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研究生:謝祥遇
研究生(外文):Hsiang-Yu Hsieh
論文名稱:滾珠自動平衡裝置應用於撓性軸轉子的制振
論文名稱(外文):Application of Automatic Ball-Type Balancers on a Flexible-Shaft Rotor System
指導教授:盧中仁
指導教授(外文):Chung-Jen Lu
口試委員:伍次寅蘇春
口試委員(外文):Tzu-yin WuChun-Hsi Su
口試日期:2015-07-24
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
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:2015
畢業學年度:103
語文別:中文
論文頁數:49
中文關鍵詞:撓性軸轉子自動平衡裝置平衡解
外文關鍵詞:flexible shaft rotorautomatic balancerequilibrium configurations
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  • 被引用被引用:0
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為了避免運轉時產生過大的振動,高速旋轉機械需要正確的動態平衡校正。當轉子的偏心量隨工作情況改變時,可因應不同的偏心量而調整的自動平衡裝置對抑制旋轉所造成的偏心振動極有助益。滾珠型自動平衡裝置已證實可有效的抑制二維、三維剛性轉子系統的偏心振動,但是對於應用在撓性軸轉子的研究則較不完備。隨著旋轉機械的轉速的提高,轉軸的撓性變形效應也愈重要,因此有必要完整探討滾珠自動平衡裝置對撓性軸轉子偏心振動抑制的功效及限制。本論文研究配置滾珠自動平衡裝置的撓性軸轉子系統的行為。為了便於模擬不同的轉子偏心量型態與自動平衡裝置安裝的位置,首先利用有限元素法建立轉子系統的離散模型,再由Lagrange方程式推導運動方程式。採用旋轉座標系做為參考座標以得到自治(autonomous)運動方程式,由此可以較容易的分析平衡解。由各個元件所對應的矩陣的組合,可以得到不同型態的系統的統御方程式。本文探討轉速、偏心量型態、轉軸撓性、自動平衡裝置位置及其它重要參數對系統穩態行為的影響。由此可以了解自動平衡裝置的制振效能及工作限制。

To avoid large vibrations, high speed rotating machines have to be balanced precisely. When the imbalance varies with the working conditions, it is desirable to have a balancer that can suppress rotational vibrations automatically. Ball-type automatic balancers have been applied to reduce imbalance vibrations of two- and three-dimensional rigid rotors. However, the study of the application of auto-balancers to the flexible shaft rotor system is not complete. With the increasing speed of rotating machinery, the flexible deflection of the shaft becomes more and more significant. Consequently, it is essential to conduct a comprehensive investigation on the efficiency and restrictions when apply auto-balancers to the flexible shaft rotor system. In this thesis, we carry out a dynamical analysis of the auto-balancer-flexible shaft rotor system. We study the dynamical behavior of the system under different kinds of imbalance. For the convenience of modeling arbitrary imbalance, we first construct a finite element model of the rotor and then employ Lagrange’s equations to derive the governing equations. A rotating coordinate system is used as the reference frame to have autonomous governing equations. In this case, the equilibrium solutions can be analyzed conveniently. The effects of important parameters, such as rotational speed, flexibility of the shaft, and locations of the auto-balancers on the steady state behavior of the system are investigated. On the basis of these results, we can understand the efficiency and restrictions of auto-balancers on the suppression of unbalance vibrations of flexible-shaft rotor systems.

致謝 ii
滾珠自動平衡裝置應用於撓性軸轉子的制振 iii
摘要 iii
Application of Automatic Ball-Type Balancers on a Flexible-Shaft Rotor System iv
Abstract iv
目錄 vi
圖目錄 viii
表目錄 ix
第 一 章 緒論 1
1-1 研究動機 1
1-2 參考文獻 2
1-3 論文架構 5
第 二 章 理論分析 6
2-1 理論模型 6
2-2 統御方程式 11
2-2-1撓性軸的統御方程式 11
2-2-2碟片的統御方程式 17
2-2-3滾珠的統御方程式 19
2-2-4偏心質量的統御方程式 21
2-3 平面完全制振條件 22
第 三 章 數值分析 24
3-1 模型驗證 24
3-1-1兩端固定梁的自然頻率 24
3-1-2Campbell diagram of the Stodola-Green rotor 25
3-2 兩端固定-自動平衡裝置與偏心質量位於中央 27
3-3 兩端彈性支承的轉子 32
3-3-1兩組自動平衡裝置與偏心質量分別安裝於轉子兩端 33
3-3-2兩組滾珠自動平衡裝置分別安裝於轉子兩端且偏心質量位於中央 36
3-3-3滾珠自動平衡裝置與偏心質量距離對其制振效果的影響 39
3-3-4轉子兩端及中央分皆安裝滾珠自動平衡裝置及偏心質量 41
第 四 章 結論 43
參考文獻 44



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