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首页> 外文期刊>The International Journal of Advanced Manufacturing Technology >A study on optimal design of process parameters in single point incremental forming of sheet metal by combining Box-Behnken design of experiments, response surface methods and genetic algorithms
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A study on optimal design of process parameters in single point incremental forming of sheet metal by combining Box-Behnken design of experiments, response surface methods and genetic algorithms

机译：结合Box-Behnken实验设计，响应面法和遗传算法优化钣金单点渐进成形工艺参数的优化设计

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摘要

Incremental forming is a sheet metal forming process characterized by high flexibility; for this reason, it is suggested for rapid prototyping and customized products. On the other hand, this process is slower than traditional ones and requires in-depth studies to know the influence and the optimization of certain process parameters. In this paper, a complete optimization procedure starting from modeling and leading to the search of robust optimal process parameters is proposed. A numerical model of single point incremental forming of aluminum truncated cone geometries is developed by means of Finite Element simulation code ABAQUS and validated experimentally. One of the problems to be solved in the metal forming processes of thin sheets is the taking into account of the effects of technological process parameters so that the part takes the desired mechanical and geometrical characteristics. The control parameters for the study included wall inclination angle (α), tool size (D), material thickness (Th_(ini)), and vertical step size (In). A total of 27 numerical tests were conducted based on a 4-factor, 3-level Box-Behnken Design of Experiments approach along with FEA. An analysis of variance (ANOVA) test was carried out to obtain the relative importance of each single factor in terms of their main effects on the response variable. The main and interaction effects of the process parameters on sheet thinning rate and the punch forces were studied in more detail and presented in graphical form that helps in selecting quickly the process parameters to achieve the desired results. The main objective of this work is to examine and minimize the sheet thinning rate and the punch loads generated in this forming process. A first optimization procedure is based on the use of graphical response surfaces methodology (RSM). Quadratic mathematical models of the process were formulated correlating for the important controllable process parameters with the considered responses. The adequacies of the models were checked using analysis of variance technique. These analytical formulations allow the identification of the influential parameters of an optimization problem and the reduction of the number of evaluations of the objective functions. Taking the models as objective functions further optimization has been carried out using a genetic algorithm (GA) developed in order to compute the optimum solutions defined by the minimum values of sheet thinning and the punch loads and their corresponding combinations of optimum process parameters. For validation of its accuracy and generalization, the genetic algorithm was tested by using two analytical test functions as benchmarks of which global and local minima are known. It was demonstrated that the developed method can solve high nonlinear problems successfully. Finally, it is observed that the numerical results showed the suitability of the proposed approaches, and some comparative studies of the optimum solutions obtained by these algorithms developed in this work are shown here.
机译：增量成型是一种具有高柔韧性的钣金成型工艺。因此，建议用于快速成型和定制产品。另一方面，此过程比传统过程慢，需要深入研究才能了解某些过程参数的影响和优化。本文提出了一个完整的优化过程，该过程从建模开始，并导致对鲁棒的最佳过程参数的搜索。利用有限元仿真代码ABAQUS建立了铝截锥几何形状的单点增量成形数值模型，并进行了实验验证。在薄板的金属成型过程中要解决的问题之一是考虑到工艺过程参数的影响，从而使零件具有所需的机械和几何特性。该研究的控制参数包括壁倾角（α），工具尺寸（D），材料厚度（Th_（ini））和垂直台阶尺寸（In）。基于4因子，3级Box-Behnken实验设计方法以及FEA，总共进行了27个数值测试。进行了方差分析（ANOVA）检验，以得出每个因素对响应变量的主要影响的相对重要性。工艺参数对板材稀化率和冲模力的主要和相互作用影响进行了更详细的研究，并以图形形式显示，有助于快速选择工艺参数以获得理想的结果。这项工作的主要目的是检查并使该成形过程中产生的薄板减薄率和冲头载荷最小。第一优化程序是基于图形响应曲面方法（RSM）的使用。制定了过程的二次数学模型，将重要的可控制过程参数与考虑的响应相关联。使用方差分析技术检查模型的充分性。这些分析公式可以确定优化问题的影响参数，并减少目标函数的评估次数。以模型为目标函数，已使用遗传算法（GA）进行了进一步优化，以计算由薄板厚度和冲头载荷的最小值以及最佳工艺参数的相应组合定义的最佳解决方案。为了验证其准确性和通用性，通过使用两个分析测试函数作为基准来测试遗传算法，其中已知全局和局部最小值。实践证明，该方法可以成功解决非线性问题。最后，观察到数值结果表明了所提出方法的适用性，并在此显示了通过这项工作中开发的这些算法获得的最优解的一些比较研究。

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