斜裂纹旋转叶片动力学建模及振动响应分析

Dynamic modeling and vibration response analysis of rotating bladewith slant crack

为分析航空发动机裂纹叶片的动力学特性,提高航空发动机的可靠性,尽可能避免灾难性事故的发生。本研究基于应变能释放率和Castigliano定理,结合Timoshenko梁理论,考虑裂纹角度的影响,推导了新的裂纹梁单元的应力强度因子与柔度矩阵,根据裂纹面在振动过程中的应力变化,提出了一种根据裂纹面接触区域来计算裂纹梁单元时变刚度的方法,建立了含呼吸效应的斜裂纹扭形叶片动力学模型。通过将本研究模型和ANSYS Solid186单元有限元模型得到的固有频率和振动响应进行对比,验证了所建动力学模型的有效性。结果表明:当裂纹角度从0°增加到80°时,固有频率增加了约3%,即随着裂纹角度的增加(裂纹尖端更靠近叶尖),裂纹叶片固有频率越大;同时,裂纹角度越大,旋转裂纹叶片的振动位移幅值越小,其频谱中常值分量及倍频处的幅值越小,并且第1阶共振状态下1.0倍频的幅值降低了约40%;本研究模型的动力学响应计算速度较ANSYS更快,提高了约22倍。

The purpose of this study is to analyze the dynamic characteristics of cracked blades of aero-engines,improve the reliability of aero-engines and minimize the occurance of catastrophic accidents.This study is based on the strain energy release rate and Castigliano s theorem,combined with Timoshenko beam theory,a new stress intensity factor and flexibility matrix of the cracked beam element is derived,considering the effect of the angles of the slant crack.According to the stress change of the cracked surface during vibration,a method is proposed for calculating time-varying stiffness of the cracked beam element based on the contact area of the cracked surface.A dynamic model of the slant cracked twisted blade with breathing effect is established.By comparing the natural frequencies and vibration responses obtained by the proposed model and the finite element model of the ANSYS Solid186 element,the validity of the proposed model is verified.The results show that as the crack angle increases from 0°to 80°,the natural frequency increases by approximate 3%,that is,as the crack angle increases(the crack front is closer to the blade tip),the natural frequency of the cracked blade increases.Additionally,as the crack angle increases,the vibration displacement amplitude of the rotating cracked blade decreases.The amplitudes of the constant component and the multi-frequency in the spectrum also decreases.Furthermore,the amplitude of the 1.0 f e under the first order resonance state is reduced by about 40%.The calculation speed of the dynamics response of the proposed model is faster than that of ANSYS model,with an improvement of about 22 times.