基于Rayleigh法的风机塔筒预应力基本频率解析计算方法

Analytical calculation method for the pre-stress basic frequency of wind turbine towers based on Rayleigh method

风机大型化发展趋势使塔筒高度更高、柔性更大,塔筒直径及壁厚随高度变化更加多样,使传统简化基频解析计算方法计算精度大幅下降,较难满足塔筒设计前期基频估算要求。引入等效壁厚、平均等效当量惯性矩考虑塔筒直径和壁厚沿高度的多种变化情况,简化塔筒刚度计算;基于Rayleigh能量法基本原理,考虑风轮和机舱质量对塔筒预压应力、质量偏心以及塔筒不同变形形式对基频计算的影响,提出了相应的塔筒基频解析计算方法。塔筒数值算例和实验室缩尺试验表明:顶部机舱、叶轮质量偏心对塔筒基频影响较大,解析计算时应考虑其影响;均布荷载变形下的塔筒基频解析值更接近真实值;所提解析法与精细化有限元模型计算值的偏差小于4%,与缩尺模型实测值的偏差小于5%。

The large-scale development trend of wind turbines makes its tower taller and more flexible,and the diameter and wall thickness along the height of the tower become more and more diversified.Therefore,the calculation accuracy of the traditional simplified fundamental frequency analytical calculation method is greatly reduced,and it is difficult to meet the requirement of the fundamental frequency estimation in the early stage of tower design.In the paper,the equivalent wall thickness and average equivalent moment of inertia were proposed to consider the various changes in tower diameter and wall thickness along the height,so as to simplify the calculation of tower stiffness.Based on the basic principle of Rayleigh energy method,considering the influences of the masses of the wind turbine and nacelle on the pre-compression stress,mass eccentricity and deformation form of the tower and then on the fundamental frequency calculation,a corresponding analytical calculation method for the fundamental frequency of tower was proposed.A numerical example and the scale test show that the eccentricity of the top nacelle and impeller mass have a great influence on the fundamental frequency of the tower,which should be considered in the analytical calculation.The analytical result of the tower fundamental frequency under uniform load is closer to the true value.The deviation between the proposed analytical method and the calculated value of the refined finite element model is less than 4%,and the deviation from the measured value of the scale model is less than 5%.