A NURBS interpolation algorithm with continuous feedrate

  • Jichun WuEmail author
  • Huicheng Zhou
  • Xiaoqi Tang
  • Jihong Chen


The high-speed precision machining of a part requires minimal feedrate fluctuation and contour error, and parametric spline interpolations have proven to be superior over linear and circular interpolations. However, parametric spline interpolations may result in large feedrate fluctuation due to an inaccurate mapping between the spline parameter u and the displacement S. This paper presents a non-uniform rational B-spline interpolation algorithm with compensatory parameter to minimize feedrate fluctuation and contour error. Since the cubic or quintic polynomials expressing the u-S mapping are acquired, they can be calculated by two consecutive interpolation points with the continuity condition. Thus, the parameter u can be calculated quickly and accurately by substituting the desired displacement S into the cubic or quintic polynomials. Simulation shows that the feedrate fluctuation of the proposed algorithm is much smaller than that of Taylor interpolation algorithms and Feed correction algorithm.


NURBS interpolation Feedrate fluctuation Contour error u-S modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ding GL (2008) Research on modeling and interpolation of the tool-path based on cylindrical helix spline. Dissertation, Huazhong University of Science and Technology.Google Scholar
  2. 2.
    Chen Y, Ni J, Wu S (1993) Real-time CNC tool path generation for machining IGES surface. ASME J Eng Ind 11:480–486CrossRefGoogle Scholar
  3. 3.
    Bedi S, Ali I, Quan N (1993) Advanced interpolation techniques for NC machines. Trans ASME J Eng Ind 115:329–336Google Scholar
  4. 4.
    Shpitalni M, Koren Y, Lo CC (1994) Realtime curve interpolators. Comput Aided Des 26(11):832–838zbMATHCrossRefGoogle Scholar
  5. 5.
    Yang DCH, Kong T (1994) Parametric interpolator versus linear interpolator for precision CNC machining. Comput Aided Des 26(3):225–234MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int J Mach Tools Manuf 41:1323–1345CrossRefGoogle Scholar
  7. 7.
    Yeh SS, Hsu PL (1999) The speed-controlled interpolator for machining parametric curves. Comput-Aided Des 31:349–357zbMATHCrossRefGoogle Scholar
  8. 8.
    Yeh SS, Hsu PL (2002) Adaptive-feedrate interpolation for parametric curves with a confined chord error. Comput-Aided Des 34(3):229–237MathSciNetCrossRefGoogle Scholar
  9. 9.
    Li W, Liu YD, Yamazaki K, Fujisima M, Mori M (2008) The design of a NURBS pre-interpolator for five-axis machining. Int J Adv Manuf Technol. doi: 10.1007/s00170-006-0905-8
  10. 10.
    Yong T, Narayanaswami R (2003) A parametric interpolator with confined chord errors, acceleration, deceleration for NC machining. Comput Aided Des 35:1249–1259CrossRefGoogle Scholar
  11. 11.
    Nam SH, Yang MY (2004) A study on a generalized parametric interpolator with real-time jerk-limited acceleration. Comput-Aided Des 36(1):27–36CrossRefGoogle Scholar
  12. 12.
    Xu RZ, Xie L, Li CX, Du DS (2008) Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining. Int J Adv Manuf Technol. doi: 10.1007/s00170-006-0834-6
  13. 13.
    Lin MT, Tsai MS (2006) Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm. Int J Mach Tools Manuf 46:235–242CrossRefGoogle Scholar
  14. 14.
    Tsai MS, Nien HW, Yau HT (2008) Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery. Comput-Aided Des 40:554–566CrossRefGoogle Scholar
  15. 15.
    Farouki RT, Tsai YF, Yuan GF (1999) Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Comput-Aided Geom Des 16:61–76MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Suna YW, Wang J, Guo D (2006) Guide curve based interpolation scheme of parametric curves for precision CNC machining. Int J Mach Tool Manufact 46:235–242CrossRefGoogle Scholar
  17. 17.
    Sun YW, Jia ZY, Ren F, Guo DM (2008) Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties. Int J Adv Manuf Technol. doi: 10.1007/s00170-006-0817-7
  18. 18.
    Wang JB, Yau HT (2009) Real-time NURBS interpolator: application to short linear segments. Int J Adv Manuf Technol 41:1169–1185CrossRefGoogle Scholar
  19. 19.
    Heng M, Erkorkmaz K (2009) Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability. Int J Mach Tools Manuf. doi: 10.1016/j.ijm achtools.2009.11.005
  20. 20.
    Erkorkmaz K, Altintas Y (2005) Quintic spline interpolation with minimal feed fluctuation. ASME J Manuf Sci Eng 127(2):339–349CrossRefGoogle Scholar
  21. 21.
    Liua X, Ahmada F, Yamazakia K, Morib M (2005) Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics. Int J Mach Tools Manuf 45:433–444CrossRefGoogle Scholar
  22. 22.
    Piegl L, Tiller W (2003) The NURBS book, 2nd edn. Springer, BerlinGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Jichun Wu
    • 1
    Email author
  • Huicheng Zhou
    • 1
  • Xiaoqi Tang
    • 1
  • Jihong Chen
    • 1
  1. 1.National NC System Engineering Research CenterHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations