基于蒙特卡罗法的MEMS测力计不确定性分析  

Uncertainty analysis of MEMS force gauges based on Monte Carlo method

作　　者：韩琪[1] 陈贵敏[1] 邵晓东[1] HAN Qi;CHEN Gui-min;SHAO Xiao-dong(School of Mechano-Electronic Engineering,Xidian University,Xi′an 710071,China)

机构地区：[1]西安电子科技大学机电工程学院,陕西西安710071

出　　处：《光学精密工程》2018年第9期2289-2293,共5页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.51675396)

摘　　要：由于结构尺寸小,微电子机械系统(MEMS)的性能易受到加工工艺过程中各种不确定因素的影响,设计阶段存在着不确定性。本文针对一种典型的MEMS测力计进行不确定性分析,在考虑大挠度变形的条件下,基于完备椭圆积分解给出了测力计的载荷-位移模型,模型结果表明测力计在位移超过30μm后表现出显著的非线性。基于该模型,综合考虑材料参数和结构尺寸参数的随机性,研究了测力计不确定性分析的蒙特卡罗法,并给出了直接对蒙特卡罗抽样数据实施线性回归获得各参数敏度的计算方法,用于便捷地分析各参数对测力计不确定性的贡献。所得到的结果与文献吻合非常好,验证了该方法的正确性和有效性,并为测力计的鲁棒设计以及工艺改进提供参考。本文给出的系统不确定性分析方法具有通用性强、使用简单等优点,同时避免了对解析模型的依赖,证明其可应用于难以显式表达输入与输出关系的系统的不确定性分析。Due to their small size,the performances of microelectromechanical systems(MEMS)are susceptible to uncertainties associated with the micro-fabrication processes;thus,it is necessary to consider these uncertainties during the design stage.By conducting an uncertainty analysis of a typical MEMS force gauge,a load-deflection model was first derived based on the comprehensive elliptic integral solution.The model showed that the force gauge exhibits a nonlinear load-deflection relationship when the deflection surpasses 30μm.Based on the model,the uncertainty of the force gauge was analyzed using the Monte-Carlo method,by considering the variations of the material and dimensional parameters,and the contributions of the parameters to the uncertainty were analyzed using their sensitivities directly obtained from the linear regression of the Monte-Carlo samples.The results agree well with those presented in Ref.[1],indicating the correctness and effectiveness of the method.The results could be helpful for the robustness design of the force gauge,and provide guidance for improving the micro-fabrication processes.The uncertainty analysis method presented in this work is versatile,easy to use,and does not rely on analytical models;it can thus be applied to the uncertainty analysis of systems whose input-output relations cannot be explicitly formulated.

关 键 词：MEMS测力计 椭圆积分解 不确定性 蒙特卡罗法 

分 类 号：TH712[机械工程—测试计量技术及仪器]