基于多模态传递比的旋转叶片动应变场重构方法

Dynamic strain field reconstruction method of rotating blade based on multi-mode transfer ratio

针对旋转叶片非接触式应力/应变测试的需求,本文提出一种基于多模态传递比的叶片动应变场重构方法。首先,基于多自由度(MDOF)系统的振动微分方程,在模态坐标系下建立位移频响函数(FRF)和应变频响函数,进而得到位移-应变响应传递比表达式;以某12扇区的叶盘为分析对象,建立叶片有限元模型并进行模态分析,通过提取多模态叶尖位移和叶身应变,得到总位移-应变传递比矩阵和定向位移-应变传递比矩阵;最后,基于Simulink平台进行旋转叶片叶尖定时采样(BTT)仿真模拟,通过周向傅里叶拟合算法(CFF)对欠采样信号进行振动位移重构,将得到的叶尖位移代入传递比表达式,得到叶身应变。研究结果表明:在非共振态下,由叶尖位移重构得到的叶身总应变与有限元分析得到的总应变相对误差为0.12%~14.56%,定向应变相对误差为1.92%~14.70%,验证了本文提出的基于多模态传递比的叶片动应变场重构方法的有效性。

Aiming at the non-contact stress/strain test of rotating blades,a dynamic strain field reconstruction method was proposed in this paper,based on multi-mode transfer ratio between displacement and strain.Firstly,based on the forced vibration differential equation of the MDOF system,the displacement FRF and the strain FRF were established in modal coordinate system.And then the expression of displacement-strain transfer ratio was obtained.By taking a bladed disk with 12 sectors as the analysis object,finite element model of the blade was established and modal analysis was carried out.The total displacement-strain transfer ratio matrix and the directional displacement-strain transfer ratio matrix were obtained by extracting the tip displacement and the blade strain of multiple modes.Finally,based on the Simulink platform,the blade tip timing(BTT)sampling simulation experiment was carried out.The tip vibration displacement obtained by the simulated BTT system,which was reconstructed by Circumferential Fourier fitting(CFF)with subsampling data,was substituted into the transfer ratio expression to obtain the strain of blade body.The results show that in the off-resonance state,the relative error of the total strain obtained by the dynamic strain field reconstruction method is in the range of 0.12%−14.56%and the relative error of the directional strain is in the range of 1.92%−14.70%,compared with the finite element analysis results,which verifies the feasibility and accuracy of the proposed method based on multi-mode transfer ratio.