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Thermal error is one of the significant motion errors in machine tools. It is often evaluated in terms of the relative displacement between the tool and the workpiece. However, relying solely on relative displacement measurements fails to capture the individual thermal deformations of the tool and workpiece, which can lead to incomplete or inaccurate understanding of the thermal error mechanisms. In contrast, vision-based measurements, using multiple target markers, allow for the evaluation of the absolute displacements of both the tool and workpiece. This approach provides a more comprehensive understanding of thermal error mechanisms. However, achieving sufficient accurate measurements in machine tools requires highly accurate camera calibration. In vision-based measurements, to ensure accurate transformations between world and image coordinates, the camera's intrinsic and extrinsic parameters must first be determined before measuring 3D positions. This study aims to determine the necessary calibration accuracy for vision-based thermal error measurements. The impact of error factors in camera calibration on measurement accuracy is investigated by Monte Carlo simulations and experiments. The simulations assessed the influence of the calibration board accuracy and the accuracy in the board pattern detection. Furthermore, experiments were conducted using different calibration patterns to estimate camera parameters, and the resulting measurement accuracy with calibrated images was compared. The Monte Carlo simulation results revealed that a board error of less than 1 µm and a detection error of less than 0.01 pixel are necessary to achieve the required measurement accuracy. Furthermore, the simulation results indicated that using more than 200 feature points is preferable to achieve a sufficient averaging effect in calibration. Experimental results showed that the calibration boards used in the experiment could not achieve the target measurement accuracy due to insufficient accuracy in both the board error and detection error. Additionally, enlarging the board size relative to the field of view improved the estimation accuracy of the higher-order coefficients of radial distortion, contributing to higher calibration accuracy.

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Necessary Camera Calibration Accuracy for Vision-Based Thermal Error Measurement in Machine Tools

  • 会议论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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  • Eri Tsuchiya,
  • Shunsuke Ohmae,
  • Daisuke Kono

摘要

Thermal error is one of the significant motion errors in machine tools. It is often evaluated in terms of the relative displacement between the tool and the workpiece. However, relying solely on relative displacement measurements fails to capture the individual thermal deformations of the tool and workpiece, which can lead to incomplete or inaccurate understanding of the thermal error mechanisms. In contrast, vision-based measurements, using multiple target markers, allow for the evaluation of the absolute displacements of both the tool and workpiece. This approach provides a more comprehensive understanding of thermal error mechanisms. However, achieving sufficient accurate measurements in machine tools requires highly accurate camera calibration. In vision-based measurements, to ensure accurate transformations between world and image coordinates, the camera's intrinsic and extrinsic parameters must first be determined before measuring 3D positions. This study aims to determine the necessary calibration accuracy for vision-based thermal error measurements. The impact of error factors in camera calibration on measurement accuracy is investigated by Monte Carlo simulations and experiments. The simulations assessed the influence of the calibration board accuracy and the accuracy in the board pattern detection. Furthermore, experiments were conducted using different calibration patterns to estimate camera parameters, and the resulting measurement accuracy with calibrated images was compared. The Monte Carlo simulation results revealed that a board error of less than 1 µm and a detection error of less than 0.01 pixel are necessary to achieve the required measurement accuracy. Furthermore, the simulation results indicated that using more than 200 feature points is preferable to achieve a sufficient averaging effect in calibration. Experimental results showed that the calibration boards used in the experiment could not achieve the target measurement accuracy due to insufficient accuracy in both the board error and detection error. Additionally, enlarging the board size relative to the field of view improved the estimation accuracy of the higher-order coefficients of radial distortion, contributing to higher calibration accuracy.