无速度波动的NURBS曲线二次插补算法原理及其实现

发布时间：2018-07-04 10:49

本文选题：非均匀有理B样条 + 插补　；参考：《计算机集成制造系统》2015年10期

【摘要】：针对NURBS插补中的速度波动与计算效率两大问题,提出无速度波动的NURBS割线二次插补算法与NURBS快速求值求导算法。在割线二次插补法中,采用二阶Taylor法对NURBS曲线进行一次插补,在此基础上使用根据无速度波动要求给定插补步长的割线逼近原曲线,从而计算插补点,以消除因截断误差和弦线逼近偏差引起的速度波动。在NURBS快速求值求导算法中,预先计算并存储NURBS表达式中分子式与分母式在节点值处的各阶非零导数,实时插补中使用Taylor公式快速计算NURBS各阶导数,从而避免计算B样条基函数,达到提高计算效率的目的。在自主研发的数控平台上实现了基于所提算法的NURBS插补器,并通过仿真分析与加工实验验证了该插补器是有效且可行的。
[Abstract]:Aiming at the two major problems of velocity fluctuation and computational efficiency in Nurbs interpolation, a Nurbs Secant Quadratic interpolation algorithm and a Nurbs Fast derivation algorithm are proposed. In the Secant Quadratic interpolation method, the Nurbs curve is interpolated by the second order Taylor method. On this basis, the original curve is approximated by the Secant which is given the interpolation step size according to the requirement of no velocity fluctuation, and the interpolation point is calculated. In order to eliminate the velocity fluctuation caused by the truncation error and the deviation of the chord approximation. In the fast derivation algorithm of Nurbs, the nonzero derivatives of the molecular formula and denominator of Nurbs expression at the node value are calculated and stored in advance. Taylor formula is used to calculate the Nurbs derivatives quickly in real time interpolation, thus avoiding the calculation of B-spline basis functions. To achieve the purpose of improving the efficiency of calculation. The Nurbs interpolator based on the proposed algorithm is implemented on the NC platform, and the simulation analysis and processing experiments show that the interpolation is effective and feasible.
【作者单位】：北京航空航天大学机械工程及自动化学院;北京市高效绿色数控加工工艺及装备工程技术研究中心;
【基金】：国家自然科学基金重大资助项目(11290144)~~
【分类号】：TG659

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