Geometric Error Sensitivity Analysis of Machine Tool Based on Polynomial Chaos

ZHENG Hualin; ZHAO Xing; HU Teng; WEI Xiaojian; WANG Xiaohu

doi:10.16080/j.issn1671-833x.2024.06.024

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Geometric Error Sensitivity Analysis of Machine Tool Based on Polynomial Chaos

更新时间：2025-10-30

- Geometric Error Sensitivity Analysis of Machine Tool Based on Polynomial Chaos
- Aeronautical Manufacturing Technology Vol. 67, Issue 6, Pages: 24-31(2024)
- 作者机构：
  
  1. 西南石油大学,成都,610500
  2. 石油天然气装备技术四川省科技资源共享服务平台,成都,610500
- 作者简介：
- 基金信息：
- DOI：10.16080/j.issn1671-833x.2024.06.024
  CLC：
- Published：2024
- 稿件说明：
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郑华林，赵兴，胡腾，魏小建，王小虎. 基于多项式混沌的机床几何误差灵敏度分析[J]. 航空制造技术, 2024, 67(6): 24-31.

ZHENG Hualin, ZHAO Xing, HU Teng, WEI Xiaojian, WANG Xiaohu. Geometric Error Sensitivity Analysis of Machine Tool Based on Polynomial Chaos[J]. Aeronautical Manufacturing Technology, 2024, 67(6): 24-31.
郑华林，赵兴，胡腾，魏小建，王小虎. 基于多项式混沌的机床几何误差灵敏度分析[J]. 航空制造技术, 2024, 67(6): 24-31. DOI： 10.16080/j.issn1671-833x.2024.06.024.

ZHENG Hualin, ZHAO Xing, HU Teng, WEI Xiaojian, WANG Xiaohu. Geometric Error Sensitivity Analysis of Machine Tool Based on Polynomial Chaos[J]. Aeronautical Manufacturing Technology, 2024, 67(6): 24-31. DOI： 10.16080/j.issn1671-833x.2024.06.024.

摘要

为解决目前灵敏度分析方法普遍存在的样本需求量大且计算效率不高的问题，提出了一种基于多项式混沌展开的全局灵敏度分析方法。首先，以AC型双转台五轴数控机床为研究对象，根据旋量理论建立了完备的空间误差模型。其次，构建了机床几何误差的多项式混沌展开模型，采用正交匹配追踪实现模型的稀疏化，并给出了基于该方法的 Sobol灵敏度指数。进而，对五轴数控机床几何误差进行了实例分析，测量并统计出41项误差的近似概率分布，分析了影响各方向位姿误差分量的关键几何误差。通过与蒙特卡洛法和拉丁超立方法进行对比，多项式混沌展开方法的正确性得到验证，且在不降低计算精度的前提下，样本量从1×10

降低到1×10

，计算时间分别减少96.8%和98.1%，计算效率显著提高。

Abstract

In order to solve the problem of large sample demand and low computational efficiency in the current sensitivity analysis method

a global sensitivity analysis method based on polynomial chaos expansion was proposed. Firstly

a complete spatial error model was established based on the screw theory by taking the AC type double turntable five-axis CNC machine tool as the research object. Secondly

the polynomial chaos expansion model of machine tool geometric error was constructed. The orthogonal matching pursuit was used to sparse the model

and the Sobol sensitivity index based on this method was given. Furthermore

the geometric errors of five-axis CNC machine tools were analyzed. he approximate probability distribution of 41 errors are measured and count

and the key geometric errors affecting he pose error components in each direction are analyzed. Compared with Monte Carlo simulation and Latin hypercube ampling

the correctness of the polynomial chaos expansion method is verified. Under the premise of not reducing the calculation accuracy

the sample size is reduced from 1×10

to 1×10

the calculation time is reduced by 96.8% and 98.1% respectively

and the calculation efficiency is significantly improved.

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