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研究生:魏瑞宏
研究生(外文):Rui-Hong Wei
論文名稱:旋轉軸系統之振動與控制-兩種數學模式之比較
論文名稱(外文):Studies of Vibration and Control of Rotating Shaft Systems
指導教授:張銘永
指導教授(外文):Min-Yung Chang
學位類別:碩士
校院名稱:國立中興大學
系所名稱:機械工程學系
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:2001
畢業學年度:89
語文別:中文
論文頁數:120
中文關鍵詞:旋轉軸振動控制模態方法
外文關鍵詞:rotating shaftvibrationcontrolmodal method
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  • 被引用被引用:4
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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。
上述的分析結果顯示,動座標與慣性座標等兩種軸系統模式,所模擬的結果也都很相近。因此,上述兩種模式應皆可供軸系統設計之應用與參考。

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.

中文摘要 ………………………………………………………… Ⅰ
英文摘要 ………………………………………………………… Ⅱ
章節目錄 ………………………………………………………… Ⅲ
圖目錄 …………………………………………………………… Ⅳ
表目錄 …………………………………………………………… ⅤⅡ
符號索引 ………………………………………………………… ⅩⅡ
第一章 緒論 …………………………………………………… 1
1.1 引介………………………………………………………… 1
1.2 研究動機、目的與內容…………………………………… 3
第二章 含加速效應之旋轉軸的理論基礎與推導…………… 5
2.1 引介 ……………………………………………………… 5
2.2 系統說明 ………………………………………………… 6
2.3 旋轉軸系統之加速度模型 ……………………………… 6
2.4 含加速效應之旋轉軸理論基礎與推導………………… 10
2.4.1 動座標系統下之運動方程…………………………… 11
2.4.1.1 軸之動能…………………………………………… 11
2.4.1.2 軸的應變能 ……………………………………… 13
2.4.1.3 轉盤動能 ………………………………………… 16
2.4.1.4 軸承作用力所做的功 …………………………… 17
2.4.1.5 軸系統之運動方程式 …………………………… 19
2.4.1.6 有限元素模式 …………………………………… 20
2.4.2 慣性座標系統下之運動方程 ……………………… 25
第三章 軸系統的暫態特性與控制分析方法介紹 …… 30
3.1 暫態特性分析的方法 ………………………………… 30
3.2 模態分析方法 ………………………………………… 33
3.3 狀態回授控制 ………………………………………… 36
第四章實例分析與討論 ………………………………… 43
4.1 馬達驅動剛性軸系統的旋轉運動模擬 ……………… 43
4.2 旋轉軸系統振動頻率、模態與暫態響應的比較 …… 60
4.2.1 不含轉盤之軸系統 ………………………………… 60
4.2.2 含單轉盤之軸系統 ………………………………… 66
4.3 旋轉軸系統的振動控制 ……………………………… 81
第五章 結論與未來展望 ………………………………… 103
5.1 結論 ………………………………………………… 103
5.2 未來展望 …………………………………………… 104
參考文獻 …………………………………………………… 105
作者簡介 …………………………………………………… 107

[1] Lalanne, M. and Ferrarris, G., Rotordynamics Prediction in Engineering, John Wiley And Sons, Chichester/New York/Brisbane/Toronto/Singapore (1990).
[2] Lee, C. W., Vibration Analysis of Rotor, Kluwer Academic Publishers, Dordrecht/Boston/London (1993).
[3] Ehrich, F. F., Handbook of Rotordynamics, McGraw-Hill, New York (1992).
[4] Khader, N., “ Stability Analysis for the Dynamic Design of Rotors,” Journal of Sound and Vibration, Vol. 207(3), pp.287 -299 (1997).
[5] Wettergren, H. L. and Olsson, K.-O., “ Dynamic Instability of a Rotating Asymmetric Shaft with Internal Viscous Damping Supported in Anisotropic Bearings,” Journal of Sound and Vibration, Vol. 195(1), pp.75-84 (1996).
[6] Shabaneh, N. H., “ Dynamic Analysis of Rotor-Shaft Systems with Viscoelastically Supported Bearings, “ Mechanism and Machine Theory, Vol. 35, pp.1313-1330 (2000).
[7] Chen, L.-W. and Peng, W.-K., “Dynamic Stability of Rotating Composite Shafts under Periodic Axial Compressive Loads,” Journal of Sound and Vibration, Vol. 212(2), pp.215-230 (1998).
[8] Jia, H. S., “On the Bending Coupled Natural Frequencies of a Spinning, Multispan Timoshenko Shaft Carrying Elastic Disks,” Journal of Sound and Vibration, Vol. 221(4), pp.623- 649 (1999).
[9] Ganesan, R., “Effects of Bearing and Shaft Asymmetries on the Instability of Rotors Operating at Near — Critical Speeds,” Mechanism and Machine Theory, Vol. 35, pp.737-752 (2000).
[10] Young, T. H. and Liou G. T., “ Coriolis Effect on the Vibration of a Cantilever Plate With Time-Varying Rotating Speed,” Journal of Vibration and Acoustics, Trans., ASME,Vol. 114, pp.232-241 (1992).
[11] Lee, H. P., Tan, T. H. and Leng, G. S. B.,“ Dynamic Stability of Spinning Timoshenko Shafts with a Time-Dependent Spin Rate,”Journal of Sound and Vibration, Vol. 199(3), pp.401-415 (1997).
[12] 詹正川,“ 承受持續外激勵旋轉軸振動之主動控制,” 碩士論 文,中興大學機械研究所 (1996).
[13] Reddy, J. N., An Introduction to the Finite Element Method, McGraw-Hill, New York (1984).
[14] Bathe, R. R. and Wilson, E. L., Numerical Methods in Finite Element Methods, Prentice-Hill (1976).
[15] Belytschko, T. and Hughes, T. J. R., Computational Methods for Tranient Analysis, Elsevier Science Publisher B. V., Amsterdam/New York/Oxford/Tokyo (1980).
[16] Tedesco, J. W., McDougal, W. G. and Ros, C. A., Structural Dynamics Theory and Applications, Addison Wesley Longman, California (1999).
[17] Lee, F. L. and Syrmos, V. L., Optimal Control, John Wiley And Sons, New York/Chichester/Brisbane/Toronto/Singapore (1995).
[1] Lalanne, M. and Ferrarris, G., Rotordynamics Prediction in Engineering, John Wiley And Sons, Chichester/New York/Brisbane/Toronto/Singapore (1990).
[2] Lee, C. W., Vibration Analysis of Rotor, Kluwer Academic Publishers, Dordrecht/Boston/London (1993).
[3] Ehrich, F. F., Handbook of Rotordynamics, McGraw-Hill, New York (1992).
[4] Khader, N., “ Stability Analysis for the Dynamic Design of Rotors,” Journal of Sound and Vibration, Vol. 207(3), pp.287 -299 (1997).
[5] Wettergren, H. L. and Olsson, K.-O., “ Dynamic Instability of a Rotating Asymmetric Shaft with Internal Viscous Damping Supported in Anisotropic Bearings,” Journal of Sound and Vibration, Vol. 195(1), pp.75-84 (1996).
[6] Shabaneh, N. H., “ Dynamic Analysis of Rotor-Shaft Systems with Viscoelastically Supported Bearings, “ Mechanism and Machine Theory, Vol. 35, pp.1313-1330 (2000).
[7] Chen, L.-W. and Peng, W.-K., “Dynamic Stability of Rotating Composite Shafts under Periodic Axial Compressive Loads,” Journal of Sound and Vibration, Vol. 212(2), pp.215-230 (1998).
[8] Jia, H. S., “On the Bending Coupled Natural Frequencies of a Spinning, Multispan Timoshenko Shaft Carrying Elastic Disks,” Journal of Sound and Vibration, Vol. 221(4), pp.623- 649 (1999).
[9] Ganesan, R., “Effects of Bearing and Shaft Asymmetries on the Instability of Rotors Operating at Near — Critical Speeds,” Mechanism and Machine Theory, Vol. 35, pp.737-752 (2000).
[10] Young, T. H. and Liou G. T., “ Coriolis Effect on the Vibration of a Cantilever Plate With Time-Varying Rotating Speed,” Journal of Vibration and Acoustics, Trans., ASME,Vol. 114, pp.232-241 (1992).
[11] Lee, H. P., Tan, T. H. and Leng, G. S. B.,“ Dynamic Stability of Spinning Timoshenko Shafts with a Time-Dependent Spin Rate,”Journal of Sound and Vibration, Vol. 199(3), pp.401-415 (1997).
[12] 詹正川,“ 承受持續外激勵旋轉軸振動之主動控制,” 碩士論 文,中興大學機械研究所 (1996).
[13] Reddy, J. N., An Introduction to the Finite Element Method, McGraw-Hill, New York (1984).
[14] Bathe, R. R. and Wilson, E. L., Numerical Methods in Finite Element Methods, Prentice-Hill (1976).
[15] Belytschko, T. and Hughes, T. J. R., Computational Methods for Tranient Analysis, Elsevier Science Publisher B. V., Amsterdam/New York/Oxford/Tokyo (1980).
[16] Tedesco, J. W., McDougal, W. G. and Ros, C. A., Structural Dynamics Theory and Applications, Addison Wesley Longman, California (1999).
[17] Lee, F. L. and Syrmos, V. L., Optimal Control, John Wiley And Sons, New York/Chichester/Brisbane/Toronto/Singapore (1995).

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