以虛擬模態振形法建立轉子系統基座模型之研究

Modeling of the Foundations of Rotor-Bearing Systems by Using Pseudo Mode Shape Method

陳孟乾(Meng-Chien Chen)

指導教授 ： 楊大中

元智大學/工程學院/機械工程學系/碩士(2005年)

摘要

大型複雜結構以有限元素模擬分析，常遭遇元素過多，計算耗時且模擬不精確等問題。做模態測試則常礙於結構複雜，使得感測器不易設置，而且現場的維修時間有限，無法提供足夠的時間做完整的測試，故常僅做少部分的模態測試，以致無法求出完整的模態振形及對應的質量、勁度、阻尼矩陣。所以必須要有一個方法來彌補實務上模擬分析與模態測試的困難。
蒸汽渦輪發電機組之基座，係指下軸承座以下之結構，包括下軸承座，墊片，鋼結構，與混凝土基礎，其體積龐大，形狀與結構相當複雜。因為結構複雜，不易以有限元素模擬，所以大多數討論轉子系統都忽略基座的效應。當轉子、軸承、基座的勁度比是屬於同一個量級，此時基座效應將是一個影響轉子系統振動的重要因素。本文使用虛擬模態振形法，將軸承位置之少數實測頻率響應函數轉換成質量、阻尼、勁度矩陣，達到能夠涵蓋較大頻率範圍及涵蓋多數模態之基座效應。且與現有轉子動力學分析軟體結合，進行整體轉子-軸承-基座系統之動態分析。
本文提出之虛擬模態振形法，其優點為使用實測之頻率響應函數，能真實代表結構之振動特性。本方法將子結構接點位置之少數實測頻率響應函數轉換成質量、阻尼、勁度矩陣，能夠充分代表複雜子結構對母結構之影響，不需子結構其他邊界或內部點之振動資訊。克服以往要將頻率響應函數轉為質量、阻尼、勁度矩陣，須有完整的模態振形資訊才可能轉換的限制。且具有簡化矩陣自由度，涵蓋較大頻率範圍及涵蓋多數模態，容易與現有有限元素工程分析軟體結合等優點。
本文以二維的樑，簡易轉子系統，與MODIAROT轉子系統分別搭配不同的基座型式，驗證此方法的可行性與精準性。過往研究對於連續體的基座，因其結構複雜，在做模擬分析時，常將各基座支撐視為獨立支撐系統，不考慮交互影響之效應。本文對基座支撐交互影響之效應進行探討，其結果可供工業界做參考。

關鍵字

基座 ； 模態振形 ； 頻率響應函數 ； 轉子

並列摘要

Problems of huge amount of elements and time consuming in computation often occur in finite element modeling of large complicated structures, such as foundations of steam turbine-generators. Modal testing data obtained on foundations are limited due to test restrictions, such as limited test points and lack of test time during maintenance or overhauling, which results in incomplete mode shapes and unsatisfied mass, damping, and stiffness matrices corresponding to the foundation effects. A practical method is needed to overcome the difficulties in both simulation and testing.
The foundations of the steam turbine-generator include the lower parts of the pedestals, shims, steel frameworks and concrete foundation structures. The shapes and structures of the foundations are very complicated such that accurate modeling of the foundations by finite element method is not feasible. The effects of the foundation are usually ignored in the dynamic analyses. However, when the stiffness of the foundations is of the same order of magnitude of the stiffness of the rotor-bearing systems, the effects of the foundation can not be neglected in the vibration analysis of the complete systems. This research work used a pseudo mode shape method to establish the equivalent mass, damping, and stiffness matrices of the foundations from a few frequency response functions measured at the pedestal locations. The resultant matrices cover much wider frequency ranges and more modes of the foundation effects, and can be easily incorporated into the existing rotordynamic programs to perform the dynamic analyses of the complete rotor-bearing-foundation systems.
In this thesis, the pseudo mode shape method was proposed to establish the mass, damping, and stiffness matrices for a substructure by converting the limited frequency response functions measured at the joints of the substructure. These matrices are much smaller in size compared with the resultant matrices of finite element modeling, and can properly represent the influence of the substructure on the mother structure. This method does not need to know the vibration information on the other boundary points or interior points of the substructure, which conquer the restriction of limited test points and incomplete mode shapes.
Verification of this method is presented by using a 2-D beam structure, a simple rotor system and the MODIAROT rotor test rig as examples. In addition, The cross interaction of the foundation supports are not considered in most analyses due to the complication of the structures, in which the individual supports are regarded as independent supports. The cross interaction effects of the individual supports were also investigated in this work.

並列關鍵字

foundation ； mode shape ； frequency response function ； rotor

參考文獻

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