微构件弹性模量悬臂梁法测量的模糊建模及分析  

Analysis and Fuzzy Modeling of Elastic Modulus of Microcomponent by Microcantilever Deflection

作　　者：朱强[1] 蒋庄德[1] 王海容[1] 赵则祥[2] 

机构地区：[1]西安交通大学机械制造系统工程国家重点实验室,西安710049 [2]中原工学院纺织工程技术中心,郑州450007

出　　处：《西安交通大学学报》2005年第5期517-521,共5页Journal of Xi'an Jiaotong University

基　　金：国家重点基础研究发展规划资助项目(G1999033103)

摘　　要：在介绍悬臂梁法测量微构件弹性模量原理的基础上,分析了测量和评价过程的主要不确定因素,将模糊数学方法引入弹性模量的评价过程.在常规模型中,给予有关参数一定的变动范围,以隶属函数表示其取值分布情况,建立了基于模糊集的评价模型.其中,悬臂梁试件的刚度系数由载荷有效挠度曲线经模糊加权线性回归拟合获得,其几何尺寸考虑为正态分布模糊数,利用水平截集概念转化为普通集规划问题求解.对单晶硅(100)悬臂梁试件的实验数据进行了计算,得到不同置信水平下的弹性模量评价区间.研究结果表明,带有模糊参数的弹性模量评价模型能适当吸收一些不确定因素,同时由于考虑了测量中多种因素的影响,评价结果与实际情况符合较好,因此更具有参考价值.The primary uncertain factors in the elastic modulus measurement of microcomponent by micro-cantilever deflection are analyzed and the fuzzy mathematic method is introduced to the evaluation process. The relevant parameters are allowed to variate within a certain range, a new evaluation model is established based on fuzzy sets, where the stiffness constant of microcantilever beam is acquired by linear regression of the effective load-deflection curve with fuzzy weight, and the beam geometry dimensions regarded as Gaussian fuzzy numbers are obtained from programming of equivalent common sets by level-cuts concepts. The experiments of silicon (100) microcantilever beam are conducted, and the elastic modulus is calculated in ranges of different confidence levels, which is agreeable to the real situations. The qualitative uncertainties in the measurement can be absorbed by the established model with fuzzy parameters, which implies that the evaluated elastic modulus is more valuable for the practice.

关 键 词：悬臂梁法 微构件 弹性模量 模糊模型 隶属函数 

分 类 号：TG115.5[金属学及工艺—物理冶金]