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<p>We consider available approaches to elevation of the volumetric accuracy in the design and operation of coordinate measuring systems. At present, there exist numerous methods aimed at the evaluation and correction of volumetric errors developed for the technological and measuring machines with specific kinematic schemes but there is no universal method suitable for different coordinate measuring systems. To get a&#xa0;unified methodical approach to the evaluation and correction of volumetric errors of the technological and measuring machines with different kinematic schemes, it is proposed to use the concepts of differential geometry. We develop a&#xa0;method intended for the evaluation and correction of the errors of two-dimensional coordinate measuring systems. This method is based on concepts of differential geometry; geometric errors are understood as discrepancies between the coordinates recorded by the reference system of the measuring system (digital coordinates) and the actual coordinates of the same point. Note that the indicated sets of coordinates are connected by a&#xa0;transformation described with the help of a&#xa0;Jacobian matrix. The proposed method includes the determination of elements of the Jacobian matrix according to the results of measuring of the positioning errors, deviations from rectilinearity, angular deviations, and deviations from the mutual perpendicularity of the axes carried out with the help of an XL-80 laser interferometer (Renishaw, UK). In the case of correction of the errors by the developed method, we applied numerical differentiation and integration, as well as a&#xa0;moving-average filter to minimize random noise. The method was experimentally validated by using a&#xa0;computerized universal measuring microscope (UIM-21). We experimentally establish a&#xa0;substantial decrease in the spread of measurement data after correction, which confirms that the geometric error decreases. The application of the developed correction method makes it possible to reduce the time and the costs of adjustment of the coordinate measuring systems and to adapt the computational procedures and the software developed by the authors for the purposes of the current investigation to different configurations of coordinate measuring systems. The results of the performed theoretical and experimental investigations not only guarantee an increase in the accuracy of in-plane measurement of the geometric parameters but also enable us to extend the proposed method for the evaluation and correction of errors to more complicated multicoordinate measuring systems.</p>

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Estimation and correction of geometric errors in the two-dimensional moving structures of coordinate measuring machines

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • D. A. Masterenko,
  • Tran Ngoc Anh,
  • V. A. Sokolov

摘要

We consider available approaches to elevation of the volumetric accuracy in the design and operation of coordinate measuring systems. At present, there exist numerous methods aimed at the evaluation and correction of volumetric errors developed for the technological and measuring machines with specific kinematic schemes but there is no universal method suitable for different coordinate measuring systems. To get a unified methodical approach to the evaluation and correction of volumetric errors of the technological and measuring machines with different kinematic schemes, it is proposed to use the concepts of differential geometry. We develop a method intended for the evaluation and correction of the errors of two-dimensional coordinate measuring systems. This method is based on concepts of differential geometry; geometric errors are understood as discrepancies between the coordinates recorded by the reference system of the measuring system (digital coordinates) and the actual coordinates of the same point. Note that the indicated sets of coordinates are connected by a transformation described with the help of a Jacobian matrix. The proposed method includes the determination of elements of the Jacobian matrix according to the results of measuring of the positioning errors, deviations from rectilinearity, angular deviations, and deviations from the mutual perpendicularity of the axes carried out with the help of an XL-80 laser interferometer (Renishaw, UK). In the case of correction of the errors by the developed method, we applied numerical differentiation and integration, as well as a moving-average filter to minimize random noise. The method was experimentally validated by using a computerized universal measuring microscope (UIM-21). We experimentally establish a substantial decrease in the spread of measurement data after correction, which confirms that the geometric error decreases. The application of the developed correction method makes it possible to reduce the time and the costs of adjustment of the coordinate measuring systems and to adapt the computational procedures and the software developed by the authors for the purposes of the current investigation to different configurations of coordinate measuring systems. The results of the performed theoretical and experimental investigations not only guarantee an increase in the accuracy of in-plane measurement of the geometric parameters but also enable us to extend the proposed method for the evaluation and correction of errors to more complicated multicoordinate measuring systems.