五轴数控加工中扫掠轮廓线的B样条表达

摘要

提出用B样条表示五轴加工中刀具扫掠轮廓线的算法。首先根据轮廓线的显式方程计算其二阶导矢，然后基于二阶导矢界估算轮廓线上的采样点数，接着通过B样条插值、节点消去和组合等曲线近似技术求得B样条曲线。所得的曲线具有控制顶点少且误差在给定范围内的特点，从而实现了对轮廓线的有效计算机表达，同时该方法可推广到刀具扫掠面的B样条表达。%This paper presents an algorithms to represent the cutter swept profile which determines the machined surface in five-aixs NC machining by the B-spline. Firstly, the second derivative of swept profile is explicitly evaluated, and based on which the number of sampling points is calculated. Then the sampling points are interpolated by a B-spline curve, and its unwanted nodes are removed by using the approximation tolerance. The obtained B-spline curve has a small number of control points and its error is restricted within the tolerance. Therefore, the cutter swept profile is effectively represented. The presented method can also be extended to the B-spline representation for a cutter swept surface.