Fast and Precision NURBS Interpolator for CNC Systems

다국어 초록 (Multilingual Abstract)

This paper presents a performance evaluation of a NURBS interpolator that uses not Taylor’s expansion method but the recursive characteristics of NURBS. Taylor’s expansion has mostly been used for NURBS interpolation. However, it is very complicated and gives an indispensable truncation error. A fast and precision NURBS interpolator replacing Taylor’s expansion is presented for CNC systems in robots and CNC machine tools. The presented interpolation algorithm uses the recursive equation of the NURBS formula rather than Taylor’s expansion. A simulation study is conducted to demonstrate the advantages of this proposed interpolator compared with those using Taylor’s equation. The feedrate error and calculation time are simulated in the performance evaluation. The recursive method of NURBS interpolation is faster and more accurate than Taylor’s expansion.

참고문헌 (Reference)

1 Yeh, S. S., "The speed-controlled interpolator for machining parametric curves" 31 (31): 349-357, 1999

2 Piegl, L., "The NURBS Book, 2nd ed" Springer 1997

3 Baek, D. K, "Precision NURBS interpolator based on recursive characteristics of NURBS" 2012

4 Yang, D. C. H., "Parametric interpolator versus linear interpolator for precision CNC machining" 26 (26): 225-234, 1994

5 Sekar Mohan, "Parametric NURBS Curve Interpolators : A Review" 한국정밀공학회 9 (9): 84-92, 2008

6 Lai, J. Y, "On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk" 37 (37): 104-121, 2008

7 Tikhon, M., "NURBS interpolator for constant material removal rate in open NC machine tools" 44 (44): 237-245, 2004

8 Farouki, R. T, "Exact Taylor series coefficients for variable-feedrate CNC curve interpolators" 33 (33): 155-165, 2001

9 Lin, M. T, "Development of a dynamic-based NURBS interpolator with real-time look ahead algorithm" 47 (47): 2246-2262, 2007

10 Zhang, Q. G, "Development and implementation of a NURBS curve motion interpolator" 14 (14): 27-36, 1998

11 Seker, M, "Design of jerk bounded feedrate with ripple effect for adaptive NURBS interpolator" 37 (37): 545-552, 2008

12 Cheng, M. Y, "Contour error reduction for free-form contour following task of biaxial motion control systems" 25 (25): 323-333, 2009

13 Koren, Y., "CNC interpolators: algorithms and analysis" 64 : 83-92, 1993

14 Du, D., "An accurate adaptive parametric curve interpolator for NURBS curve interpolation" 32 (32): 999-1008, 2007

15 Du, D., "An accurate adaptive NURBS curve interpolator with real-timeflexible acceleration/deceleration control" 26 (26): 273-281, 2010

16 Xu, R. Z, "Adaptive parametric interpolation scheme with limited acceleration and jerk for NC machining" 36 (36): 343-354, 2008

17 Liu, X., "Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics" 45 (45): 433-444, 2005

18 Yong, T., "A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining" 35 (35): 1249-1259, 2003