空间等半径过渡曲面成形刀纵向加工的算法

An Interpolation Algorithm for Cubic Parametric Spline Curve in CNC Systems

根据三次参数样条曲线的矢量表示方法，导出了一种ＣＮＣ系统中样条曲线的实时插补算法．该算法不仅精度高，理论上可使所有插补点都落在曲线上，而且计算量不大，插补速度快．插补轮廓步长由允许弓高误差及编程速度决定．理论分析和实验表明，这种算法能获得加工要求的插补精度，其插补速度能满足ＣＮＣ系统的实时性要求．

Based on the vector equation, a real time interpolation algorithm for the cubic parametric spline curve in CNC systems is proposed. The algorithm is free from accumulated error and all the interpolated points will be on the curve in theory. The process of interpolation is short owing to a limited number of multiplication and division. The interpolation contour step is selected by the given tolerance of the segment and the programmed feedrate. Theoretical analysis and experimental results show that the algorithm can always give the accuracy required and the interpolation process can meet the requirements of CNC systems.