臺灣博碩士論文加值系統

本論文旨在針對渦輪機械群組裂紋葉片振動特性之探討。裂紋不僅影響葉片本身的動態特性，甚至影響群組葉片系統的動態特性。因群組葉片系統為一週期性葉片系統，一旦系統中任意一葉片產生了裂縫，可能導致群組系統發生振動現象，此時系統的振動能量與應力會集中在裂紋葉片附近，使系統因此而破壞。本文將對此裂紋現象與其造成不穩定現象加以探討。藉由漢米爾頓原理（Hamilton’s principle）來推導其運動方程式與邊界條件，並使用數學模式及MATLAB套裝軟體分析之結果比較，來印證系統之數學模組所得之數值近似解的合理性。

群組葉片之數學模式，考慮葉片群組根部具有線性及旋轉彈性效應，護環位於自由端，葉片為尤拉樑假設，以連續性之能量法及變分學理論，建立該結構模向振動之運動方程式。該運動方程式，可依截面特性採用不同之形狀函數，以求得頻率方程式，如Bessel函數、多項式函數等。數值分析模擬將以長方形截面探討其幾何參數改變對群組葉片結構振動特性之影響。

由於群組葉片之特殊邊界條件，將激發Cantilever mode以及Fixed-Supported mode，故此部份則以研究根部剛性、旋轉與群組葉片數目等效應於Cantilever mode以及Fixed-Supported mode對此系統之振動特性的影響。

The purposes of this thesis are to study the crack effects to the vibration behavior of large size turbine blades. The vibration caused by the crack is not only to effect the dynamic characteristics of the blade, but also the dynamic characteristics of grouped blade system. Because grouped blade system is the periodically coupled blades system, once a crack appears in any blade of it, that will make the system to experience the vibration phenomenon, which causes the vibration energy and stress around the crack of the blade and then destroy the system﹒In this thesis, the dynamic characteristics caused by the crack effects are investigated. The equation of motions and boundary conditions are derived by Hamilton’s principle. The software MATLAB will be used to simulate the mathematical model developed in this thesis.
The crack blade can be considered as two segments of blade. Crack effect is modeled as torsional spring to connect the two segments with proper compatibility conditions.
Because of the special boundary conditions of grouped blade system, the cantilever modes and fixed-supported modes will be excited. Finally, the parameters of crack location, crack length and crack in the blade are considered to elucidate the dynamic behavior of the group blades. Through the combination of exploring process of the analysis, the knowledge are developed and an erected in a manner to upgrade technology in our living.

中文摘要 ……………………………………………………………. I
英文摘要 ……………………………………………………………. II
誌謝 …………………………………………………………………..III
目錄 ………………………………………………………………..…IV
圖目錄 ……………………………………………………………….V
表目錄 ………………………………………………..…………VII
第一章 序論 …………………………………………………………1
1.1 研究動機與目的 ……………………………………1
1.2 文獻回顧 ………………………………………………3
第二章 方形截面樑葉片之群組葉片系統振動分析 ………………7
2.1 前言 …………………………………………………...7
2.2 系統描述與運動方程式推導 …...................................8
2.3 固定截面之群組裂紋葉片分析 …………………….17
2.4 裂紋繞性效應 ……………………………………….22
2.5 群組裂紋葉片系統描述 …………………………….25
第三章 數值分析與探討 …………………………………………..49
3.1 前言 ………………………………………………….49
3.2 葉片幾何與材料參數 ……………………………….49
3.3 數值分析探討 ……………………………………….50
3.4 葉片根部加入彈性效應之群組裂紋葉片分析 …….64
3.5 群組裂紋位於連續第一、二支葉片分析 ………….72
第四章 結果與展望 ………………………………………………..76
參考文獻 …………………………………………………………....79

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