An interpolation algorithm based on improved S-type velocity planning and Steffensen-like parameter calculating was proposed in order to improve accuracy of non-uniform rational b-spline (NURBS) interpolation and reduce feedrate fluctuation. The adaptive interpolation method was used to obtain information of each curve segment. S-type velocity planning method was improved by adaptively adjusting jerk and accurately controlling feedrate based on the information of curvature of these segments. Then the optimal interpolation that satisfied all the error constraints everywhere was realized. The proposed algorithm determined the starting point of deceleration area precisely by the way of positive and reverse interpolation. Steffensen-like method with parameters was used to calculate the interpolation parameters without derivative calculation in order to improve real time performance and to control feedrate fluctuation availably, The experimental results show that ,the proposed method can effectively improve the interpolation accuracy and reduce feedrate fluctuation compared to other methods.
WEI Dong,ZHANG Shu you,LIU Xiao jian. NURBS curve interpolation algorithm with high accuracy and minimal feedrate fluctuation. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2016, 50(11): 2215-2223.
［1］TILLER W, PIEGL L. The NURBS book ［M］. 2nd ed. Heidelberg: Springer, 1997: 86-93．
［2］FAN W, LEE C H, CHEN J H. A realtime curvaturesmooth interpolation scheme and motion planning for CNC machining of short line segments ［J］. International Journal of Mac hine Tools & Manufacture. 2015, 96(3): 27-46．
［3］CHEN Y D, WEI H X, SUN K. Algorithm for smooth s-curve feedrate profiling generation ［J］. Chinese Journal of Mechanical Engineering , 2011, 24(2): 237-247．
［4］金育安, 贺 永, 傅建中.NURBS及Hermite混合高速加工插补算法［J］.浙江大学学报:工学版,2014,48(4): 641-648．
JIN Yuan, HE Yong, FU Jianzhong. NURBSHermite hybrid interpolation for highspeed machining［J］. Journal of Zhejiang University: Engineering Science, 2014,48(4): 641-648．
［5］ WANG J B,YAU H T. Realtime NURBS interpolator: application to short linear segments ［J］. International Journal of Advanced Manufacturing Technology, 2009, 41(11/12): 1169-1185．
［6］季国顺, 王 文, 陈子辰. 基于预估—校正公式的参数曲线插补算法［J］.浙江大学学报:工学版, 2008, 42(10): 1765-17- 69．
JI Guoshun, WANG Wen, CHEN Zichen. Parametric curve interpolation algorithm based on predictorcorrector formula［J］Journal of Zhejiang University: Engineering Science, 2008, 42(10): 1765-1769．
［7］YEH S S, HSU P L. Adaptivefeedrate interpolation for parametric curves with a confined chord error ［J］. Computer Aided Design, 2002,34(3): 229-237．
［8］王允森, 杨东升, 刘荫忠, 等. NURBS插补中的速度规划与参数计算［J］.计算机集成制造系统,2014, 20(8): 1896-19- 02．
WANG Yunsen, YANG Dongsheng, LIU Yinzhong, et al. Velocity planning and parameter calculating in NURBS inte Rpolation ［J］. Computer Integrated Manufacturing Systems, 2014, 20(8): 1896-1902．
［9］孙树杰, 林 浒, 郑飂默.反向插补的NURBS曲线前瞻插补算法［J］. 计算机辅助设计与图形学学报, 2014, 26(9): 1543-1549．
SUN Shujie, LIN Hu, ZHENG Liaomo. Lookahead interp olation algorithm with reverse interpolation for NURBS cur- ves ［J］. Journal of Computer Aided Design & Computer Graphics, 2014, 26(9): 1543-1549.
［10］徐水龙,徐周波,古天龙,等. 基于干涉预处理的NURBS曲线前瞻插补算法［J］. 计算机集成制造系统, 2015, 21(5): 1229-1236．
XU Shuilong, XU Zhou bo, GU Tianlong, et al. Look-ahea-D interpolation of NURBS curve based on interference pretr-Eatment ［J］. Computer Integrated Manufacturing Systems,2015, 21(5): 1229-1236．
［11］罗 钧, 汪 俊, 刘学明,等. 基于S型加减速的自适应前瞻曲线插补算法［J］. 计算机集成制造系统,2013,19(1): 55-60．
LUO Jun, WANG Jun, LIU Xueming, et al. Adaptive NURBS interpolation algorithm with lookahead function based on S-shape acceleration/deceleration［J］. Computer Intergrated Manufacturing Systems, 2013,19(1): 55-60．
［12］李建伟,林 浒,孙玉娥. 基于S曲线加减速的NURBS实时插补前瞻控制方法［J］. 组合机床与自动化加工技术,2009(11)：41-49.
LI Jianwei, LIN Hu, SUN Yue. A realtime lookingfor ward nurbs interpolation algorithm based on s-shape［J］．Modular Machine Tool & Automatic Manufacturing Te chnique, 2009(11)：41-49．
［13］罗福源, 游有鹏, 尹 涓. NURBS曲线 S 形加减速双向寻优插补算法研究［J］. 机械工程学报, 2012,48(5): 147-156.
LUO Fuyuan, YOU Youpeng, YIN Juan. Research on the algorithm of NURBS curve bidirectional optimization in terpolation with stype acceleration and deceleration cont rol ［J］. Journal of Mechanical Engineering, 2012,48(5): 147-156.
［14］ DAVID K, WARD C. Numerical Analysis: Mathematics of Scientific Computing［M］. 3rd ed. New York: American Mathem atical Society, 2009．
［15］ PORTRA F A, PTAK V. Nondiscrete induction and itera tive processes［M］. Boston: Pitman Press, 1984．
［16］DEHGHAN M, HAJARIAN M. some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations ［J］.Computational and Applied Mathematics, 2010,29(1): 19-30.
