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Ball End Mill—Tool Radius Compensation of Complex NURBS Surfaces for 3-Axis CNC Milling Machines

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Abstract

In order to extend the 2D-TRC (tool radius compensation) function of 3-axis CNC milling machines to ball end mills (BEMs), a new TRC named BEM-TRC is proposed to achieve successful milling of complex surfaces without over-cut. The implementation of the BEM-TRC for complex surfaces depicted in NURBS model is divided into three steps. The first one is to search the cutting point (CP) on a NURBS surface using equi-arc length interpolation in u or v direction. The second one is to accomplish BEM-TRC at the CP through offsetting the CP to the cutter center point (CCP) of a BEM along the normal vector at CP. The third one is to compute the cutter location point (CLP) of the BEM according to the BEM-CCP. The simulation and experiment verifies that the BEM-TRC is feasible and effective, and can avoid over-cut phenomenon successfully. The BEM-TRC extends the ability of the traditional 2D-TRC function, and makes 3-axis CNC milling machines to accomplish the milling process of complex NURBS surfaces.

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Acknowledgements

This project is supported by National Science and Technology Major Project (2017-VII-0003–0096-4, 2017-VII-0012–0108), National Natural Science Foundation of China (Grant no. 51764038 and 51465030), Gansu Science and Technology Planning Project (17YF1GA018, 17CX1JA117, and 18JR3RA132), Western Young Scholars of Chinese Academy of Sciences, Lanzhou Talent Innovation and Entrepreneurship Project (2019-RC-102 and 2018-RC-108), Longyuan Youth Innovative and Entrepreneurial Talents Project, Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University, and Gansu Provincial Employee Technology Innovation Subsidy Fund Project.

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Authors and Affiliations

  1. School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou, 730010, China

    Zhaoqin Wang, Xiaorong Wang & Yusen Wang

  2. Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment of Gansu Province, Lanzhou Jiaotong University, Lanzhou, 730010, China

    Zhaoqin Wang & Xiaorong Wang

  3. State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals, Lanzhou University of Technology, Lanzhou, 730050, China

    Zhaoqin Wang

  4. Beijing JinLunKunTian Special Machine Co. LTD., Beijing, 100083, China

    Ruijun Wang & Manyu Bao

  5. State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, 150001, China

    Tiesong Lin & Peng He

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  1. Zhaoqin Wang
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  2. Xiaorong Wang
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  3. Yusen Wang
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  4. Ruijun Wang
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  5. Manyu Bao
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  6. Tiesong Lin
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  7. Peng He
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Correspondence to Zhaoqin Wang or Xiaorong Wang.

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Appendix A

Appendix A

The parameters of P, w, U, V, p and q for the NURBS surface shown in Fig. 2 are listed as follows. P is control point, w is weight, U and V are kont vectors, and p and q is degree.

  • P = {[30 0 0], [30 − 30 0] , [0 − 30 0], [− 30 − 30 0], [− 30 0 0], [− 30 30 0], [0 30 0], [30 30 0], [30 0 0]; [26 0 3], [26 − 26 3], [0 − 26 3], [− 27 − 27 1], [− 27 0 1], [− 27 27 1], [0 26 3], [26 26 3], [26 0 3]; [24 0 3], [24 − 24 3], [0 − 22 3], [− 24 − 24 3], [− 24 0 3], [− 24 24 3], [0 22 3], [24 24 3],[24 0 3];

  • [21 0 4], [ 21 − 21 4], [0 − 18 4], [− 21 − 21 4], [− 21 0 4], [− 21 21 4], [0 18 4], [21 21 4], [21 0 4]; [19 0 4], ]19 − 19 4],[0 − 14 4], [− 18 − 18 4], [− 18 0 4], [− 18 18 4],[0 14 4],[19 19 4],[19 0 4]; [15 0 3.5],[15 − 15 3.5], [0 − 10 3.5], [− 15 − 15 3.5], [− 15 0 3.5], [− 15 15 3.5],[0 10 3.5],[15 15 3.5],[15 0 3.5]; [12 0 3],[12 − 12 3], [0 − 7 3], [− 12 − 12 3], [− 12 0 3], [− 12 12 3],[0 7 3],[12 12 3],[12 0 3]; [7 0 2], [7 − 7 2],[0 − 4 2], [− 9 − 9 2], [− 9 0 2], [− 9 9 2], [0 4 2], [7 7 2], [7 0 2]; [− 5 0 2], [− 5 0 2], [− 5 0 2], [− 5 0 2], [− 5 0 2], [− 5 0 2], [− 5 0 2], [− 5 0 2], [− 5 0 2]};

  • w = [1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1; 1 0.707 1 0.707 1 0.707 1 0.707 1];

  • U = [0 0 0 1/4 1/4 1/2 1/2 3/4 3/4 1 1 1];

  • V = [0 0 0 1/4 1/4 1/2 1/2 3/4 3/4 1 1 1];

  • p = 2;

  • q = 2.

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Wang, Z., Wang, X., Wang, Y. et al. Ball End Mill—Tool Radius Compensation of Complex NURBS Surfaces for 3-Axis CNC Milling Machines. Int. J. Precis. Eng. Manuf. 21, 1409–1419 (2020). https://doi.org/10.1007/s12541-020-00345-5

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  • DOI: https://doi.org/10.1007/s12541-020-00345-5

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