地铁车体底架断面设计的全阶段多目标优化研究

doi:10.3901/JME.2025.24.202

摘要/Abstract

摘要： 针对地铁车体底架优化过程中存在的产品设计阶段与结构优化层次考虑不全面、两者对应关系不明确的问题，以及传统有限元模型优化方法计算量大、耗时长且难以满足实际编程需求等挑战，提出一种基于断面性能参数化的产品设计全阶段多目标优化设计方法。首先，推导出影响底架质量与刚度的断面性能参数理论计算公式。随后，针对铝合金地铁车体底架，实施产品设计全阶段的多目标优化。在此优化过程中，以加权柔度最小(即刚度最大)作为优化目标，在底架断面的概念设计阶段，采用变密度法进行拓扑优化；而在基本设计阶段和详细设计阶段，则结合推导的底架断面性能参数理论计算公式，利用带精英策略的非支配排序遗传算法(Non-dominated sorting genetic algorithm Ⅱ，NSGA-Ⅱ)进行形状-自由尺寸协同优化。最后，对拓扑优化结果以及全阶段的优化结果分别进行了重构，并进行了详细的分析校核。结果表明：该方法能够显著提升底架断面静刚度的同时达到了轻量化的目的，三块型材断面面积A(质量)分别减少了4.06%、1.31%、5.17%，弯曲惯性矩I_x分别增加了9.50%、5.21%、9.00%，设计的型材断面性能优异，对产品系统性的优化设计有指导借鉴意义。

关键词: 地铁底架, 断面设计, 全阶段多目标优化, 断面性能参数化, 拓扑优化, 带精英策略的非支配排序遗传算法

Abstract: Aiming at the problems of incomplete consideration of product design stage and structure optimization level in the optimization process of subway car body, unclear correspondence between the two, and the challenges of traditional finite element model optimization method such as large calculation amount, long time and difficult to meet the actual programming requirements, a full-stage multi-objective optimization design method of product design based on section performance parameterization was proposed. Firstly, the theoretical calculation formula of the section performance parameters which affect the quality and stiffness of the frame is derived. Then, the multi-objective optimization of the whole stage of product design was carried out for the aluminum alloy subway body underframe. In this optimization process, the minimum weighted flexibility (i.e. maximum stiffness) is taken as the optimization objective, and the variable density method is used to optimize the topology in the conceptual design stage of the frame section. In both the basic design stage and detailed design stage, combined with the deduced theoretical calculation formula of the frame section performance parameters,Non-dominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) is used to carry out shape-free dimension collaborative optimization. Finally, the topology optimization results and the whole stage optimization results are reconstructed respectively, and the detailed analysis and check are carried out. The results show that：This method can significantly improve the static rigidity of the bottom frame section and achieve the purpose of lightweight. The section area A (mass) of the three profiles is reduced by 4.06%, 1.31% and 5.17% respectively, and the bending moment of inertia I_x is increased by 9.50%, 5.21% and 9.00% respectively. The section performance of the designed profiles is excellent. It has guiding significance for systematic optimization design of products.

Key words: subway underframe, section design, full stage multi-objective optimization, section performance parameterization, topology optimization, Non-dominated sorting genetic algorithm Ⅱ

中图分类号:

U270

张曼, 李娅娜, 史鑫鹏. 地铁车体底架断面设计的全阶段多目标优化研究[J]. 机械工程学报, 2025, 61(24): 202-212.

ZHANG Man, LI Yana, SHI Xinpeng. Research on Full-stage Multi-objective Optimization of the Section Design of Subway Car Body Underframe[J]. Journal of Mechanical Engineering, 2025, 61(24): 202-212.

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