一种双NURBS曲线的参数迭代插补算法
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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。
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.
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.
引文
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[15] Les P,Wayne T.Non-uniform Rational B-spline[M].2nd ed.Beijing:Tsinghua University Press,2010
[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
[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
[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
[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):291-294Zhao 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)
[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
[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
[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
[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
[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
[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):383-388,434Luo 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)
[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
[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):2659-2667Liu 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)
[15] Les P,Wayne T.Non-uniform Rational B-spline[M].2nd ed.Beijing:Tsinghua University Press,2010