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標題: 旋轉軸系統之振動與控制-兩種數學模式之比較
Studies of Vibration and Control of Rotating Shaft Systems
作者: 魏瑞宏
Wei, Rui-Hong
關鍵字: rotating shaft;旋轉軸;vibration;control;modal method;振動;控制;模態方法
出版社: 機械工程學系
本論文主要比較兩種旋轉軸系統模式的動態特性與其在振動控制上之應用。所分析軸系統為含剛性轉盤之撓性軸,並以含阻尼與勁度模擬軸承支撐。本文中分別使用動座標與慣性座標系統,建立兩種軸系統的運動方程式。推導運動方程時,考慮旋轉軸動能、旋轉軸應變能、轉盤動能、軸承支撐作用力所作的功等,採用漢米爾頓定理(Hamilton’s principle)配合有限元素法,推導出含加速效應的旋轉軸系統動態運動方程式。
利用上述動座標與慣性座標兩種軸系統模式,本文針對旋轉軸系統的迴旋速度、振動模態圖、暫態響應,以及振動控制等做分析,並進行比較。分析軸系統的暫態響應時,採用直接積分法中的Newmark方法。而於振動控制應用方面,則採用模態分析的觀念,配合LQG (linear quadratic Gaussian)的控制方法設計控制器,模擬軸系統受控制時的運轉振動軌跡。

The objective of this thesis is to evaluate two different finite element models on studies of dynamic responses and of vibration control of rotating shaft systems. The rotating shaft systems being considered contain rigid disks, a flexible shaft, and bearing supports modeled as springs and viscous dampers. One of the models is derived referring to a moving coordinate system, while the other is formulated in the inertia coordinate system. In both models, the kinetic energy and the strain energy of the rotating shaft, the kinetic energy of the rigid disks, and the work done by support forces of the bearings are considered. By employing the Hamilton's principle together with the finite element method, the equations of motion of the rotating shaft systems including the angular acceleration effect are derived
With these two finite element models of rotating shaft systems, the whirl speeds, mode shapes, transient responses and vibration control of the shaft systems are analyzed and compared. In the studying of transient responses, the Newmark's method is used. As for the vibration control problem, the modal control concept with the controller designed in the framework of linear quadratic Gaussian control theory is implemented.
The results from examples obtained using both models are shown to be close or similar to each other. Therefore, for the problems studied here, both rotating shaft models may be employed.
Appears in Collections:機械工程學系所

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