Skip to main content
SpringerLink
Log in

Research on adaptive non-uniform rational B-spline real-time interpolation technology based on acceleration constraints

The International Journal of Advanced Manufacturing Technology volume 91, pages 2089–2100 (2017)Cite this article

Abstract

In order to solve the problems of low machining precision and efficiency in machining complicated parametric curves in traditional computer numeric control systems, non-uniform rational B-spline (NURBS) real-time interpolation was studied. Considering the problem of feed speed fluctuation in a traditional NURBS interpolation method, the adaptive correction interpolation algorithm that is proposed corrects the calculational accuracy of the next interpolation point parameter value, and the correction time is mutated adaptively according to the length of the interpolation precision and interpolation cycle. This approach is based on the premise that the interpolation cycle will improve the correction accuracy as much as possible, thereby minimizing the interpolation feed speed fluctuation. To mitigate the problem of a large number of calculations and high calculational complexity in feed speed planning of NURBS real-time interpolation, we use a velocity planning algorithm based on a feed speed pretreatment curve; thus, the interpolation feed velocity planning tasks are completed on a non-real-time cycle, the maximum acceleration and jerk requirements of the machine tool are fully considered, and each interpolation point is planned during the speed planning period, which avoids the use of a complex planning algorithm and obtains a smoother velocity curve. Finally, the correctness and effectiveness of the proposed approach were verified by simulation.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

References

  1. Emami MM, Arezoo B (2010) A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length. Comput Aided Des 42(7):625–632

    Article  Google Scholar 

  2. Lin MT, Tsai MS, Yau HT (2007) Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm. Int J Mach Tools Manuf 47(15):2246–2262

    Article  Google Scholar 

  3. Liu X, Ahmad F, Yamazaki K, Mori M (2005) Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics. Int J Mach Tools Manuf 45(4):433–444

    Article  Google Scholar 

  4. Wang JB, Yau HT (2009) Real-time NURBS interpolator: application to short linear segments. Int J Adv Manuf Technol 41(11–12):1169–1185

    Article  Google Scholar 

  5. Lin KY, Ueng WD, Lai JY (2008) CNC codes conversion from linear and circular paths to NURBS curves. Int J Adv Manuf Technol 39(7–8):760–773

    Article  Google Scholar 

  6. Koren Y, Lo CC, Shpitalni M (1993) CNC interpolators: algorithms and analysis. ASME PROD ENG DIV PUBL PED, ASME, NEW YORK, NY,(USA), 1993 64:83–92

    Google Scholar 

  7. Cheng MY, Tsai MC, Kuo JC (2002) Real-time NURBS command generators for CNC servo controllers. Int J Mach Tools Manuf 42(7):801–813

    Article  Google Scholar 

  8. Lei WT, Sung MP, Lin LY, Huang JJ (2007) Fast real-time NURBS path interpolation for CNC machine tools. Int J Mach Tools Manuf 47(10):1530–1541

    Article  Google Scholar 

  9. Wu J, Zhou H, Tang X, Chen J (2012) A NURBS interpolation algorithm with continuous feedrate. Int J Adv Manuf Technol 59(5–8):623–632

    Article  Google Scholar 

  10. Tsai MC, Cheng CW (2003) A real-time predictor-corrector interpolator for CNC machining. J Manuf Sci Eng 125(3):449–460

    Article  Google Scholar 

  11. Wang Y, Yang D, Liu Y (2014) A real-time look-ahead interpolation algorithm based on Akima curve fitting. Int J Mach Tools Manuf 85:122–130

    Article  Google Scholar 

  12. Tsai MS, Nien HW, Yau HT (2011) Development of integrated acceleration/deceleration look-ahead interpolation technique for multi-blocks NURBS curves. Int J Adv Manuf Technol 56(5–8):601–618

    Article  Google Scholar 

  13. Wang Y, Yang D, Gai R, Wang S, Sun S (2015) Design of trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation. Int J Mach Tools Manuf 96:94–105

    Article  Google Scholar 

  14. De Boor C, De Boor C, Mathématicien EU, De Boor C, De Boor C (2001) A practical guide to splines (Vol. 27, p. 325). Springer-Verlag, New York

    MATH  Google Scholar 

  15. Jianxin J (2000) Prearranged step interpolation method for random-space-curve in CNC machine-tool-system. Chinese Journal of Mechanical Engineering 36(4):95–97

    Article  Google Scholar 

  16. Wang GX, Shu QL, Wang J, Wang WS (2012) Algorithm of fast evaluation and derivation for the technique of NURBS direct interpolation. Journal of Northeastern University (Natural Science) 7:028

    Google Scholar 

  17. Xinhua, L., Junquan, P., Lei, S., & Zhongbin, W. (2016). A novel approach for NURBS interpolation through the integration of acc-jerk-continuous-based control method and look-ahead algorithm. The International Journal of Advanced Manufacturing Technology, 1–9

  18. Wang X, Wang J, Rao Z (2010) An adaptive parametric interpolator for trajectory planning. Adv Eng Softw 41(2):180–187

    Article  MATH  Google Scholar 

  19. Wu J, Zhou H, Tang X, Chen J (2012) Fast NURBS interpolation based on the biarc guide curve. Int J Adv Manuf Technol 58(5–8):597–605

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Shenyang Ligong University, Shenyang, People’s Republic of China

    Guoxun Wang, Qinlin Shu & Jun Wang

  2. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110159, People’s Republic of China

    Li Li

Authors
  1. Guoxun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qinlin Shu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guoxun Wang.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, G., Shu, Q., Wang, J. et al. Research on adaptive non-uniform rational B-spline real-time interpolation technology based on acceleration constraints. Int J Adv Manuf Technol 91, 2089–2100 (2017). https://doi.org/10.1007/s00170-016-9914-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-016-9914-4

Keywords

search

Navigation