傳遞矩陣法在非對稱轉子系統的側向及扭轉耦合振動之研究

Abstract

本論文主要之目的係在建構一傳遞矩陣法，藉以分析非對稱轉子-軸承系統的側向及扭轉耦合振動。分析中，使用尤拉角來描述撓性轉軸及剛性轉盤在空間中之方位，並推得其旋轉動能。為使模擬更接近實際情形，有別於傳統之堆化系統(lumped system)處理方式，本文藉由連續系統(continuous system)的觀念，以Timoshenko樑模擬非對稱撓性轉軸。所發展之分析方法，運用harmonic balance method之技巧，藉以分析，由同步渦旋及其他倍頻渦旋所構成之穩態響應。 依據數值分析結果，當偏心力、重量及n倍頻外施扭轉同時激振非對稱軸非等向性軸承之轉子系統時，系統之穩態響應，除了包含有同步、2倍頻、3倍頻及4倍頻渦旋分量外，亦同時具有(n+1)倍頻及(n-1)倍頻渦旋分量。 在電腦數值模擬分析中，以四種不同類型之轉子系統為例，作穩態振動分析，並就分析之結果與相關文獻作比較，以驗正傳遞矩陣分析方法之適用性及準確性，並瞭解不同類型之轉子系統的動態特性。

This thesis develops a modified transfer matrix method for analyzing the coupling lateral and torsional vibrations of the asymmetric rotor-bearing system with an external torque. Euler’s angles are used to describe the orientations of the shaft element and disk. Rather than the conventional “lumped system”, the asymmetric rotating shaft is modeled by the Timoshenko beam in a continuous-system concept. Moreover, the harmonic balance method is adopted in this approach to determine the steady-state responses comprising the synchronous and superharmonic whirls. According to our analysis, when the unbalance force, weight and the torque with n× frequency of the rotating speed excite the asymmetric anisotropic bearing-rotor system, the (n+1)× and (n-1)× whirls appear, along with synchronous, 2×, 3× and 4× whirls. Finally, several numerical examples are presented to demonstrate the applicability of this approach.