- 學位論文
迴轉機械動態行為之系統化分析程序研究開發
Development of Systematic Analysis Procedures for Investigating the Dynamic Behavior of Rotating Machinery
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摘要
現今使用之迴轉機械，不論是蒸氣渦輪機、離心壓縮機與工具母機等設備，設計上以高輸出能量或高轉速為其追求目標。為了避免劇烈的振動導致機械損壞，在設計階段通常使用有限元素模型來預測系統動態特性。若要預測結果能夠準確，唯有具備建立全系統模型(轉子-軸承-基座模型)功能的轉子動力分析軟體方可達成此一需求。然而，全系統分析若使用基座有限元素模型將花費大量的電腦計算時間，加上軟體在有效模擬基座特性上之模組尚未發展完善，這些因素往往局限了全系統分析的應用。 本論文旨在發展系統化轉子動力分析程序，並藉由建構專屬的子結構鑑別演算法模組來克服上述商用軟體的缺點。本文先以有限元素法理論建立動態分析程序中的基本模組與求解模組來探討轉子-軸承系統的動態特性。轉子振動行為藉由頻率響應函數曲線、模態振型、旋振頻率圖以及時變軌跡等方式來呈現。為了確保基本模組與求解模組的正確性，本文以兩個實際迴轉機械系統為探討例證。 第一個案例探討感應馬達轉子振動量的增加與軸承磨耗之間的關係。當後軸承與前軸承剛性比值為0.003時系統發生共振現象，此時外加平衡質量於平衡面上可以有效抑制轉子的振幅。研究結果發現臨界外加質量比值與質量偏心比值具有線性關係，因此臨界外加質量比值可經由此關係進行預測。第二個案例計算工具機主軸臨界轉速的分佈情形，討論不同的液靜壓軸承流體供給列數對系統第一與第二臨界轉速的變化趨勢。研究結果顯示當前軸承或後軸承採用單列供給設計時會直接增加第一與第二臨界轉速值之間的差異量，而採用較高供給列數設計之後軸承搭配二或三列供給列數之前軸承則可以局限此差異量在8%–12%之內。 本文亦發展新的子結構鑑別理論(修正型虛擬模態振型法)作為擴充模組的核心技術。此法僅需使用基座(子結構)在軸承座(接點位置)產生的頻率響應函數曲線來建立基座等效質量、阻尼與剛性矩陣，同時輔以轉子-軸承-實體基座有限元素模型與實際感應馬達定子來進行演算法的驗證。測試結果證實以等效矩陣取代原始基座可以實現高精度動態分析。因此，對於一個典型的轉子-軸承-基座而言，此鑑別技術可用於簡化複雜基座的模擬。未來經由本模組的導入，將有助於提升分析程序於設計精密迴轉機械與故障診斷方面的能力。
並列摘要
Rotating machinery in modern applications such as steam turbines, centrifugal compressors, and machine tools is designed with high transmission power or high speed of revolution. To avoid mechanical failures due to strong vibrations, it is common to predict dynamic characteristics in the design stage using the finite element (FE) model. To accurately predict results, it is often necessary to use rotordynamic analysis programs to establish whole system models, i.e., rotor-bearing-foundation models. However, using the FE model in whole system analysis is time consuming and requires substantial computer capacity. Moreover, commercial software cannot effectively simulate foundation properties. These factors limit the application of whole system analysis. The goal of this dissertation is to overcome these commercial software limitations by developing systematic rotordynamic analysis procedures as well as a special module: the algorithm module of substructure identification. The basic and solution modules of dynamic analysis procedures are established by using the FE method to explore the dynamic properties of rotor-bearing systems. Rotor vibration behavior can be represented by frequency response function (FRF) curves, mode shapes, Campbell diagrams, and time-varying orbits. To ensure the validity of the basic and solution modules, two realistic rotating machine systems are used as case studies. The first case explores how vibration associated with bearing wear arises in an induction motor rotor. When the ratio of the rear bearing stiffness to the front bearing stiffness is equal to 0.003, resonance occurs. The adding of balance masses at the balance planes effectively suppresses the vibration amplitude of the rotor. The study finds that the critical adding mass ratio can be predicted through its linear relationship with the mass eccentricity ratio. The second case estimates the distributions of critical speeds for a machine tool spindle system. Varying trends of the first and second critical speeds in the system with variations in the number of feeding rows in the hydrostatic bearings are discussed. The results show that the differences between the first and second critical speeds increase directly when one-row feeding is adopted in the front or rear bearings. A greater number of feeding rows in the rear bearing with two- or three-row feeding in the front bearing constrains the critical speed difference within 8%–12%. Meanwhile, a novel substructure identification method (the modified pseudo mode shape method, or modified PMSM) is developed as the primary technique of an extended module. The method uses only the produced FRF curves of bearing supports (joint positions) of the foundation (substructure) to establish the equivalent mass, damping, and stiffness matrices of the foundation. Both the FE model of the rotor-bearing-solid foundation system and the stator of a realistic induction motor are tested to verify the algorithm. The results confirm that the modified PMSM can achieve a highly accurate dynamic analysis by replacing the original foundation with the equivalent matrices. Therefore, the method can be used to simplify the simulation of the complex foundation structure in a typical rotor-bearing-foundation system. In short, the extended module introduced here will improve the capabilities of proposed analysis procedures for designing precision rotating machinery and for use in fault diagnosis applications.
參考文獻
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