悬臂梁应变测量数学模型研究

Research on mathematical model of cantilever beam strain measurement

以材料力学为理论基础,为研究悬臂梁测试系统中应变片丝栅增长量与其中线位置挠度的关系,建立多种几何微分模型,推导各模型中应变片位置的平均应变。对悬臂梁测试实验系统建立有限元模型进行应变分析,通过与有限元分析结果和实验测量数据进行分别对比得出,建立的切线夹角微分模型与有限元分析和实验结果相符,验证了针对悬臂梁测量系统,切线夹角微分理论模型的可行性。为标定悬臂梁测试系统提供了理论支持,为悬臂梁系统表面应变的推导计算提供参考。

Based on the theory of mechanics of materials, in order to study the relationship between the growth of strain gauge wire grid in the cantilever beam testing system and the deflection of the center line, a variety of geometric differential models were established, and the average strain of strain gauge position in each model was derived.Of cantilever beam test experiment system, a strain analysis based on the finite element model is established with finite element analysis results and the experimental measurement data were compared, the tangent angle of differential model consistent with the finite element analysis and experimental results, in view of the cantilever beam measurement system is verified, the tangent angle of the feasibility of the differential theory model.It provides theoretical support for calibrating the cantilever beam test system and provides reference for calculating the surface strain of the cantilever beam system.