An integrated multi-objective topology optimization method for automobile wheels made of lightweight materials

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.