# 臺灣博碩士論文加值系統

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 本文之主旨在於利用轉移矩陣法來求解由一系列的軸與圓盤所構成的轉子系統，在油膜軸承支撐下的旋動頻率(whirling frequency)。文中以二維的樑來介紹轉移矩陣法之基本原理，然後再用三維的樑理論來推導軸、圓盤及油膜軸承的轉移矩陣。最後再用轉移矩陣法來求得系統的特徵方程式，則與特徵方程式之極小值對應之特徵值即為轉子軸承系統的旋動頻率。本文對於旋動頻率與一般旋轉軸之臨界轉速的關係亦有扼要的探討。
 The purpose of this paper is determining the whirling frequency of rotor systems, mounted on oil-film bearings. The rotor is described by a series of shafts and disks. Transfer matrix methods are used to determine the characteristic determinant of system. In this paper we use the beam of two dimensions to introduce the basic theorem of the transfer matrix method. Then, we use the theory of the beam of three dimensions to derive the transfer matrices of shafts, disks and oil-filmed bearings. Finally, we use the transfer matrix method to determine the characteristic equations, and the minimum corresponding eigenvalues are the whirling frequencies of the rotor-bearing system. In this paper we have the summary discussing with the whirling frequency and critical speed.
 Abstract IV摘要 V誌謝 VI目錄 VII表目錄 IX圖目錄 X符號說明 XI第一章 緒論 1第二章 轉移矩陣法之基本原理 3第三章 油膜軸承支撐之轉子系統的旋動頻率 103.1 段軸(場)的轉移矩陣 113.2 圓盤(站)的轉移矩陣 133.3 油膜軸承的轉移矩陣 153.4 系統的旋動頻率 19第四章 旋動頻率與臨界速度 244.1 臨界速度之定義 244.2 臨界速度之求法 25第五章 數值分析結果與討論 27第六章 結論 36參考文獻 37附錄一、均勻段軸的轉移矩陣公式之推導 39自述 44
 1.H.D.NELSON and J. M. MCVAUGH, The dynamics of rotor bearing systems using finite elements, Transactions of the ASME, Journal of Engineering for Industry 98,pp.593-600,1976.2.G. W. FAN, H. D. NELSON and M. P. MIGNOLET, Optimal output feedback control of asymmetric systems using complex modes, Transactions of the ASME Journal of Engineering for Gas Turbines and Power 115, pp.307-330,1993.3.C. R. BURROWS and M. N. SAHINKAYA, Vibration control of multi-mode rotor-bearing systems ,Proceedings of Royal Society of London, Part A ,pp.386,77-94,1983.4.N. O. MYKLESTAD , A new method of calculating natural modes of uncoupled bending vibration of aeroplane wings and other type of beams ,Journal of Aerosol Science, Vol. 11, pp.153-162,1944.5.M. A. PROHL, A general method for calculating critical speeds of flexible rotors, Journal of Applied Mechanics 12, pp.142-148,1945.6.J. W. LUND, Stability and damped critical speeds of a flexible rotor in fluid-film bearings, Transactions of the ASME, Journal of Engineering for Industry, Vol. 96, pp.509-517,1974.7.R. FIROOZIAN and H. ZHU, A hybrid method for the vibration analysis of rotor-bearing systems, Proceedings of the Institution of Mechanical Engineers, part C 205,pp.131-137,1991.8.A. C. LEE, Y. KANG and S. L. LIU, A modified transfer matrix method for linear rotor-bearing systems, Transactions of the ASME, Journal of Applied Mechanics 58, pp.776-783, 1991.9.M. ALEYAASIN, M. EBRAHIMI and R. WHALLEY, Multivariable hybrid models for rotor-bearing systems , Journal of Sound and Vibration 233, pp.835-856,2000.10.H. OKAMURA, A. SHINNO, T. YAMANAKA, A. SUZUKI and K. SOGABE, Simple modeling and analysis for crankshaft three dimensional vibrations, Part 1: background and application to free vibrations, Transactions of the ASME, Journal of Vibration and Acoustics 117,pp.70-79,1995.11.顧德銘,”旋轉軸之振動與穩定性分析” 國立成功大學機械工程研究所博士論文,民國80年。12.M. Rajan, H. D. Nelson and W. J. Chen, Parameter sensitivity in the dynamics of rotor-bearing systems, Transactions of the ASME Journal of Vibration, Acoustics, Stress and Reliability in Design 108, pp.197-206,1986.13.L. Meirovitch, Analytical Methods in Vibrations, 1967, Macmillan Company, London.
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 1 旋轉軸之振動與穩定性分析 2 新型雙軸驅動自動平衡之研究與設計 3 連續模式之轉子系統的橫向振動分析 4 主動式旋轉自動平衡儀之分析與最佳化設計 5 轉子-軸承系統振動及靈敏度分析 6 齒輪轉子軸承系統之疲勞壽命預估

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