動態勁度法應用於非對稱轉子軸承系統之研究

The Applications of Dynamic Stiffness Method on the Analysis of Asymmetric Rotor-Bearing Systems

彭韋翰(Wei-Han Peng)

指導教授 ： 楊大中

元智大學/工程學院/機械工程學系/碩士(1999年)

摘要

本文是以動態勁度法(DSM)求解在等向性軸承支撐下的非對稱轉子軸承系統之臨界轉速。所謂的非對稱轉子軸承系統和一般常見的對稱轉子軸承系統，最大的差別在於轉軸橫斷面上有不同的勁度與慣性矩，此即為非對稱轉軸之特性。
用Rayleigh Beam的模型理論，把轉軸、圓盤和軸承的動態勁度矩陣分別推導出來後，再應用各連接點的幾何相適條件與力平衡條件，組合成非對稱轉子軸承系統的動態勁度矩陣。
求出非對稱轉子軸承系統之臨界轉速，並分析在各種條件下對系統次臨界轉速(subcritical speed)和兩個分岔的同步臨界轉速之影響。另外針對軸承阻尼效應所造成非對稱轉軸穩定性的影響，也將一併探討。

關鍵字

動態勁度法 ； 等向性軸承 ； 同步臨界轉速 ； 次臨界轉速

並列摘要

In this research, critical speed analysis of asymmetric rotor systems was performed by using the dynamic stiffness method. The asymmetric rotors are different from the common symmetric rotors in that the properties at the cross sections of the rotors are not axisymmtric.
The dynamic stiffness matrices of shaft elements are derived with Rayleigh beam modeling. The element matrices are assembled with the matrices of disks and bearings to form the system matrix, where the compatibility and equilibrium conditions have to be fulfilled at the joints of the elements.
Synchronous critical speeds and subcritical speeds of the asymmetric rotor-bearing systems are analyzed under the effects of various conditions. Damping effects on the stability of the asymmetric rotors are also investigated.

並列關鍵字

Dynamic Stiffness Method ； Isotropic Bearing ； Synchronous critical Speed ； Subcritical Speed

參考文獻

Ardayfio, D., and Frohrib, D. A., 1976, “Instabilities of an Asymmetric Rotor with Asymmetric Shaft Mounted on Symmetric Elastic Supports,” ASME Journal of Engineering for Industry, November, pp. 1161-1165.

Brosens, P. J., and Crandall, S. H., 1961, “Whirling of Unsymmetrical Rotor,” ASME Journal of Applied Mechanics, September, pp. 355-362.

Childs, D., 1993, “Turbomachinery Rotordynamics Phenomena, Modeling, and Analysis,” John Wiely & Sons, Inc.

Curiti, G., Raffa, F. A., and Vatta, F., 1991, “The Dynamic Stiffness Matrix Method in the Analysis of Rotating System,” STLE Tribology Transactions, Vol. 34, No. 1, pp. 81-85.

Geradin, M., and Chen, S. L., 1995, ”An Exact Model Reduction Technique for Beam Structures: Combination of Transfer and Dynamic Stiffness Matrices,” Journal of Sound and Vibration, Vol. 185(3), pp. 431-440.