Skip to main content
SpringerLink
Log in

Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, two new interpolation algorithms for CNC machining along curved tool pathes are proposed: a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds “under” the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cheng C W and Tsai M C, Real-time variable feed rate NURBS curve interpolator for CNC machining, The International Journal of Advanced Manufacturing Technology, 2004, 23(11–12): 865–873.

    Google Scholar 

  2. Fan W, Gao X S, Yan W, and Yuan C M, Interpolation of parametric CNC machining path under confined jounce, The International Journal of Advanced Manufacturing Technology, 2012, 62(5): 719–739.

    Article  Google Scholar 

  3. Farouki R T and Tsai Y F, Exact Taylor series coefficients for variable-feedrate CNC curve interpolators, Computer-Aided Design, 2001, 33(2): 155–165.

    Article  Google Scholar 

  4. Yau H T, Lin M T, and Tsai M S, Real-time NURBS interpolation using FPGA for high speed motion control, Computer-Aided Design, 2006, 38(10): 1123–1133.

    Article  Google Scholar 

  5. Bobrow J E, Dubowsky S, and Gibson J S, Time-optimal control of robotic manipulators along specified paths, Int. J. Robot. Res., 1985, 4(3): 3–17.

    Article  Google Scholar 

  6. Shiller Z, On singular time-optimal control along specified paths, IEEE Trans. Robot. Autom., 1994, 10: 561–566.

    Article  Google Scholar 

  7. Timar S D, Farouki R T, Smith T S, and Boyadjieff C L, Algorithms for time-optimal control of CNC machines along curved tool paths, Robotics and Computer-Integrated Manufacturing, 2005, 21(1): 37–53.

    Article  Google Scholar 

  8. Timar S D and Farouki R T, Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds, Robotics and Computer-Integrated Manufacturing, 2007, 23(5): 563–579.

    Article  Google Scholar 

  9. Zhang M, Yan W, Yuan C M, Wang D, and Gao X S, Curve fitting and optimal interpolation on CNC machines based on quadratic B-splines, Science China, Series E, 2011, 54(7): 1407–1418.

    MathSciNet  Google Scholar 

  10. Zhang K, Gao X S, Li H, and Yuan C M, A greedy algorithm for feed-rate planning of CNC machines along curved tool paths with confined jerk for each axis, Robotics and Computer Integrated Manufacturing, 2012, 28: 472–483.

    Article  Google Scholar 

  11. Lee A C, Lin M T, Pana Y R, and Lin W Y, The feedrate scheduling of NURBS interpolator for CNC machine tools, Computer-Aided Design, 2011, 43: 612–628.

    Article  Google Scholar 

  12. Tsai M S, Nien H W, and Yau H T, Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery, Computer-Aided Design, 2008, 40: 554–566.

    Article  Google Scholar 

  13. Yong T and Narayanaswami R, A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining, Computer-Aided Design, 2003, 35: 1249–1259.

    Article  Google Scholar 

  14. Müllera M, Erdós G, and Xirouchakis P, High accuracy spline interpolation for 5-axis machining, Computer-Aided Design, 2004, 36: 1379–1393.

    Article  Google Scholar 

  15. Dong J Y, Ferreiraa P M, and Stori J A, Feedrate optimization with jerk constraints for generating minimum-time trajectories, Int. J. of Mach. Tools. and Manu., 2007, 47: 1941–1955.

    Article  Google Scholar 

  16. Erkorkmaz K and Altintas Y, High speed CNC system design. Part I: Jerk limited trajectory generation and quintic spline interpolation, Int. J. of Mach. Tools. and Manu., 2001, 41: 1323–1345.

    Article  Google Scholar 

  17. Gasparetto A, Lanzutti A, Vidoni R, and Zanotto V, Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning, Robotics and Computer-Integrated Manufacturing, 2012, 28: 164–181.

    Article  Google Scholar 

  18. Sencer B, Altintas Y, and Croft E, Feed optimization for five-axis CNC machine tools with drive constraints, Int. J. of Mach. Tools. and Manu., 2008, 48: 733–745.

    Article  Google Scholar 

  19. Emami M M and Arezoo B, A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length, Computer-Aided Design, 2010, 4(7): 625–632.

    Article  Google Scholar 

  20. Jeong S Y, Choi Y J, and Park P, Parametric interpolation using sampled data, Computer-Aided Design, 2006, 38: 39–47.

    Article  Google Scholar 

  21. Lai J Y, Lin K Y, Tseng S J, and Ueng W D, On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk, Int. J. of Mach. Tools. and Manu., 2008, 37: 104–121.

    Google Scholar 

  22. Nam S H and Yang M Y, A study on a generalized parametric interpolator with real-time jerklimited acceleration, Computer-Aided Design, 2004, 36: 27–36.

    Article  Google Scholar 

  23. Yeh S S and Hsu P L, Adaptive-feedrate interpolation for parametric curves with a confined chord error, Computer-Aided Design, 2002, 34: 229–237.

    Article  Google Scholar 

  24. Beudaert X, Lavernhe X, and Tournier C, Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path, Int. J. of Mach. Tools and Manu., 2012, 57: 73–82.

    Article  Google Scholar 

  25. Suh S H, Kang S K, Chung D H, and Stroud I, Theory and Design of CNC Systems, Springer, London, 2008.

    MATH  Google Scholar 

  26. Farouki R T, Pythagorean-Hodograph Curves, Springer-Verlag, Berlin, Heidelberg, 2008.

    Book  MATH  Google Scholar 

  27. Birkhoff G and Rota G, Ordinary Differential Equations, New York, Blaisdell, 1969.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Chunming Yuan, Ke Zhang & Wei Fan

Authors
  1. Chunming Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunming Yuan.

Additional information

This research was supported by a National Key Basic Research Project of China under Grant No. 2011CB302400 and by the National Natural Science Foundation of China under Grant No. 60821002.

This paper was recommended for publication by Guest Editor LI Hongbo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yuan, C., Zhang, K. & Fan, W. Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error. J Syst Sci Complex 26, 836–870 (2013). https://doi.org/10.1007/s11424-013-3180-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-013-3180-4

Keywords

Search

Navigation