DOI: 10.3724/SP.J.1219.2013.00714

Information and Control (信息与控制) 2013/42:6 PP.714-722

Segment Interpolation of NURBS Curve Based on FeedrateSensitive Corner’s Sharp Points

A novel segment interpolation algorithm based on feedrate sensitive corner's sharp points is proposed to address problems in the popular non-uniform rational B-spline (NURBS) acceleration-deceleration method (Acc/Dec). In this new algorithm, NURBS curve is divided into small segments by sensitive corner's sharp points according to geometric characteristics, and a feedrate scheduling method based on S-shape Acc/Dec is proposed constrained by confined chord error and the machine's capability. In a designated NURBS curve and parameters environment, the simulation results show the effectiveness and feasibility of the new algorithm, in which maximum chord error and maximum Acc/Dec are reduced by 76.7%, maximum jerk is reduced by 94.0% compared with the adaptive feed speed interpolation algorithm.

Key words:non-uniform rational B-spline,interpolation,feedrate sensitive corner,sharp point,chord error

ReleaseDate:2015-04-15 18:52:41

[1] Shpitalni M, Koren Y, Lo C C. Realtime curve interpolators[J]. Computer-Aided Design, 1994, 26(11): 832-838.

[2] Yeh S S, Hsu P L. The speed-controlled interpolator for machining parametric curves[J]. Computer-Aided Design, 1999, 31(5): 349-357.

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

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

[5] 梁宏斌,王永章,李霞.自动调节进给速度的NURBS插补算法的研究与实现[J].计算机集成制造系统,2006,12(3):428-433. Liang H B, Wang Y Z, Li X. Research and implementation of NURBS interpolation algorithm for adaptive feed speed[J]. Computer Integrated Manufacturing Systems, 2006, 12(3): 428-433.

[6] Liu X B, Ahmad F, Yamazaki K, et al. Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics[J]. International Journal of Machine Tools and Manufacture, 2005, 45(4): 433-444.

[7] Du D S, Liu Y D, Yan C L, et al. An accurate adaptive parametric curve interpolator for NURBS curve interpolation[J]. The International Journal of Advanced Manufacturing Technology, 2007, 32(9): 999-1008.

[8] Lin M T, Tsai M S, Yau H T. Development of real-time look-ahead algorithm for NURBS interpolator with consideration of servo dynamics[C]//Proceedings of the 46th IEEE Conference on Decision and Control. Piscataway, NJ, USA: IEEE, 2007: 1862-1867.

[9] Mohammad M E, Behrooz A. A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length[J]. Computer-Aided Design, 2010, 42(7): 625-632.

[10] Alessandro B, Stefano C, Pierfrancesco F, et al. NURBS interpolator with confined chord error and tangential and centripetal acceleration control[C]//Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT). Piscataway, NJ, USA: IEEE, 2010: 489-496.

[11] Ni X Y, Wang D H, Li Y B. Real-time NURBS curve interpolator based on section[J]. The International Journal of Advanced Manufacturing Technology, 2011, 54(4): 239-249.

[12] Sekar M, Narayanan V N, Yang S H. Design of jerk bounded feedrate with ripple effect for adaptive NURBS interpolator[J]. The International Journal of Advanced Manufacturing Technology, 2008, 37(5): 545-552.

[13] Lin F, Shen X A. Feedrate profile planning based on sensitive points identification in NURBS interpolation[J]. Digital Manufacturing and Automation (ICDMA), 2010, 12(1): 729-733.

[14] Les P,Wayne T.非均匀有理B样条[M].2版.赵罡,穆国旺, 王丽柱,译.北京:清华大学出版社,2010. Les P, Wayne T. The NURBS Book[M]. 2th ed. Zhao G, Mu G W, Wang L Z, trans. Beijing: Tsinghua University Press, 2010.

[15] 游有鹏,王珉,朱剑英.NURBS 曲线高速高精度加工的插补控制[J].计算机辅助设计与图形学学报,2001,13(10):943-947. You Y P, Wang M, Zhu J Y. An interpolator for NURBS curve machining with high-speed and high accuracy[J]. Journal of Computer-Aided Design & Computer Graphics, 2001, 13(10): 943-947.

[16] 徐宏,胡自化,张平,等.基于冗余误差控制的非均匀有理B样条曲线插补算法研究[J].计算机集成制造系统,2007,13(5):961-967. Xu H, Hu Z H, Zhang P, et al. Interpolation algorithm for NURBS curve based on redundancy error[J]. Computer Integrated Manufacturing Systems, 2007, 13(5): 961-967.