一种双NURBS曲线的参数迭代插补算法

An Interpolation Algorithm by Parametric-iteration for Dual-NURBS Curve

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.