展弦比與隨機性對風機葉片顫振失效機率之影響分析

Abstract

本研究針對 NREL 5MW 大型風機葉片之顫振特性與失效風險進行系統性探討，分析展弦比變化與參數不確定性對顫振臨界速度與系統可靠度之影響。隨著風機設計朝大型化發展，模態耦合顫振已成為結構設計中不可忽視的關鍵議題。為探究此一現象，本文基於旋轉梁理論建立有限元素模型，結合 P-K 法進行臨界顫振速度分析，並引入模態追蹤技術進行模態識別後處理。隨機分析方面，導入 以 Chebyshev 採樣與插值法構成之蒙地卡羅模擬替代模型，以高效評估不同參數變異條件下之臨界顫振速度機率分布與系統可靠度。為進一步量化系統風險，本研究提出失效機率、安全裕度與臨界展弦比等三項可靠度指標。研究結果顯示，扭轉勁度對臨界顫振轉速影響較升力係數斜率顯著，且當兩者同時存在不確定性時，整體安全裕度相較單變數結果降低約 10–20%，顯示耦合不確定性將提前引發失效風險。進一步比較不同展弦比之分布結果，提高展弦比雖有助於提升風機輸出功率，但同時也降低葉片臨界顫振速度，增加模態耦合與系統不穩定風險。此外，高展弦比葉片在考慮扭轉勁度與升力係數斜率之不確定性時，可能會發生模態跳轉與臨界速度高度集中現象，導致臨界速度分布呈現雙峰、波動與局部極端尖峰等現象。整體而言，本研究深入分析展弦比與參數變異性交互作用對顫振穩定性之重要影響，並建立一套可應用於工程實務之高效率風機葉片顫振風險分析流程，有助於提升未來離岸風電結構之設計與可靠度評估。

This study investigates the flutter characteristics and failure risks of the NREL 5MW large-scale wind turbine blade. The analysis focuses on the influence of aspect ratio variation and parametric uncertainty on the critical flutter speed and system reliability. As wind turbine designs continue to scale up, coupled-mode flutter has emerged as a critical consideration in the structural design of wind turbine blades. To address this, a finite element model based on rotating beam theory was developed, and the P-K method was employed for flutter analysis, integrated with a mode tracking technique for post-processing modal identification.For the stochastic analysis, this study introduces a surrogate model combining Chebyshev sampling and interpolation methods within a Monte Carlo simulation framework to efficiently evaluate the probability distribution of flutter speeds and associated reliability indicators under various uncertainty conditions. Three reliability indexes — failure probability, safety margin, and critical aspect ratio were proposed to quantify the impact of parameter uncertainty on flutter risks. The results indicate that torsional stiffness has a more significant impact on the critical flutter speed than the slope of lift coefficient. When both parameters exhibit uncertainty, the safety margin is reduced by approximately 10–20% compared to single-variable cases, revealing the interactive effects of multiple uncertainties. Moreover, increasing the aspect ratio improves power output but also lowers the critical flutter speed and increases the likelihood of mode coupling and dynamic instability. High-aspect-ratio blades subjected to uncertainty in both torsional stiffness and slope of lift coefficient exhibit phenomena such as mode switching and concentrated critical speeds, leading to double-peaked, fluctuating, and locally spiked distributions of flutter speed. In summary, this study presents a comprehensive investigation of the effects of aspect ratio and parametric uncertainty on flutter stability, and proposes an efficient flutter risk evaluation framework applicable to engineering practice. The proposed method offers useful insights for future offshore wind turbine blade design and reliability assessment.