臺灣博碩士論文加值系統

本研究旨在探討具長度失調、攻角失序、裂縫缺陷及拉筋連接葉片之軸-圓盤-葉片系統之軸扭振、圓盤彎振與葉片彎振三者間的耦合特性。首先求得各撓性元件之能量式，並應用假設模態法離散此能量式，再利用拉格朗日方程式，以導得系統之離散化運動方程式。
本文首先針對調諧(tuned)系統，其圓盤及轉軸具撓性對系統之固有頻率及耦合效應之影響，分成以下兩個研究：
(1)圓盤撓性對系統之影響：當軸-圓盤-葉片轉子系統之圓盤為剛性時，其葉片間耦合振動(BB)模態存在有(N-1)個重根。當圓盤為撓性時， BB模態在奇數與偶數根葉片之系統頻率分別存在(N-1)/2與(N-2)/2個重複值。系統之圓盤彎振-葉片彎振(DB)模態，此模態為剛性圓盤系統之BB模態所衍生之新模態。圓盤彎振-葉片彎振(SB)模態，會因圓盤的耦合，而成為軸扭振-圓盤彎振-葉片彎振(SDB)模態。
(2)當轉軸由剛性變成撓性時，則會發生四種現象，首先為BB模態保持BB模態。第二為節徑數與葉片數相等的1a (DB)模態，將轉變成SDB模態，且頻率會下降。第三為其他的DB模態仍保持DB模態，且頻率相等。最後為由扭轉振動之第一個頻率為系統頻率之主導的SDB模態將出現。
接著針對具長度失調、攻角失序及裂縫缺陷葉片特性對系統之固有頻率及耦合效應之影響，分成以下三個研究主題：
(1)葉片長度失調影響：當葉片長度失調，會產生兩種現象。首先，所有的DB模態會被SDB模態取代。故系統僅存在SDB模態與BB模態兩種耦合模態。圓盤模態會因葉片長度失調影響，而產生局部化現象(Localization)。在葉片長度失調因子的研究中發現，系統頻率隨著失調比值呈線性變化，但僅限於單一方向。
(2)葉片攻角角度失序影響：當葉片攻角角度失序，相同的會產生兩種現象。由數值結果發現，所有的DB模態會被SDB模態取代。故系統僅存在SDB模態與BB模態兩種耦合模態。圓盤模態會因葉片攻角角度失序影響，而產生局部化現象。在葉片攻角角度失序因子的研究中發現，系統頻率隨著失序比值呈現近似線性變化。
(3)葉片具裂縫缺陷影響：就葉片具裂縫缺陷情況下，探討系統之耦合振動特性，由論例中發現，所有的DB模態會被SDB模態取代。故系統僅存在SDB模態與BB模態兩種耦合模態。相同的，圓盤模態會受葉片裂縫影響，而產生局部化現象。數值結果也表現了葉片裂縫深度及位置的變化。
在上述三個主題的旋轉效應的研究中發現，系統的不穩定現象，僅存在於是由軸扭轉所主導的模態。換句話來說，調諧系統中由葉片主導所產生之不穩定，會因葉片具長度失調、攻角角度失序與裂縫缺陷，破壞系統模態的平衡，而使不穩定消失。
最後針對具拉筋連接葉片系統動態特性進行研究探討，由論例中發現以下現象：
(1)無拉筋失調時：SB模態不受拉筋影響，且頻率也不改變，不論是在勁度或位置的研究均是。原始的BB模態，在中等耦合勁度中，將分裂出較多系統頻率，因葉片的耦合作用，故受拉筋影響甚大。彈簧連接自由端時，系統固有頻率有最大值，由此可知當彈簧連接於葉片最末端時，與葉片間之耦合最為明顯。最後，在旋轉效應的研究中發現，原始的不穩定現象，並不被拉筋所影響，且拉筋並不增加額外的不穩定。
(2)當拉筋失調時：中等耦合勁度中，分裂出來的BB模態，會再次分裂而存在N-1個頻率。在旋轉效應的研究中發現，原始的不穩定現象，並不被拉筋所影響，故拉筋失調並不增加額外的不穩定。
由數值結果發現，不論葉片長度失調、葉片攻角角度失序、葉片具裂縫缺陷或具拉筋連接葉片均對系統耦合振動特性有顯著的效應，系統幾何參數亦有明顯的影響，本研究之結果，可提供工程人員有用的資訊，並可作為工程設計之參考。

The coupling vibrations among shaft-torsion, disk-transverse and blade-bending in a shaft-disk-blade unit are investigated in this dissertation. An energy principle in conjunction with the assumed modes method and the Lagrange equations are employed to yield the discrete equations of motion.
First, the study explored the influence on coupling vibration of a tuned rotor due to disk and shaft flexibility. Two topics as the follows are conducted and corresponding numerical examples are illustrated.
(1) For a rigid disk system, the coupling modes could be grouped into two categories, the shaft-blade (SB), and blade-blade (BB). Once the disk flexibility enters the system there are three types of coupling modes, shaft-disk-blade (SDB), disk-blade (DB), and BB. The SDB mode is evolved from the SB mode and is of lower frequency due to disk flexibility. The originally repeated BB modes bifurcate into the BB and the DB modes. The BB modes were of repeated frequencies of (N-1)/2 and (N-2)/2 multiplicity for odd and even number blades.
(2) A shaft-disk-blade system has been found existing two types of coupling vibrations, DB and BB modes when the shaft was assumed rigid. If the shaft’s torsional flexibility was taken into account, an additional type of coupling modes, SDB, appeared.
The present research focuses on mistuned blade onto the coupling characteristic. Three topics as the follows are conducted and corresponding numerical examples are illustrated.
(1) The effect of mistuned blade length: A mistuned blade was found to change not only the natural frequencies but also the types of coupling modes. First, the DB modes in a tuned system disappeared and instead they are replaced by SDB modes. Second, the disk experienced mode localization due to the mistuned blade. The results also showed that every mode’s frequency varied with the mistuned error linearly in one direction, either positive or negative, but not in both directions.
(2) The influence of mistuned blade’s stagger angle: When an angle-disordered blade existed, the blades periodicity was destroyed and it was found to change not only the natural frequencies but also the types of modes. Due to blade’s stagger angle disorder, the shaft torsion had to participate to balance such that DB modes vanished and replaced by SDB modes. The disk experienced mode localization due to stagger angle disorder. A disordered stagger angle was numerically found to alter the natural frequencies in an almost linear trend.
(3) The effect of cracked blade: A cracked blade was found to change not only the natural frequencies but also the types of coupling modes. First, the DB modes disappeared and were replaced by SDB modes. Second, in some modes the disk experienced mode localization due to the cracked blade. Numerical results showed that natural frequencies varied with the blade’s crack location and depth.
A mistuned, disorder and cracked blade shows instability exists only at the mode, in which the shaft’s torsion dominates. In words, all the blade-dominating modes show no instability due to a mistuned, disorder and cracked blade destroying the periodic property. From the viewpoint, a mistuned, disorder and cracked diminishes some instability that exists in a perfect rotor.
At last, this dissertation discussed the shaft-torsion and blade-bending coupling vibrations of a rotor system, in which the blades were grouped with lacing wires. Two topics as the follows are conducted and corresponding numerical examples are illustrated.
(1) The lacing wire without mistuned: Numerical results showed how the natural frequencies varied with the wire stiffness, connecting position, and the rotational speed. From the results, it was found that lacing wire did not affect the SB modes, but the BB modes were indeed affected by the lacing wire. At moderate range of wire stiffness, the repeated BB modes split into more distinct modes. The wires connecting near outer edge would strengthen the system structure and increasing the natural frequencies of BB modes. At last, the lacing wires are found not to cause any extra instability.
(2) The lacing wire with mistuned: At moderate range of wire stiffness, the repeated BB modes split into more distinct modes due to a mistuned lacing wire. The lacing wires are not found to cause any extra instability, so the mistuned could not cause extra instability
According to the numerical results, the variations of mistuned, disorder, or cracked blade are very significant to coupling characteristics. The system’s geometrical parameters reveal the similar effects as well. The results of this research provide the engineers with very useful information in understanding the vibration behavior of shaft-disk-blades systems.

論文摘要……………………………………………………………………I
ABSTRACT…………………………………………………………IV
誌謝………………………………………………………………………VII
目錄………………………………………………………………………VIII
符號索引…………………………………………………………………X
圖表索引…………………………………………………………………XIII
第一章 緒論…………………………………………………………1
1.1 文獻回顧……………………………………………………1
1.1.1 軸-圓盤-葉片系統……………………………………………1
1.1.2 轉子具裂縫系統………………………………………………6
1.1.3 轉子具拉筋(覆環)系統…………………………………………7
1.2 研究動機與目的………………………………………………9
1.3 本文簡介……………………………………………………10
第二章 軸-圓盤-葉片系統之振動分析………………………………12
2.1 轉軸之基本假設與能量式……………………………………12
2.2 旋轉圓盤系統之基本假設與能量式…………………………13
2.3 旋轉葉片系統之基本假設與能量式………………………14
2.4 系統能量式之離散化與運動方程式………………………15
2.4.1 系統能量式之離散化………………………………15
2.4.2 系統之運動方程式……………………………19
2.5 調諧系統之數值結果與討論…………………………………21
第三章 葉片失調或失序時之動態特性………………………………40
3.1 葉片長度失調………………………………………………40
3.1.1 運動方程式…………………………………………………40
3.1.2 數值結果與討論……………………………………………41
3.2 葉片攻角角度失序…………………………………………42
3.2.1 運動方程式…………………………………………………42
3.2.2 數值結果與討論……………………………………………43
第四章 葉片裂縫缺陷時之動態特性…………………………………57
4.1 基本假設……………………………………………………57
4.2 運動方程式…………………………………………………58
4.3 數值結果與討論…………………………………………58
第五章 具拉筋連接葉片之動態特性…………………………………69
5.1 無失調拉筋連接葉片系統……………………………………69
5.1.1 運動方程式………………………………………………69
5.1.2 數值結果與討論…………………………………………70
5.2 具失調拉筋連接葉片系統………………………………………73
5.2.1 運動方程式…………………………………………………73
5.2.2 數值結果與討論…………………………………………74
第六章 結論與未來研究方向…………………………………………93
6.1 結論…………………………………………………………93
6.2 未來可行之研究方向……………………………………………97
參考文獻…………………………………………………………………100
附錄…………………………………………………………………110
作者簡介..……………………………………………..…………………..115

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