應用有限單元法於轉子之振動分析及驗證

洪振義 ； 施光宇 ； 湯榮祥 ； 葉承修

《中華民國振動與噪音工程學會論文集》 1998 (1998/05) Pp. 285-291

https://doi.org/10.30028/CSSVANNUAL.199805.0285

摘要

本文旨在發展一彈性運算系統用以輔助建立轉動元素的數學模式。並探討在迴轉的保守系統下。轉子在等速或變速轉動下的動態特性。以Hamilton原理來推導，然後應用有限元素法處理系統的控制方程式，將之轉換成標準的特徵值問題。並接著寫成電腦程式以求得自然頻率。同時利用實驗的方法來量測轉動軸在旋轉時所呈現出來的動態反應，並且將實驗所得到的結果與有限單元法所分析出的結果進行比較，來比對二者之間的差異。

並列摘要

The purposes of the paper are to develop an elastic formulation system of rotary elements and to approach the curve of rotors' frequencies with respect to angular velocity in the gyroscopic conservative system.
In the study, the analysis of free vibration with gyroscope is divided into the following objects, first, to formulate the governing equations of the element using Hamilton's principle. second, to employ the finite element method with governing equations, we convert successfully into standard form of eigenvalue problems, third, to run a FORTRAN program written under the VAX computer to calculate complex form of eigenvalues.
The element used in the paper is a rotary model based on uniform 3D beam element which has two nodes with one reference point and has three translations and three rotational deformations each one nodes in the three dimension space system which undergoes a general rotational motion, so the proper composition can model driving shaft, rotating beam, crankshaft, and so on. For confirming it's feasibility and correctness, we have some cases respectively to be compared with the finite element program COSMOSM and papers, that have good results under both stationary and rotational conditions.
In addition, we can skillfully obtain the matrix form of governing equations for the nodes of the element through the help of the sym-bolic computation program, and convert into the program language form. Its advantages are to decrease the time spent on writing a program and to avoid the human errors. The elastic formulation system has haply finished by the symbolic computation program in conjunction with finite element method.