臺灣博碩士論文加值系統

本文主要是針對俱裂縫葉片之旋轉週期性系統之局部振動與穩定性
之探討。文中的旋轉週期性系統是以渦輪葉片系統為主要模擬對像，
如蒸汽渦輪機葉片與燃氣渦輪機葉片系統…等等的渦輪葉片系統，因
系統操作時葉片長時間受冷熱反複衝擊，葉片因熱應力循環而常有裂縫
產生。裂縫不僅影響葉片本身的動態特性，甚至影響整組葉片系統的
動態特性。因整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，可能導至整組系統發生了局部振動現象，此時系統
的振動能量與應力會集中在此俱裂縫葉片附近，使得系統因此而破壞
。本文即對此現象與其造成均不穩定現象加以探討。
文中俱有裂縫葉片之運動方程式是以下列兩種方法求得;第一為
雙跨距樑與一扭轉彈簧來模擬葉片裂縫，此扭轉彈簧可由裂縫參數解
得;其次是以能量法直接解山俱裂縫之葉片運動方程式。直樑與錐型
預扭角樑同時用來模擬此系統的葉片，為方便起見，使用尤拉樑理論
推導出系統每根葉片運動方程式。系統的統御方程式可由葛樂金方法
及哈米頓原理推導出，由以上的推導即可求得週期性系統之局部振動
現象。週期性系統的不穩定問題也是本文主要探討題目。文中假設系
統旋轉時俱有微小變動量，此微小轉速變動即為系統的擾動參數，基
於多尺度法可求得此週期性系統之不穩定區。
探討葉片裂縫深度、轉速、葉片間耘合剛度…等參數，對此週期性
系統的局部振動現象與不穩定性的影響。研究証實葉片裂縫、轉速、
葉片間璃合剛度對此類系統之局部振動現象與不穩定性影響甚鉅。

Cracks frequently appear in the rotating machinery, for
as much as manufacturing flaws or cyclic fatigue during operation. Especially for the turbo-disk, numerous cracks
were observed after severe operation. In this dissertation,
the effect of blade crack on the mode localization and
dynamic stability of a rotating turbo-blade-disk is
studied.
Mode localization phenomenon and dynamic stability of
a mistuned system should be worthy of attention, because
the structural or material irregularities and non-constant rotating speed in blade-disks system are unavoidable.
However, only few investigations have dealt with this
mode localization and dynamic stability in those mistuned systems, with cracked blades. In this article, an
investigation of the effect of blade crack on the
stability and mode localization in a rotating blade-
disk is studied. Blades of a blade-disk are simulated respectively by the uniform and pretwisted taper beams.
The crack on the blade can be regarded as a local
disorder of this periodically coupled blades system.
Galerkin''s method and Hamilton''s principle are used to formulate the unperturbation equations of motion of the mistuned system. An application of the perturbation
multiple scales method is employed to derive the
approximate solution for the boundary of instability of
the mistuned system.
The effects of pretwisted angle, rotating speed and
crack size of the blade on the mode localization and
stability in a rotating system are studied. Numerical
results indicate that the increase of pretwisted angle, rotating speed and crack depth could affect the mode localization phenomenon and stability of this mistuned
system significantly.

Cover
Acknowledgements
Contents
List of Figures
List of Tables
Nomenclature
Abstract in Chinese
Abstract in English
Chapter 1 Introduction
Chapter 2 Mode Localization Theoretical Derivation
2.1 Uniform Blade System
2.2 Uniform Blade with Grouped Arrangement System
2.3 Tapered Pretwisted Blade System
Chapter 3 Dynamic Stability Theoretical Derivation
3.1 Uniform Blade System
3.2 Uniform Blade System with Coupled Longitudinal and Bending Vibrations
3.3 Tapered Pretwisted Blade System
Chapter 4 Numerical Results and Discussions
4.1 Mode Localization in the Uniform Blade System
4.2 Mode Localization in the Uniform Blade with Grouped Arrangement System
4.3 Mode Localization in the Tapered Pretwisted Blade System
4.4 Dynamic stability in the Uniform Blade System
4.5 Dynamic stability in the Uniform Blade System with Couped Longitudinal and Bending Vibration
4.6 Dynamic stability in the Tapered Pretwisted Blade System
Chapter 5 Conclusions
References
Appendix A Mode Localization in a Rotating Mistuned Turbo Disk with Coriolos Effect
Appendix B A Study on a Tapered Pretwisted Beam with Different Solving Different Methods
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