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Variable feedrate interpolation of NURBS Toolpath with geometric and kinematical constraints for five-axis CNC machining

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Abstract

Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promising but still rather limited currently. In this paper, an off-line feedrate scheduling method of dual NURBS curve is presented with geometric and kinematical constraints. For a given dual parametric curve, the feedrates of sampling points are first scheduled sequent with confined feedrate of cutter tip and machine pivot, chord error, normal acceleration and angular feedrate. Then, the feedrate profiles of angular feed acceleration sensitive regions of the path are adjusted using a bi-directional scanning algorithm. After that, a linear programming method is used to adjust the feedrate profiles of linear feed acceleration sensitive regions and control the linear feed acceleration of both cutter tip and machine pivot within preset values. Further, a NURBS curve is used to fit the feedrates of sampling points. Finally, illustrative examples are carried out to validate the feasibility of the proposed feedrate scheduling method. The results show that the proposed method has the ability of effectively controlling the angular feed characters of cutter axis as well as the chord error and linear feed characters of cutter tip and machine pivot, and it has potential to be used in high accuracy and high quality five-axis machining.

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References

  1. Guo D M, Function-geometry integrated precision machining methods and technologies for high performance workpieces, Engineering Science, 2011, 13(10): 47–57 (in Chinese).

    Google Scholar 

  2. Geng C, Yu D, Zheng L M, Zhang H, and Wang F, A tool path correction and compression algorithm for five-axis CNC machining, Journal of Systems Science and Complexity, 2013, 26(5): 799–816.

    Article  Google Scholar 

  3. Guo J X, Zhang Q, and Gao X S, Tracking error reduction in CNC machining by reshaping the kinematic trajectory, Journal of Systems Science and Complexity, 2013, 26(5): 817–835.

    Article  Google Scholar 

  4. Zhang X J, Xiong C H, Ding Y, and Xiong Y L, Variable-step integration method for milling chatter stability prediction with multiple delays, Science China Technological Sciences, 2011, 54(12): 3137–3154.

    Article  MATH  Google Scholar 

  5. Zhao J B, Zhong B, Zou Q, and Liu H J, Tool axis orientation planning for five-axis CNC machining of open free-form surfaces, Journal of Systems Science and Complexity, 2013, 26(5): 667–675.

    Article  Google Scholar 

  6. Zhang L X, Sun R Y, Gao X S, and Li H B, High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining, Science China Technological Sciences, 2011, 54(6): 1481–1495.

    Article  Google Scholar 

  7. Yau H T and Wang J B, Fast Bezier interpolator with real-time look-ahead function for highaccuracy machining, International Journal of Machine Tools and Manufacture, 2007, 47(10): 1518–1529.

    Article  Google Scholar 

  8. Lartigue C, Thiebaut F, and Maekawa T, CNC tool path in terms of B-spline curves, Computer-Aided Design, 2001, 33(4): 307–319.

    Article  Google Scholar 

  9. Tsai Y F, Farouki R T, and Feldman B, Performance analysis of CNC interpolators for timedependent feedrates along PH curves, Computer Aided Geometric Design, 2001, 18(3): 245–265.

    Article  MathSciNet  MATH  Google Scholar 

  10. Yeh S S and Hsu P L, Adaptive-feedrate interpolation for parametric curves with a confined chord error, Computer-Aided Design, 2002, 34(3): 229–237.

    Article  MathSciNet  Google Scholar 

  11. Zhang L, Bian Y, Chen H, and Wang K, Implementation of a CNC NURBS curve interpolator based on control of speed and precision, International Journal of Production Research, 2009, 6: 1505–1519.

    Article  Google Scholar 

  12. Liu Q, Jin X J, and Long Y H, A real-time high-precision interpolation algorithm for generaltyped parametric curves in CNC machine tools, International Journal of Computer Integrated Manufacturing, 2010, 23(2): 168–176.

    Article  Google Scholar 

  13. Sun Y W, Jia Z Y, Ren F, and Guo D M, Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties, The International Journal of Advanced Manufacturing Technology, 2008, 36(1–2): 60–68.

    Article  Google Scholar 

  14. Conway J R, Darling A L, Ernesto C A, Farouki R T, and Christine A, Palomares experimental study of contouring accuracy for CNC machines executing curved paths with constant and curvature-dependent feedrates, Robotics and Computer-Integrated Manufacturing, 2013, 29(2): 357–369.

    Article  Google Scholar 

  15. Tikhon M, Ko T J, Lee S H, and Kim H S, NURBS interpolator for constant material removal rate in open NC machine tools, International Journal of Machine Tools and Manufacture, 2004, 44(2–3): 237–245.

    Article  Google Scholar 

  16. Lotfi B, Zhong Z W, Khoo L P, Variable feed rates and variable machine forces for a constant material removal rate and constant cutting force along Pythagorean-hodograph curves, The International Journal of Advanced Manufacturing Technology, 2009, 40(1–2): 171–178.

    Article  Google Scholar 

  17. Heng M and Erkorkmaz K, Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability, International Journal of Machine Tools and Manufacture, 2010, 50(3): 281–293.

    Article  Google Scholar 

  18. Wu J C, Zhou H C, Tang X Q, and Chen J H, Fast NURBS interpolation based on the biarc guide curve, The International Journal of Advanced Manufacturing Technology, 2012, 58(5–8): 597–605.

    Article  Google Scholar 

  19. 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 

  20. Lin M T, Tsai M S, and Yau H T, Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm, International Journal of Machine Tools and Manufacture, 2007, 47(15): 2246–2262.

    Article  Google Scholar 

  21. Liu X B, Ahmad F, Yamazaki K Z, and Mori M, Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics, International Journal of Machine Tools and Manufacture, 2005, 45(4–5): 433–444.

    Article  Google Scholar 

  22. Lee A C, Lin M Z, Pan Y R, and Lin W Y, The feedrate scheduling of NURBS interpolator for CNC machine tools, Computer-Aided Design, 2011, 43(6): 612–628.

    Article  Google Scholar 

  23. Sarma R and Rao A, Discretizors and interpolators for five-axis CNC machines, Transactions of the ASME, Journal of Manufacturing Science and Engineering, 2000, 122(2): 191–197.

    Article  Google Scholar 

  24. Dong J Y, Ferreira P M, and Stori J A, Feed-rate optimization with jerk constraints for generating minimum-time trajectories, International Journal of Machine Tools and Manufacture, 2007, 47: 1941–1955.

    Article  Google Scholar 

  25. 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 

  26. Li H B, Geometric error control in the parabola-blending linear interpolator, Journal of Systems Science and Complexity, 2013, 26(5): 777–798.

    Article  MATH  MathSciNet  Google Scholar 

  27. Fleisig R V and Spence A D, A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining, Computer-Aided Design, 2001, 33(1): 1–15.

    Article  Google Scholar 

  28. Muller M, Erdos G, and Xirouchakis P, High accuracy spline interpolation for 5-axis machining, Computer-Aided Design, 2004, 36(13): 1379–1393.

    Article  Google Scholar 

  29. Langeron J M, Duc E, Lartigue C, and Bourdet P, A new format for 5-axis tool path computation using Bspline curves, Computer-Aided Design, 2004, 36(12): 1219–1229.

    Article  Google Scholar 

  30. Qiao Z F, Wang T Y, Wang Y F, Hu M, and Liu Q J, Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining, International Journal of Machine Tools and Manufacture, 2012, 53: 107–117.

    Article  Google Scholar 

  31. Chu C H, Huang WN, and Hsu Y Y, Machining accuracy improvement in five-axis flank milling of ruled surfaces, International Journal of Machine Tools and Manufacture, 2008, 48(7–8): 914–921.

    Article  Google Scholar 

  32. Xu H Y, Zhou Y H, and Zhang J J, Angular interpolation of bi-parameter curves, Computer-Aided Design, 2003, 35(13): 1211–1220.

    Article  Google Scholar 

  33. Sun Y W, Bao Y R, Kang K X, and Guo D M, An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining, The International Journal of Advanced Manufacturing Technology, 2013, doi: 10.1007/s00170-013-4816-1.

    Google Scholar 

  34. Sencer B, Altintas Y, and Croft E, Feed optimization for five-axis CNC machine tools with drive constraints, International Journal of Machine Tools and Manufacture, 2008, 48(7–8): 733–745.

    Article  Google Scholar 

  35. Zhang K, Yuan C M, and Gao X S, Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration, The International Journal of Advanced Manufacturing Technology, 2012, 66(9–12): 1685–1697.

    Google Scholar 

  36. 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(5–8): 719–739.

    Article  Google Scholar 

  37. Zhang K, Yuan C M, Gao X S, and Li H B, A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk, Robotics and Computer-Integrated Manufacturing, 2012, 28(4): 472–483.

    Article  Google Scholar 

  38. Yuan C M, Zhang K, Fan W, and Gao X S, Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error, Journal of Systems Science and Complexity, 2013, 26(5): 836–870.

    Article  MathSciNet  Google Scholar 

  39. Fan W, Gao X S, and Zhang K, Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming, MM-Preprints, 2012, 31: 21–42.

    Google Scholar 

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Correspondence to Yuwen Sun.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 51075054 and 11290143, and the National Basic Research Program of China under Grant No. 2011CB716800.

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

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Sun, Y., Zhou, J. & Guo, D. Variable feedrate interpolation of NURBS Toolpath with geometric and kinematical constraints for five-axis CNC machining. J Syst Sci Complex 26, 757–776 (2013). https://doi.org/10.1007/s11424-013-3177-z

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  • DOI: https://doi.org/10.1007/s11424-013-3177-z

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