多目标粒子群优化算法在薄板冲压成形中的应用

Application of Multi-objective Particle Swarm Optimization in Sheet Metal Forming

有限元分析与优化算法相结合来提高板料的成形质量、缩短设计周期已在板料成形领域得到广泛的研究。传统的优化方法主要是将多目标问题转化为单目标问题进行研究,然而,评价一个板料的成形质量应该是多方面的(如拉裂、起皱和成形不足等)并且各个质量特性之间可能会发生相互冲突。因此直接采用多目标优化算法来提高板料的成形性具有非常重要的现实意义。采用自主开发的STLMesher软件建立模具的参数化模型,在此基础上将试验设计、能代表实际冲压过程精度较高的近似模型和多目标粒子群优化算法相结合,获得了一组最小化起皱和拉裂缺陷的非劣解。在板料成形优化过程中调用的是近似模型,大大减少了调用有限元模型的次数,提高了优化效率。为指导工程设计人员快速有效地从非劣解集中挑选出一组成形效果最好的解,提出最小距离选解法,选出的解实现了对起皱和拉裂缺陷的优化,提高了板料的成形性能。数字算例表明,该方法具有较高的精度和较强的工程实用性。

Finite element simulation combined with optimization algorithm has been extensively researched in the sheet metal forming field to improve design quality and shorten design cycle. Conventional optimization techniques are mainly to transform multi-objective problem into a single-objective problem to solve. However, products are typically characterized by numerous quality characteristics （for example： rupture, wrinkling, insufficient stretching, etc.） and quality characteristics could conflict with each other. Therefore, it is of important significance to directly adopt a multi-objective optimization methodology to improve the formability of sheet metal. A parametric mould model is built by using an independently developed STLMesher software. On this basis, we obtain a set of non-dominated solutions which make wrinkle and rupture minimized simultaneously through combination of design of experiments, response surface models and multi-objective particle swarm optimization. In order to instruct engineering designers to quickly and effectively choose a set of solutions for best formability from the set of non-dominated solutions, the minimum distance solution method is proposed, with the selected solution realizing the optimization of wrinkle and rupture, hence enhancing the formbility of the sheet. The numeral example indicates that this method has higher precision and stronger engineering practicability.