声弹效应测量螺栓轴向应力的有限元计算分析

为促进超声技术在定量评价螺栓拧紧状态中的有效应用,结合实际检测需求,对基于声弹效应的螺栓轴向应力测量方法构建了合适的有限元模型。使用二维轴对称方式模拟M8×25的螺栓,螺栓头部安放10MHz的超声波探头;有限元计算时,采用具有默纳汉三阶弹性常数的超弹性材料,将结构场与声场进行耦合分析,通过前后两个研究步骤,确定出螺栓在轴向拉伸状态下的超声波形信号;有限元计算结果表征了声传播时间差(ns)、轴向载荷(MPa)间的线性关系,此线性关系随螺栓夹紧长度、螺栓材料的不同而相应地改变;计算表明,对基于声弹效应的轴向应力测量方法而言,线性系数的准确测定非常重要;对有限元计算结果进行深入分析,可知螺栓内部应力状态对于超声传播声时变化存在叠加影响;因螺栓夹紧长度不同会引起声弹效应的较大变化,在实际测量时应对此足够重视。有限元计算结果与解析计算结果、实际试验测试结果对比,结果吻合性良好;所建立的超声法测量螺栓轴向应力的有限元模型,解决了对声弹效应进行数值模拟分析的难题,可为检测方法分析、专用仪器研发提供技术指导。

Finite element analysis for bolt axial stress measurement based on acoustoelastic effect

To promote the effective application of ultrasonic wave technique in quantitative evaluation of bolt tightening state, combining with requirements of actual detection, an appropriate finite element (FE) model was established for the bolt axial stress measurement method based on acoustoelastic effect. A2-D axisymmetric mode was used to simulate bolt M8×25, and a 10 MHz ultrasonic transducer was placed on the bolt head. In FE simulation, a hyper-elastic material with Murnaghan third-order elastic constants was used to do coupling analysis for structural field and acoustic one. Through two studying steps, the ultrasonic waveform signal for bolt axial tension state was determined. The FE computation results showed that there is a linear relationship between time difference of ultrasonic wave propagation (ns) and bolt axial stress (MPa), and this relationship varies with change of bolt clamped length and its material;for the bolt axial stress measurement method based on acoustoelastic effect, the linear coefficient’s correct measurement is very important. The FE computation results were analyzed deeply, it was shown that bolt stress state has a superposition effect on ultrasonic wave propagation change in bolt;different bolt clamped length causes larger change of acoustoelastic effect, this should be paid enough attentions to;the FE computation results agree well with those of analytical calculation and practical test measurement;the proposed FE model for bolt axial stress measurement with the ultrasonic wave method can be used to solve the difficult problem of acoustoelastic effect’s numerical simulation and analysis, and provide a technical guidance for analysis of detection methods and development of specific instruments.