Scholarlink

<p>The volumetric error model essentially represents the mapping relationship between geometric errors and tool center point (TCP) displacement errors in the workspace. When fitting irregular and nonlinear geometric errors, high-order least squares(LS) fitting results in noticeable oscillations between measuring points, leading to a decrease in the accuracy of the volumetric error model. To enhance the volumetric accuracy of a 3-axis vertical machine tool, this paper proposes the moving least squares (MLS) method for the approximation of the volumetric error model derived from muti-body kinematic theory and the homogeneous transformation matrix (HTM). A comparative analysis between MLS and LS in terms of positioning error data approximation is conducted to evaluate the impact of fitting on the accuracy of the volumetric error model. To address the issue of insufficient local fitting caused by the weight function in MLS, interpolation conditions are constructed to improve MLS. To simplify the MLS fitting calculations, a continuous volumetric error compensation model is developed by inverse distance weighting interpolation(IDW). Compared with LS, the range of approximation residuals for this model is reduced by 63%. The error compensation experiment results indicate that the volumetric accuracy of the MLS-based model is improved by at least 79.3% after compensation. Compared to the compensation model established by LS, it improves by at least 25.3%. This paper demonstrates the effectiveness and applicability of MLS in volumetric accuracy enhancement.</p>

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Improvement of volumetric accuracy in CNC machine tools based on moving least squares

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Xinbo Zhang,
  • Wenxue Zhu,
  • Shuixuan Chen,
  • Xiaobing Zhang,
  • Yujie Zhang

摘要

The volumetric error model essentially represents the mapping relationship between geometric errors and tool center point (TCP) displacement errors in the workspace. When fitting irregular and nonlinear geometric errors, high-order least squares(LS) fitting results in noticeable oscillations between measuring points, leading to a decrease in the accuracy of the volumetric error model. To enhance the volumetric accuracy of a 3-axis vertical machine tool, this paper proposes the moving least squares (MLS) method for the approximation of the volumetric error model derived from muti-body kinematic theory and the homogeneous transformation matrix (HTM). A comparative analysis between MLS and LS in terms of positioning error data approximation is conducted to evaluate the impact of fitting on the accuracy of the volumetric error model. To address the issue of insufficient local fitting caused by the weight function in MLS, interpolation conditions are constructed to improve MLS. To simplify the MLS fitting calculations, a continuous volumetric error compensation model is developed by inverse distance weighting interpolation(IDW). Compared with LS, the range of approximation residuals for this model is reduced by 63%. The error compensation experiment results indicate that the volumetric accuracy of the MLS-based model is improved by at least 79.3% after compensation. Compared to the compensation model established by LS, it improves by at least 25.3%. This paper demonstrates the effectiveness and applicability of MLS in volumetric accuracy enhancement.