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Correlation assessment and modeling of intra-axis errors of prismatic axes for CNC machine tools

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Abstract

This paper presents an experimental study conducted to assess the correlation between the intra-axis errors of prismatic axes for CNC machine tools. The validity and reliability of parametric models for the modeling of intra-axis errors (IAEs) of CNC machine tools in the context of indirect calibration are also assessed in this work. Three CNC machine tools with various controllers and guidance technologies were tested using two different measuring instruments. Two predictive models, namely Bézier and B-spline curves, are described and compared for the first time in this work. Both models are experimentally evaluated for accuracy and predictive efficiency using four evaluation criteria and new data sets from the three tested CNC machine tools. Results show a strong correlation between the positioning errors and the pitch and yaw errors for all the tested machines. The results also show that both proposed models are appropriate for the modeling of intra-axis errors, with the B-spline curves coming slightly on top in terms of performance. Moreover, with the same number of control points (n = 5), the two models provide residuals that are lower than the repeatability of the machine for most intra-axis errors tested. This experimental study thus confirms that a Bézier model of degree four and a B-spline model of degree two, both with five control points, are sufficient to represent the intra-axis errors for the tested CNC machine tools.

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Acknowledgements

The authors would like to thank Yan Boutin and Bu Khanh Vo, manufacturing engineers, for their assistance during the laboratory tests.

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Authors and Affiliations

  1. MMS Lab, Faculty of Technology, University of M’sila, M’Sila, Algeria

    Ahlem Mechta, Mohamed Slamani & Moussa Zaoui

  2. Mechanical Engineering Department, École de technologie supérieure, Montreal, Canada

    Mohamed Slamani & Jean-François Chatelain

  3. Mechanical Engineering Department, École Polytechnique de Montréal, Montreal, Canada

    René Mayer

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  1. Ahlem Mechta
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  2. Mohamed Slamani
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Contributions

AM was responsible for the literature study, data analysis, and writing the paper. MS was the supervisor of this work. He proposed the research idea, technical scheme, and all needed support conditions. He has also participated in data analysis and was responsible for completing the article. MZ was involved in the discussion and data analysis. RM and J-FC were involved in the discussion and significantly contributed to making the final draft of the article. All the authors read and approved the final manuscript.

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Correspondence to Mohamed Slamani.

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Appendix

Appendix

Table 8 Estimated control points of the Bezier (Bz) and B-spline (Bs) models for the intra-axis errors (IAEs) in the forward direction of the X-axis of the Matsuura machine tool
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Table 9 Estimated control points of the Bezier (Bz) and B-spline (Bs) models for the intra-axis errors in the backward direction of the X-axis of the Matsuura machine tool
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Table 10 Estimated control points of the Bezier (Bz) and B-spline (Bs) models for the intra-axis errors in the forward direction of the Y-axis of the Matsuura machine tool
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Table 11 Estimated control points of the Bezier (Bz) and B-spline (Bs) models for the intra-axis errors in the backward direction of the Y-axis of the Matsuura machine tool
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Table 12 Estimated control points of the Bezier (Bz) and B-spline (Bs) models for the intra-axis errors in the forward direction of the Z-axis of the Matsuura machine tool
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Table 13 Estimated control points of the Bezier (Bz) and B-spline (Bs) models for the intra-axis errors in the backward direction of the Z-axis of the Matsuura machine tool
Full size table

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Mechta, A., Slamani, M., Zaoui, M. et al. Correlation assessment and modeling of intra-axis errors of prismatic axes for CNC machine tools. Int J Adv Manuf Technol 120, 5093–5115 (2022). https://doi.org/10.1007/s00170-022-09074-7

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