冲床套料中模拟重力算法的仿真研究

Simulation Research on an Algorithm Based on Gravity Principles in Punching Nesting

装载问题是数学上的一类最优化问题,一种常见情形是在二维封闭容器内放置尽可能多的等大圆形,且这些圆形不能互相重叠。上述问题在冲床优化套料方面有明确的应用价值。从“在板料上冲压更多的工件”这一实际问题出发,讨论特殊形式下装载问题的一种模拟重力算法,以提高材料的利用率。针对冲床优化套料的具体应用情况,推导了旋转前后的坐标转换公式。最后将上述算法与其它几种常见的冲床套料算法进行了对比,结果表明,提出的算法在套料效果上优于其它几种算法,但是耗时相对较长,适用于对运算时间要求低、对套料效果要求高的场合。

Packing problem is a class of optimization problem in mathematics. A common circumstance of packing problems is to pack a given two - dimensional closed container with as many circles as possible where these circles have the same size and cannot overlap each other. This problem has clear values of application in punching nesting optimization. This paper starts out from the practical problem that is to punch more work-pieces in specific materials. A nesting algorithm was proposed based on gravity principles of this circumstance, which is to improve the utilization rate of the materials. Coordinates transformation formula of rotation was derived according to specific circumstances of nesting in punching system. Furthermore, comparisons with other common nesting algorithms were made. The result shows that the algorithm proposed in this paper has better effects but lower operation speeds than other algorithms. Therefore this algorithm is applicable to the occasions which have strict requirements on nesting effect and loose requirements on operation time.