基于G2连续Bézier曲线的刀具轨迹压缩算法

A Data Compression Algorithm Based on G2 Continuous Bézier Curves for Tool Paths

针对复杂曲面的数控加工,提出一种基于Bézier曲线的刀具轨迹数据压缩算法.根据连续小线段的几何特征来筛选适用于被压缩的区域,将各个区域内的形值点转化为特殊的3阶Bézier曲线,选用最小二乘法拟合形值点,通过调整参数曲线控制点和插入过渡曲线,使得加工路径光顺并保证G2连续性,采用2阶Taylor展开来估计误差和控制拟合精度.结果表明:所提出的算法无迭代、实时性好,算法数据的压缩比高;采用Taylor展开估计的误差与真实误差很接近,可以有效控制拟合精度.

The machining of continuous short blocks is a hot and difficult point for CNC machining. In this paper, a data compression algorithm based on the Bezier curve was proposed. First, the areas suitable for compression were screened out based on the geometric characteristics of continuous short blocks. Then, G01 points in each area were converted to special 3 order Bezier curves. To decrease the fluctuation of cur- vature and increase the compression ratio, the least square method was chosen to fit points. By adjusting the control points and inserting transition curves, the machining path was made G2 continuous. The fitting error was estimated by 2-order Taylor formula. Without iteration, the algorithm was real-time. The ex- periment proved that the compression ratio was high. The errors estimated by Taylor formula was ex- tremely close to the real ones, indicating that the fitting accuracy could be controlled effectively.