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Six-dimensional B-spline fitting method for five-axis tool paths

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Abstract

Piecewise linear segments (presented by a sequence of G01 G-Codes) are the widely adopted tool path format for five-axis computer numerical control (CNC) machining. Nevertheless, the G01 tool path has only G0 continuity, which may lead to feedrate and acceleration fluctuation, and produce machinery vibration and unexpected slowdowns during the process. Thus, tool path smoothing method such as B-spline fitting is developed to increase the continuity of the tool paths. This work proposes a six-dimensional B-spline fitting method with arc-length parameterization and quality evaluation/refinement for five-axis tool paths. First, establish the relationship of cutter contact (CC) error, and cutter location (CL) error and tool-axis error to ensure that the CC error of five-axis B-spline tool path can be accurately computed. Second, six-dimensional B-spline tool paths generated by three-axis B-spline fitting method in six-dimensional space are parameterized with arc-length, satisfying the stability condition of tool axis. Third, the chord errors of the fitted six-dimensional B-spline tool paths are computed using the Hausdorff distance. The chord error computation, smoothness assessment, and refinement algorithm are performed together to ensure the fitting quality. The simulation result demonstrates that the proposed six-dimensional fitting method is effective and suitable for five-axis blade machining, and the evaluation/refinement algorithm can ensure that the five-axis B-spline tool paths are shape-preserving strictly and satisfy the chord error constraint. The experimental results show that the proposed six-dimensional fitting method improves the machining quality and is suitable for industrial applications.

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Acknowledgments

The authors gratefully acknowledge the help of Jie Qin and Haiqing Jiang.

Funding

The project is supported by the National Natural Science Foundation of China (Nos. 51575386, 61605182), and National Science and Technology Major Project of the Ministry of Science and Technology of China (No. 2013ZX04007-041).

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Authors and Affiliations

  1. Huazhong University of Science and Technology, Wuhan, China

    Kang Min, Chen-Han Lee & Pengcheng Hu

  2. Wuhan Institute of Technology, Wuhan, China

    Chen-Han Lee & Changya Yan

  3. Institute of Mechanical and Manufacturing Technology, China Academy of Engineering Physics, Chengdu, China

    Wei Fan

Authors
  1. Kang Min
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  2. Chen-Han Lee
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  3. Changya Yan
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  4. Wei Fan
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  5. Pengcheng Hu
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Correspondence to Changya Yan.

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Min, K., Lee, CH., Yan, C. et al. Six-dimensional B-spline fitting method for five-axis tool paths. Int J Adv Manuf Technol 107, 2041–2054 (2020). https://doi.org/10.1007/s00170-020-05139-7

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  • DOI: https://doi.org/10.1007/s00170-020-05139-7

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