改进Sobol法在自由曲面测量仪几何误差分析中的应用  

Application of the Improved Sobol Method to the Analysis of Geometric Errors in Free-Form Surface Measuring Instrument

作　　者：席建普[1] 张通通 邓丽娟 岳永高 聂子凯 刘释聪 XI Jianpu;ZHANG Tongtong;DENG Lijuan;YUE Yonggao;NIE Zikai;LIU Shicong(School of Intelligent Mechatronics Engineering,Zhongyuan University of Technology,Zhengzhou Henan 450007,China)

机构地区：[1]中原工学院智能机电工程学院,河南郑州450007

出　　处：《机床与液压》2025年第4期62-67,共6页Machine Tool & Hydraulics

基　　金：国家自然科学基金青年科学基金项目(51705546);河南省自然科学基金项目(242300421259);中国纺织工业联合会指导性项目(2020073);中原工学院自然基金项目(K2023MS015);机械工业光学传感与测试技术重点实验室(2022SA-04-15)。

摘　　要：在自由曲面的测量过程中,几何误差的引入几乎无法避免,而这些误差会严重影响测量结果的精度。针对此问题,以自由曲面测量仪为研究对象,基于多体系统理论建立误差模型,然后运用Sobol方法和准Monte Carlo算法对几何误差元素及其耦合效应进行灵敏度分析,识别严重影响测量结果的关键误差元素。通过分析自由曲面测量仪在不同位置下的几何误差元素灵敏度系数,从21项几何误差中识别出9项对自由曲面测量仪测量精度影响较大的关键项,并对灵敏度分析结果进行了误差补偿仿真验证。结果表明:补偿关键误差后,沿X、Y和Z方向的测量精度分别提升了77.1%、65%和83.3%,说明该方法能够有效辨识出自由曲面测量仪的关键几何误差项。In the process of measuring free-form surfaces,the introduction of geometric errors is almost inevitable,and these errors will have a significant impact on the accuracy of the measurement results.In view of this problem,taking the free-form surface measuring instrument as the research object,a multi-body system theory-based error model was constructed.Subsequently,the Sobol method and the quasi-Monte Carlo algorithm were employed to conduct a sensitivity analysis on the geometrical error elements and their coupling effects,thereby identifying the key error elements that significantly impact the measurement results.By analyzing the sensitivity coefficients of the geometric error elements of the free-form surface measuring instrument at different positions,in the 21 geometric errors,9 key items were identified as having a significant influence on the measurement accuracy of the free-form surface measuring instrument.The results of the sensitivity analysis were verified by simulation of the error compensation.The results demonstrate that after the compensation of the key errors,the measurement accuracies along the X,Y and Z directions are enhanced by 77.1%,65%and 83.3%,respectively.This illustrates that the method can effectively identify the key geometric error terms of the free-form surface measuring instrument.

关 键 词：自由曲面测量仪 几何误差 多体系统理论 改进Sobol方法 Monte Carlo估算 

分 类 号：TH124[机械工程—机械设计及理论]