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Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming

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Abstract

In this paper, the time-optimal velocity planning problem for five-axis computer numerical control machining along a given parametric tool path under chord error, acceleration, and jerk constraints is studied. The velocity planning problem under confined chord error, feedrate, and acceleration is reduced to an equivalent linear programming problem by discretizing the tool path and other quantities. As a consequence, a polynomial time algorithm with computational complexity O(N 3.5) is given to find the optimal solution, where N is the number of discretized segments of the tool path. The velocity planning problem under confined chord error, feedrate, acceleration, and jerk is reduced to a linear programming program by using a linear function to approximate the nonlinear jerk constraint. As a consequence, a polynomial time algorithm is given to find the approximate time-optimal solution. Simulation results are used to show the efficiency and effectiveness of the algorithms.

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Authors and Affiliations

  1. KLMM, Institute of Systems Science AMSS, Chinese Academy of Sciences, Beijing, 100190, China

    Wei Fan, Xiao-Shan Gao, Ke Zhang & Qiang Zhang

  2. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Wei Fan & Chen-Han Lee

  3. China University of Petroleum, Qingdao, 266555, China

    Qiang Zhang

Authors
  1. Wei Fan
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  2. Xiao-Shan Gao
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  3. Chen-Han Lee
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  4. Ke Zhang
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  5. Qiang Zhang
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Correspondence to Xiao-Shan Gao.

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Fan, W., Gao, XS., Lee, CH. et al. Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming. Int J Adv Manuf Technol 69, 1373–1388 (2013). https://doi.org/10.1007/s00170-013-5083-x

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  • DOI: https://doi.org/10.1007/s00170-013-5083-x

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