關係……….64
圖5-12無因次質量( )在 及 時與承載能力( )的關係……………..65
圖5-13無因次質量( )在 及 時與供壓比( )的關係…………….….66
附圖一 流體的動力黏度……………………………………...……………………74
附圖二 流體的運動黏度…………………………………………………………...75


表目錄
附表一 在標準海平面大氣壓下空氣的物理特性………………………………...76
附表二 標準大氣壓的性質………………………………………………………...76
附表三 在標準海平面大氣壓下普通液體的物理特性…………………………...77
附表四 在標準海平面大氣壓下普通氣體的物理特性…………………………...77
參考文獻
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