旋轉垂直軸風力發電機葉片之振動分析

Abstract

風能被喻為最具有發展潛力的再生能源，風力發電機主要分為水平軸風力發電機(HAWT)和垂直軸風力發電機(VAWT)，垂直軸風力發電機因為不受風向變化的影響、架設容易且運轉時噪音比水平軸風力發電機小，較適合安裝於市區，非常具有發展的潛力。不過由於垂直軸風力發電機的效率僅能達到約百分之三十，水平軸風力發電機則能達到約百分之四十，因為效率較低，使得垂直軸風力發電機的相關技術需要提升，才能在現有主流的水平軸風力發電機市場占有一席之地，如何使葉片有效的運作，不會因為旋轉時振動的關係而造成破壞，維持良好的性能是很重要的問題。 葉片在運轉的過程中承受複雜的風力負載，過去的許多文獻在探討這個問題時，對於葉片的變形僅以徑向位移和切向位移來表示，且是以力平衡的方法來推導。本文獨特的貢獻在於藉由能量法漢彌爾頓定理來推導，使得適用範圍較為廣泛，並特別將旋轉速度加入考慮，這是在旋轉時相當重要的參數，推導出葉片旋轉時自由振動的控制方程式，以解析的方式算出葉片運動時的自然頻率和振動模態。再使用工程軟體ANSYS Workbench來做模擬，對葉片做模態分析，計算出各個旋轉速度下的自然頻率，並與理論值相比較。因為本文所使用的方法，較貼近實際風力發電機運轉時的情形，使得解析解與數值模擬的結果，在低自然頻率時，也就是風力發電機實際可能運轉的頻率下，預測結果相當一致，以此解析的方法可以快速且準確的預測葉片會發生共振時的自然頻率，能夠早在設計的階段，經由變更結構的設計，來預防實際運轉時可能產生的破壞，達到提高垂直軸風力發電機效能的目的。

Wind power is the most potential source of renewable energy. There are two categories of modern wind turbines, namely horizontal axis wind turbines (HAWT) and vertical axis wind turbines (VAWT). Vertical axis wind turbines have the major benefit of operation that is independent of the wind direction. Other benefits include easier installation and lower noise radiation than the horizontal axis wind turbines. Therefore they have great potential for applications in the urban area. Nevertheless, higher efficiency is offered by a horizontal wind turbine as it has blades in perpendicular to direction of wind and hence receives more power for rotation. To ensure that the blades operate effectively, it is important that that their structure is dynamically safe when in rotation. There has been a growing interest in the investigation of free vibration characteristics of rotating beams because the topic plays an important role in the design of shafts, turbine blades, propellers and many other rotating structures. In this present paper, we use Hamilton’s principal to derive the dynamic governing equations for the rotational slender blade. We especially take rotational velocity which is a very important parameter when rotating into consideration. Theoretical natural frequencies and mode shapes for some illustrative examples are calculated and compared with the simulation of ANSYS Workbench. These results are discussed and compared with published ones, and we can predict the first few lower natural frequencies quite accurately. Vertical axis wind turbine is verified that the theoretical model can provide mechanical insight into the design of the blades. The vertical axis wind turbine blades are flexible, highly dynamic structure, with many natural modes of vibration that must be carefully analyzed to ensure the blades are dynamically stable under all operating conditions.