本研究主要模擬非接觸式量測系統（光纖位移感測器）檢測渦輪機葉片振動的特性。因此發展出兩種量測葉片位移的方法，分別為單感測點法及雙感測點法。在單一感測點分析方法中我們以質量彈簧系統模擬葉片振動模態，利用數值模擬將葉片轉動時所產生的位移模擬求解。當改變不同的模擬條件時，可看出渦輪機葉片振動的特性，尤其是發生共振時的轉速區間，此區間中葉片位移變化較非共振區間明顯，所以在共振範圍數據點的取得必須較非共振時的轉速間隔更為細密；將單純轉動時的到達時間改良成包含振動時的到達時間，設定不同的安裝位置並比較兩者間的位移差異。
雙感測點分析方法的應用則是單一感測點原理的延伸，利用兩組光纖位移感測器架設於渦輪機外殼上，針對同一葉片改變兩組感測器之間不同的相位角進行模擬。在不同的相位角下，將兩組感測器模擬得知葉片位移相對作圖可以得到近似橢圓曲線，共振級數則由感測點間分離相位角與橢圓逼近曲線的關係檢測出，而橢圓的逼近曲線則採用最小平方法求解。此外，為測試橢圓逼近曲線的精確度並求得適用範圍，本研究刻意對葉片位移加入一擾動方程式；在考量到達感測點時間的影響方面，分為因單純轉動與包含振動之到達時間的振動影響，前者求得之橢圓逼近曲線誤差量較後者小，但後者則較符合實際渦輪機葉片運轉情況時所遭遇的問題。本模擬在雙感測點方法中，葉片振動引起的誤差較單感測點方法為小。
對於渦輪機葉片振動模態的分析，單感測點法可確定葉片共振區間；雙感測點法則能夠檢測葉片的共振級數，此兩種分析方法同時並用將使得渦輪機葉片位移特性分析較為完整。

This simulation study evaluates the techniques of tip-timing measurements with non-contact measurement elements (e.g. light probes) for revealing vibration characteristics of turbomachinery blades. Two measurement methods are studied. One of them is the traditional one-probe method and the other is the recently developed two-parameter method. The one-probe method is evaluated based on a linear vibration model for the simulation of the arrival time. The simulation results show that the displacement of the blade varies extremely rapidly when the speed of rotor is traversed close to the blade resonance. It is also found that the error in the arrival time caused by blade vibrations increases with increasing blade vibration amplitude and can vary with the angular offset of the probe position.
In the two-parameter method, two probes are located with an appropriate spacing on the turbomachinery casing. Plotting the blade displacements measured by the two probes against each other for the traversed rotor speed leads the data to a shape of ellipse. The resonance order of the blade can then be obtained through the comparison the axis ratio of the ellipse that is curve-fitted using the least square technique developed in the present study. The data acquired from the two-parameter method are further perturbed to check for the deviation of the axis ratio of the ellipse. The inaccuracy in the two-parameter method caused by blade vibrations is also investigated and is found to be less significant compared to the one-probe method.

目 錄
摘要……………………………………………………………………………Ⅰ
Abstract………………………………………………………………………Ⅱ
目 錄…………………………………………………………………………Ⅲ
圖目錄…………………………………………………………………………Ⅵ
表目錄………………………………………………………………………ⅩⅠ
符號說明……………………………………………………………………ⅩⅡ
第一章 前 言………………………………………………………………1
1-1 研究動機與背景…………………………………………………………1
1-2 研究目的與方法………………………………………………………2
1-3 本文架構………………………………………………………………3
第二章 理論模式……………………………………………………………5
2-1 模擬方法簡介……………………………………………………………5
2-1.1 單一感測點模擬方法…………………………………………………5
2-1.2 雙感測點模擬方法……………………………………………………6
2-2 原理說明…………………………………………………………………8
2-2.1 單一感測點法……………………………………………………8
2-2.2 到達感測點時間…………………………………………………9
2-2.3 到達感測點時間 ……………………………………………………9
2-2.4 到達感測點時間 …………………………………………………10
2-2.5 雙感測點法…………………………………………………………11
2-3 數學模式推導…………………………………………………………12
2-3.1 單感測點之葉片位移………………………………………………12
2-3.2 百分誤差 ……………………………………………………………14
2-3.3 雙感測點之葉片位移………………………………………………15
2-3.4 橢圓之逼近曲線……………………………………………………17
第三章 數值方法……………………………………………………………19
3-1 單一感測點數值解法…………………………………………………19
3-1.1 單一感測點之模擬條件……………………………………………20
3-2 雙感測點數值解法……………………………………………………22
3-2.1 到達時間為 與 ……………………………………………………22
3-2.2 到達時間為 與 ……………………………………………………23
3-2.3 橢圓逼近曲線之數值解法…………………………………………25
第四章 模擬結果……………………………………………………………29
4-1 單一感測點模擬結果…………………………………………………29
4-1.1 =0.014之葉片最大振幅………………………………………29
4-1.2 =0.041之葉片最大振幅………………………………………34
4-1.3 到達時間之peak-to-peak位移百分誤差 …………………………39
4-1.4 共振級數 與最大振幅 ……………………………………………45
4-2 雙感測點模擬結果……………………………………………………49
4-3 橢圓逼近曲線…………………………………………………………52
4-4 方向之偏移……………………………………………………………56
4-5 方向之偏移……………………………………………………………61
4-6 雙感測點之最大振幅 變化……………………………………………66
4-6.1 雙感測點之共振級數 變化……………………………………67
第五章 結論與建議…………………………………………………………69
5-1 單感測點部分…………………………………………………………69
5-2 雙感測點部分…………………………………………………………69
5-3 未來展望………………………………………………………………70
參考文獻………………………………………………………………………71
附錄 A…………………………………………………………………………72
附錄 B…………………………………………………………………………74

參考文獻
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