基于粒子群优化算法的自由曲线双圆弧逼近

Biarc Approximation of Freeform Curves Based on Particle Swarm Optimization Algorithm

针对数控加工中常用大量直线段逼近平面自由曲线,刀具路径在误差、光顺性、程序数量等方面存在的问题,给出了基于粒子群优化算法的双圆弧逼近平面自由曲线方法。建立了优化的数学模型,并通过最大逼近误差和最大圆弧长度两个变量构造了适应度函数。使用粒子群优化算法确定双圆弧的节点,以达到逼近误差最小、圆弧数量最少的目标,进而对整条曲线的逼近进行优化。进行了试验设计,并与其他方法进行了比较,研究结果证实了方法的有效性与优越性。

In NC machining,the 2-D freeform curves are commonly approximated by a large number of line segments,and there are shortcomings in some aspects,such as errors,smoothness,program amounts,etc.To solve this problem,biarc approximation based on particle swarm optimization was proposed.In order to get the least arcs with the least approximation errors,a fitness function was established through the maximal approximation error and the maximal arc length,and the particle swarm optimization was used to find nodes of the biarcs.The test results show the availability and superiority of this method.