One of the bottlenecks encountered in the development of automobile wheels made of lightweight materials is the 13-degree bench impact test. To improve the impact resistance of lightweight material wheels, the topology optimization (TO) model of multi-design spaces and multi-load cases and the combination of gray relational analysis (GRA) and principal component analysis (PCA) are simultaneously integrated into a multi-objective topology optimization (MOTO) approach to obtain the optimized topology layout of the wheel. Firstly, a three-dimensional wheel TO model is established based on the variable density method and divided into three design spaces and two non-design spaces. Secondly, the load parameters of the wheel under cornering, radial, and 13-degree impact load cases are determined, and the corresponding finite element models are established. For the 13-degree impact load case, the real-time energy reduction coefficient is introduced to compensate for the tire absence, thereby determining the dynamic load of the striker acting on the wheel alone. And then, a series of extracted forces data during the whole impact simulation are equivalent to a concentrated load suitable for the wheel static TO through the weighted sum compliance method. Thirdly, the combination of GRA and PCA is introduced to determine the weight coefficient (WC) of each sub-objective. Next, the MOTO of the wheel is implemented, and the influence of different constraints on the wheel topology layout is analyzed. Finally, the modal analysis and 13-degree impact simulation are performed on the reconstructed wheels with different topology layouts to verify their performance. The results show that the natural frequencies of the optimized wheels meet the requirements and a variety of wheel topology layouts with improved impact resistance are obtained, which provides a valuable guidance for the development of wheel in practical engineering.

用轻质材料制成的汽车车轮在开发中遇到的瓶颈之一是13度台面冲击试验。为了提高轻质材料车轮的耐冲击性，将多设计空间和多工况的拓扑优化（TO）模型以及灰色关联分析（GRA）和主成分分析（PCA）的组合同时集成到一个-目标拓扑优化（MOTO）方法来获得车轮的优化拓扑布局。首先，基于变密度法建立了三维车轮TO模型，并将其分为三个设计空间和两个非设计空间。其次，确定车轮在转弯，径向和13度冲击载荷情况下的载荷参数，建立了相应的有限元模型。对于13度冲击载荷情况，引入实时能量降低系数以补偿轮胎的缺失，从而确定撞针单独作用在车轮上的动态载荷。然后，在整个冲击模拟过程中提取的一系列力数据等效于通过加权总和柔度法适合于车轮静态TO的集中载荷。第三，引入GRA和PCA的组合来确定每个子目标的权重系数（WC）。接下来，实现车轮的MOTO，并分析不同约束条件对车轮拓扑布局的影响。最后，对具有不同拓扑布局的重建车轮进行了模态分析和13度冲击仿真，以验证其性能。结果表明，优化后的车轮的固有频率满足要求，并获得了具有改善的抗冲击性的各种车轮拓扑布局，为实际工程中的车轮发展提供了宝贵的指导。