基于Sobol’法的机床关键几何误差元素辨识方法研究

针对机床几何误差元素多、误差测量与辨识过程繁琐等问题,利用Sobol’全局灵敏度分析方法对空间误差模型中的几何误差元素进行灵敏度分析,筛选出影响较大的几何误差元素,从而降低误差测量与辨识过程的复杂度,简化空间误差模型。以螺旋理论为建模基础,建立机床空间误差模型;对所有几何误差元素进行Sobol序列抽样并通过蒙特卡洛估计法求解灵敏度,计算各误差元素的一阶灵敏度值及全局灵敏度值,从21个误差项中筛选出对机床空间误差影响较大的12项;将简化模型与完备模型进行对比,空间误差元素简化率为48%,其预测精度大于80%,说明了误差元素筛选的有效性,为机床空间误差建模、误差元素辨识以及空间误差补偿工作的简化提供参考。

Research on Identification Method of Key Geometric Error Elements of Machine Tool Based on Sobol' Method

Aiming at the many geometric error elements of machine tools and the tedious error measurement and identification process,Sobol’global sensitivity analysis method was used to analyze the sensitivity of geometric error elements in spatial error model,and the geometric error elements with greater influence were screened out,thereby reducing the complexity of error measurement and identification process and simplify the error model.Based on the screw theory,the spatial error model of machine tool was established.All geometric errors were sampled by Sobol sequence,and the sensitivity was solved by Monte Carlo estimation method.The first-order sensitivity value and global sensitivity value of each error element were calculated,and 12 items which had greater impact on the machine tool’s spatial error were selected from the 21 errors.The simplified model was compared with the completed model,the simplification rate of spatial error elements was 48%,and its prediction accuracy was greater than 80%.It illustrates the effectiveness of error elements screening,and provides reference for the simplification of spatial error modeling,identification and compensation.