A general, fast and robust B-spline fitting scheme for micro-line tool path under chord error constraint

  • QingZhen BiEmail author
  • Jie Huang
  • YaoAn Lu
  • LiMin Zhu
  • Han Ding


The discontinuity of linear tool path (or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.


NC interpolation high speed machining micro-line segments path smoothing B-spline fitting 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • QingZhen Bi
    • 1
    Email author
  • Jie Huang
    • 1
  • YaoAn Lu
    • 2
  • LiMin Zhu
    • 1
  • Han Ding
    • 1
  1. 1.State Key Laboratory of Mechanical System and Vibration, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.School of Electromechanical EngineeringGuangdong University of TechnologyGuangzhouChina

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