基于非接触式测量的旋转叶片动应变重构方法

基于叶端定时非接触式测量和振动响应传递比的概念,开展高速旋转叶片动应变重构方法的研究。在频域内推导了叶片任意测点位移与任意测点动应变的传递比,给出了单模态共振下响应传递比关于位移和应变模态振型的解析表达式;建立旋转叶片的三维(3D)有限元模型,开展考虑旋转预应力效应的叶片模态分析,提取位移和应变模态振型,获得任意转速下叶端位移与叶根关键点动应变的传递比。开展高速旋转叶片叶端定时非接触式测量实验,采用周向傅里叶算法对叶端定时信号进行处理,获得叶片在不同转速单模态共振下的叶端位移,结合响应传递比,重构5个旋转叶片的关键点动应变。结果表明:旋转叶片在9000r/min和13000r/min转速下发生1阶共振时,与应变片实测结果相比,叶根处应力最大点、次大点和边缘点3个关键点的动应变平均重构误差均小于15%,验证了旋转叶片动应变重构方法的有效性。

Dynamic strain reconstruction method of rotating blades based on no-contact measurement

A dynamic strain reconstruction method of rotating blade based on blade tip timing non-contact measurement and transmissibility concept was proposed. The transmissibility between displacement and strain of any point was derived in the frequency domain. The analytical formula of transmissibility with respect to mode shapes was obtained. The three-dimensional (3D) finite element model of rotating blade was established to conduct modal analysis considering rotating pre-stress effect. The displacement and strain mode shapes of blade were extracted and the transmissibility between displacement at blade tip and dynamic strain of critical point at blade root under any rotational speed was calculated. The test for high-rotating blade based on blade tip timing non-contact measurement was conducted. The Circumferential Fourier transform method was applied for analyzing blade-tip displacement at different rotational speeds in case of single mode resonance. Combining with the transmissibility, the dynamic strain of five blades at some critical points was reconstructed. Results showed that when the first mode resonance at rotational speed of 9000r/min and 13000r/min occurred, comparing with the measuring results of strain gages, the average relative error of dynamic strain reconstruction of three critical points on the blade root, such as the maximum-strain point, the secondary-strain point and the edge point, was less than 15%, showing the validity of the dynamic strain reconstruction method.