Abstract:

The  particles of resonant fatigue crack propagation test vibration  system were composed of multiple different shapes and material components,which largely limited  the direct measurement of particles mass.A soft-measuring method was  proposed herein to measure the particle mass of this kind of vibration system. Firstly, three degrees of freedom vibration system mechanics model and the dynamics equation were established and the system natural frequency equation concerning system natural frequency, spring stiffness and particle mass was derived. The specimen stiffness under different crack  lengths was  calculated by finite element  method and the system natural frequency under different crack lengths  was  measured through frequency measuring experimental method.With substituting resonance frequency value under different crack lengths and the corresponding specimen stiffness into system frequency equation, the over determined equations were derived by taking the particle  mass  needed to  identify  as the unknown variables, the least-squares solution was obtained by solving the over determined equations,and this vibrating system particle mass  were obtained by further subsequent processing. The related experiments  were  performed to verify the accuracy of the proposed method.The experimental results  show  that the maximum error of main vibration mass is  as  6.76% and the proposed method has theoretical significance and application values.

Key words: resonant , fatigue crack propagation test;soft-measuring method；finite element analysis;particle mass;over determined equations

摘要：

谐振式疲劳裂纹扩展试验振动系统的质点由多个不同形状、材质的部件组成,对质点质量进行直接测量有很大的局限性。提出了一种针对此类振动系统质点质量的软测量方法，建立了系统三自由度振动力学模型和动力学方程，推导得到关于系统固有频率、弹簧刚度与质点质量关系的系统频率方程，通过有限元方法计算出不同裂纹长度下试件的刚度，通过固有频率测量实验方法测出裂纹扩展到不同长度时系统的谐振频率，将不同裂纹长度时系统谐振频率值及相应试件刚度代入系统频率方程中,得到以待识别质点质量为未知数的超定方程组，求解超定方程组得到最小二乘解,并通过后续处理得到振动系统的主振质量和激振质量。为验证该方法,进行了相关实验。实验结果表明:主振质量测量的最大误差为6.76%，表明所提出方法具有理论意义和应用价值。

关键词: 谐振式疲劳裂纹扩展试验, 软测量, 有限元分析, 质点质量, 超定方程组