- 學位論文
滾珠自動平衡裝置應用於撓性軸轉子的制振
Application of Automatic Ball-Type Balancers on a Flexible-Shaft Rotor System
摘要
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。
並列摘要
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.