三次三角插值样条曲线的数控插补计算方法

An NC Interpolation Calculation Method of Cubic Trigonometric Cardinal Interpolation Spline

摘要: 论文提出一种新的样条曲线——可调形三次三角插值样条曲线，该样条曲线实现了对直线、圆弧、椭圆以及自由曲线等常见数控运动轨迹曲线的统一精确表达，并根据参数曲线的数据采样插补原理，对三次三角插值样条曲线的插补算法进行了研究。在保证自由曲线数控插补运动高速同时兼顾运动的平稳性，采用一系列首尾相连的微小直线段逼近给定的插值样条曲线，再利用轨迹空间和参变量空间的对应关系，控制运动加速度，得到整个离散化插补轨迹。此算法提高了自由曲线的插补速度和运动平稳性，保证了曲面数控加工的表面质量。

Abstract: The paper proposes a new spline curve called cubic trigonometric cardinal interpolation spline with adjustable shape. The spline curve realized the unification to accurately represent some common NC tool motion path curves such as straight lines, arcs, ellipses and free curves, etc. An interpolation algorithm of cubic trigonometric cardinal interpolation spline based on data sampling interpolation theory is researched. This curve interpolation method ensures the high-speed of spline curve CNC interpolation while taking into account the smooth movement, using a series of conterminous short straight-line segments to approach the given interpolation spline, and then utilizing the relation between track space and parameter space to control motion acceleration and get the whole discrete interpolation trajectory. This algorithm improves the speed and motion stability of free curve interpolation and guarantees the surface quality of surface numerical control machining.