An Interpolation Algorithm by Parametric-iteration for Dual-NURBS Curve
-
摘要: 为提高非均匀有理B样条（NURBS）曲线插补的步长精度，给出了一种基于参数迭代的双NURBS曲线插补算法。先进行刀尖点曲线插补，基于NURBS的局部特性分析，利用插补步长与参数增量间的近似线性关系，通过迭代寻优，获取了精确步长所对应的插补参数；然后依据双NURBS曲线间的同步关系，计算出刀轴矢量曲线的插补参数，实现了面向五轴加工的刀具位姿插补。实验结果表明，该方法所得的步长精度优于Taylor展开插补法，并可保证刀轴矢量与工件表面法线方向的一致性，有利于获得更加光滑的加工表面。Abstract: In order to improve the step-length accuracy of the non-uniform rational B-spline (NURBS) curve interpolation, a dual-NURBS curve interpolation algorithm based on parametric iteration is presented. The interpolation of a tool-tip curve is carried out based on the local character of NURBS; the approximate linear relationship between the step-length and the parameter increment is used to obtain the interpolation parameters corresponding to the precise step-length. The interpolation parameters of the tool-axis vector curve are calculated according to the synchronous relationship between the dual-NURBS curves, thus interpolating the tool position. The experimental results show that the step-length accuracy obtained with this method is better than the Taylor expansion interpolation method and that it can ensure the consistency between the tool-axis vector and the normal direction of work-piece surface, being beneficial for obtaining a smoother machining surface.
-
Key words:
- parameter iteration /
- dual-NURBS /
- tool-axis vector /
- interpolation algorithm
-
[1] Sevilla R, Barbieri E. NURBS distance fields for extremely curved cracks[J]. Computational Mechanics, 2014, 54(6):1431-1446 doi: 10.1007/s00466-014-1067-4 [2] Yuen A, Zhang K, Altintas Y. Smooth trajectory generation for five-axis machine tools[J]. International Journal of Machine Tools and Manufacture, 2013, 71:11-19 doi: 10.1016/j.ijmachtools.2013.04.002 [3] Laseme A, Xue D Y, Gu P H. Recent development in CNC machining of freeform surface:a state-of-the-art review[J]. Computer-Aided Design, 2010, 42(7):641-654 doi: 10.1016/j.cad.2010.04.002 [4] Mohan S, Kweon S H, Lee D M, et al. Parametric NURBS curve interpolators:a review[J]. International Journal of Precision Engineering and Manufacturing, 2008, 9(2):84-92 [5] Feng J C, Li Y H, Wang Y H, et al. Design of a real-time adaptive NURBS interpolator with axis acceleration limit[J]. The International Journal of Advanced Manufacturing Technology, 2010, 48(1-4):227-241 doi: 10.1007/s00170-009-2261-y [6] 赵国勇, 徐志祥, 赵福令.高速高精度数控加工中NURBS曲线插补的研究[J].中国机械工程, 2006, 17(3):291-294 doi: 10.3321/j.issn:1004-132X.2006.03.020Zhao G Y, Xu Z X, Zhao F L. Study on NURBS curve interpolator in the high speed and high accuracy CNC machining[J]. China Mechanical Engineering, 2006, 17(3):291-294(in Chinese) doi: 10.3321/j.issn:1004-132X.2006.03.020 [7] Yeh S S, Su H C. Implementation of online NURBS curve fitting process on CNC machines[J]. The International Journal of Advanced Manufacturing Technology, 2009, 40(5-6):531-540 doi: 10.1007/s00170-007-1361-9 [8] Javad J, Mohammad R A. A novel ACC-Jerk-limited NURBS interpolation enhanced with an optimized S-shaped quintic feedrate scheduling scheme[J]. The International Journal of Advanced Manufacturing Technology, 2015, 77(9-12):1889-1905 doi: 10.1007/s00170-014-6575-z [9] Lee A C, Lin M T, Pan Y R, et al. The feedrate scheduling of NURBS interpolator for CNC machine tools[J]. Computer-Aided Design, 2011, 43(6):612-628 doi: 10.1016/j.cad.2011.02.014 [10] Tsai M S, Nien H W, Yau H T. Development of integrated acceleration/deceleration look-ahead interpolation technique for multi-blocks NURBS curves[J]. The International Journal of Advanced Manufacturing Technology, 2011, 56(5-8):601-618 doi: 10.1007/s00170-011-3214-9 [11] Emami M M, Arezoo B. 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 doi: 10.1016/j.cad.2010.04.001 [12] 罗福源, 游有鹏, 尹娟.NURBS曲线泰勒展开插补法的平稳性与改进研究[J].中国机械工程, 2012, 23(4):383-388, 434 doi: 10.3969/j.issn.1004-132X.2012.04.003Luo F Y, You Y P, Yin J. Research on stability and improvement of taylor-expansion-based approach for NURBS curve interpolation[J]. China Mechanical Engineering, 2012, 23(4):383-388, 434.in Chinese doi: 10.3969/j.issn.1004-132X.2012.04.003 [13] Sun Y W, Zhao Y, Bao Y R, et al. A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints[J]. International Journal of Machine Tools and Manufacture, 2014, 77:74-81 doi: 10.1016/j.ijmachtools.2013.11.002 [14] 刘强, 刘焕, 周胜凯, 等.无速度波动的NURBS曲线二次插补算法原理及其实现[J].计算机集成制造系统, 2015, 21(10):2659-2667 http://d.old.wanfangdata.com.cn/Periodical/jsjjczzxt201510014Liu Q, Liu H, Zhou S K, et al. Principle and development of NURBS interpolation algorithm with zero-feedrate fluctuation[J]. Computer Integrated Manufacturing System, 2015, 21(10):2659-2667(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/jsjjczzxt201510014 [15] Les P, Wayne T. Non-uniform Rational B-spline[M]. 2nd ed. Beijing:Tsinghua University Press, 2010 -
下载:
点击查看大图
图(12)
计量
- 文章访问数: 323
- HTML全文浏览量: 185
- PDF下载量: 43
- 被引次数: 0
