Babajamali Zoheir, Khabaz Mohamad Khaje, Aghadavoudi Farshid, Farhatnia Fatemeh, Eftekhari S Ali, Toghraie Davood
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran.
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran.
ISA Trans. 2022 Nov;130:399-408. doi: 10.1016/j.isatra.2022.04.002. Epub 2022 Apr 6.
In this paper, multi-objective optimization of tandem cold rolling settings for reductions and inter-stand tensions using NSGA-II and Pareto-optimal front are investigated. In this multi-objective optimization, the total power consumption and uniform power distribution are suggested as objective functions, and reduction thicknesses in each stand and inter stand tensions were selected as problem decision variables. Analytical formulations are introduced to determine the rolling forces and power based on the Stone approach. Then, the main variables of the optimization problem, objective functions, linear and nonlinear constraints, are defined. Moreover, some empirical constraints are introduced regarding the practical limitations of cold rolling equipment and the mechanical properties of the material. At first, considering the conditions of a practical tandem rolling line, single-objective optimization is performed separately, and finally, NSGA-II was used for multi-objective optimization. Compared to the initial setting of the rolling line, the obtained single objective schedules have better performance. Moreover, the multi-objective results based on the Pareto-optimal front are investigated, and an optimized setting for rolling schedule has been suggested. Using this proposed schedule the total power consumption is reduced by more than 11% comparing to the initial setting and more uniform power distribution has been obtained in rolling stands. The normalized reductions calculated from this investigation are compared with numerical and experimental results found in the literature and the similarity was observed in the pattern of thickness reduction distribution.
本文研究了使用NSGA-II和帕累托最优前沿对串联冷轧的压下率和机架间张力设定进行多目标优化。在该多目标优化中，建议将总功耗和均匀功率分布作为目标函数，并选择各机架的压下厚度和机架间张力作为问题决策变量。引入解析公式，基于斯通方法确定轧制力和功率。然后，定义优化问题的主要变量、目标函数、线性和非线性约束。此外，还引入了一些关于冷轧设备实际限制和材料力学性能的经验约束。首先，考虑实际串联轧制生产线的条件，分别进行单目标优化，最后使用NSGA-II进行多目标优化。与轧制生产线的初始设定相比，所获得的单目标轧制规程具有更好的性能。此外，研究了基于帕累托最优前沿的多目标结果，并提出了轧制规程的优化设定。使用该建议的轧制规程，与初始设定相比，总功耗降低了11%以上，并且在各机架间获得了更均匀的功率分布。将本次研究计算得到的归一化压下率与文献中的数值和实验结果进行比较，观察到厚度减薄分布模式具有相似性。
