Mechanical Engineering |
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NURBS curve interpolation algorithm with high accuracy and minimal feedrate fluctuation |
WEI Dong,ZHANG Shu you,LIU Xiao jian |
State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China |
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Abstract 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.
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Published: 01 November 2016
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非均匀有理B样条曲线的高精度低速度波动插补算法
为提高非均匀有理B样条曲线的插补精度,降低插补速度波动率,提出一种基于改进S型速度规划及Steffensen型参数计算的插补算法.通过自适应插补得到曲线分段信息,根据曲率信息自适应调整最大加加速度并进行速度精确控制,改进了传统S型速度规划算法,使得插补处处满足误差约束。采用正反向插补精确确定减速点,并利用带参数Steffensen型方法计算曲线插补参数,避免求导运算,增强插补实时性,有效控制速度波动率.实验结果表明,相对于其他算法,该算法具有更高的插补精度、更低的速度波动率,是高效可行的.
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[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. |
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