臺灣博碩士論文加值系統

本文提出混合法來分析齒輪轉子軸承系統之動態特性。混合法主要是結合
有限元素法(Finite Element Method)及廣義多項式展開法
(Generalized Polynimial Expansion Method)兩者的優點而成，此法先
用文獻中探討過的兩個範例來證明其可用性和收斂性，第一個是多級單
軸(multi-stepped single shaft)轉子系統，另一個則是雙軸轉子系統(
dual rotor system)；然後再將混合法應用於齒輪轉子軸承系統並分析之
。本文考慮齒輪轉子軸承系統的轉軸及軸承之勁度和阻尼、轉軸的剪力效
應及齒輪囓合之勁度、阻尼和壓力角等參數，並考慮齒輪囓合時橫向(
lateral)和扭轉(torsional)的偶合振動以及齒輪位置的影響。當系統的
運動方程式導出後，接著進行暫態響應的探討，其中包含迴轉速率、自然
頻率、振動模態和臨界速率的分析，再進而求出因不平衡質量及傳動誤差
所激發之穩態響應。齒輪囓合之勁度、阻尼和壓力角對系統的橫向和扭轉
的偶合振動有深遠的影響，而且系統在囓合頻率因傳動誤差所造成之穩態
振動具有大的振幅。最後，本文所提出的混合法經上述三種不同的系統分
析後證明：混合法比有限元素法有更好的效率但不失其正確性。

A new technique called Hybrid Method is proposed in the
analysis of the geared rotor-bearing system. This technique
combines the Finite Element Method and the Generalized
Polynomial Expansion Method to formulate the system equations
of motion. The compliance and shear deformation of the shaft
element, flexibility and damping of the bearings, stiffness and
damping and pressure angle of the gear mesh are considered. The
coupling between the torsional and lateral vibrations of the
gears and the effect of the location of the gear mesh are also
considered in the model. The whirl speed analyses and the
steady state responses due to mass unbalance and displacement
transmission error excitation are then calculated. Finally, the
accuracy and the efficiency of the proposed method are
demonstrated. The torsional-lateral coupled modes of the system
are greatly affected by the gear mesh. It is shown that the
stiffness, damping, and pressure angle of the gear mesh have
significant influence on these modes. The steady state
responses due to the transmission error, at tooth passing
frequency during gears meshing, are of high values. The
proposed Hybrid Method with application to geared rotor-bearing
system, multi-stepped single shaft rotor system, and dual rotor
system leads to better efficiency than the Finite Element
Method without losing the accuracy.