轉移矩陣法廣泛地應用於一般轉子系統之動態特性分析，本研究旨在擴充轉移矩陣法的理論使之可應用於失衡、對心失準轉子系統之振動分析。本文將聯結器之平行失準區分成全域及局部平行失準，個別建立其模型，並將二者對系統所產生之效應分別討論之。理論之推導以轉子系統具單一失準所對應之轉移矩陣為開端，延伸至多個失準之複雜系統，並結合常見於系統中之組成元件，從而得到一可求解系統含有失衡、多重聯結器平行失準之振動響應的方法。
首先，以修正轉移矩陣法之觀念配合旋轉軸之連續系統運動方程式，推導出旋轉軸所對應的轉移矩陣。推導過程中，發現旋轉軸之邊界在兩正交方向產生剪力藕合之現象，此剪力藕合效應對系統之臨界轉速造成了一定程度的影響，尤其在邊界條件為自由-自由的情況下，系統之第一臨界轉速降低50%左右。
研究的結果呈現，聯結器之勁度影響了系統的臨界轉速，而失準向量之效應則相似於外部負載之激振作用，並且影響至整個被驅動之所有元件。當系統同時存在圓盤失衡與聯結器失準時，由頻率響應函數可觀察出，系統之振動響應在低轉速區間由失準效應所主宰，唯系統之轉速提升至某一程度時，因離心力的增加，使失衡圓盤之效應逐漸明顯而成主導之地位。另外，在轉子系統具多重失準之分析中，本文以兩失準互為同相及反相之情況比較系統動態特性之差異，結果顯示，全域平行失準中之反相失準將導致響應振幅的明顯增加，尤其在高轉速之情況下更為顯著，且振幅之增加與平行失準距離呈線性比例關係；而全域失準中之同相失準其所對應的響應振幅較反相為低，此乃因同相失準之兩失準彼此間之響應有相互消減的作用產生，方造成同相響應低於反相響應。至於局部失準之現象，其同相與反相之響應關係恰與全域失準之響應趨勢相反。
當系統存在多重聯結器平行失準時，因系統之失準向量個數亦隨之增加及全域失準或局部失準之前後順序等因素，將使對應之矩陣方程式更趨於複雜。文中為了明確的呈現全域失準及局部失準之差異性，乃以相同的失準向量及參數對二者作比較。由公式的推演及數值分析的結果得知，無論在失準之前後，全域平行失準所產生的響應振幅皆大於局部平行失準，主要原因是全域失準向量之累積效應。最後就系統存在失衡及兩種不同的失準型態在某些臨界轉速區間，探討其渦旋軌跡之變化。
本研究所推導之理論及經由數值分析所獲得之結果，皆能以合理的物理意義解釋，故本分析方法可提供工程人員有用的資訊外，亦可作為工程師在分析轉子系統動態特性中，有價值之選擇工具。

The transfer matrix method has been widely applied to vibration analysis of rotor systems. The purpose of this research is to extend the TMM to include both imbalance and coupler’s misalignment/offset for rotor dynamics. In this study, the effect of coupler misalignment/offset was categorized into global and local misalignment/offset will be modeled and discussed separately. The derivation of the theory begins with as simple as single offset and then extends it to multiple offsets and in conjunction with other elements to form a complete tool for rotors. Furthermore the TMM proposed by this research would be applied to unbalanced disk, and multiple coupler global or/and local offsets with various boundary conditions.
First of all, the governing equations of a rotating shaft and its corresponding transfer matrix were derived via the transfer matrix method (TMM) in a continuous fashion. Through the derivation, the boundary shears induced by a rotating shaft were first discovered to be coupled in two perpendicular directions. These coupling shears might reduce the first critical speed up to 50% in the most critical free-free case.
The studies indicated that shafts coupler altered the rotor’s critical speeds and the misalignment played as an external excitation resulting through the whole driven shaft. The combined effects of disk imbalance and shaft misalignment showed that the misalignment predominated the response in lower rotational speeds but the imbalance take over at higher speeds. As to multiple offset cases, two offsets in- and anti-phase in a typical rotor were illustrated. The results showed that for the global offset in anti-phase case, the offset caused significant increase in response amplitude at high rotation and the increase was linearly proportional to offset value. As to its in-phase case, the response’s increases were insignificant. That implied an opposite offset would cancel out major response of the previous offset. However, the result of coupler local offset appears to be in contrary result to that of coupler global offset.
When a system exists multiple offsets with global and/or local, the equations of motion become much more complicated. To clearly examine the difference between global and local offset in which the offset distance is assumed the same. It is as expected that the global offset has imposed more significant dynamic effects since all the offsets accumulated thereafter. At last, the whirling orbits before and after the global and local offset as rotation fell within a certain range were illustrated as well.
The derived theory and corresponding numerical results were illustrated and explained from physical viewpoints. Though the development, this approach reveals useful information for rotor analysis and is hence expected to provide an efficient technique for rotor dynamics.

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