The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating, the theory of roller design, and the stress and strain field analysis of cold roll-beating, etc. However, the research on law of metal flow in the forming process of involute spline cold roll-beating is rare. According to the principle of involute spline cold roll-beating, the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established, and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded. A finite element model of the spline cold roll-beating process is established, the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied, and the node flow tracks of the deformation area are analyzed. The experimental research on the metal flow of cold roll-beating spline is conducted, and the metallographic structure variation, grain characteristics and metal flow line of the different tooth profile area are analyzed. The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance. There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming. The characteristics of involute spline cold roll-beating forming are given, and the forming mechanism of involute spline cold roll-beating is revealed. This paper researches the law of metal flow in the forming process of involute spline cold roll-beating, which provides theoretical supports for solving the tooth profile forming quality problem.

The explicit topology optimization method based on moving morphable component (MMC) has attracted more and more attention, and components are the basic building blocks of the implementation of MMC method. In the present work, a MMC topology optimization method based on component with void structure is followed with interest. On the basis of analyzing the characteristics of components used by MMC method, the topology description function for component with void structure is presented, where a quantitative scaling factor is introduced without increasing the number of design variables. Taking the minimum flexibility as the optimization objective, an example of short beam is analyzed with different void structure scaling factors. The results show that different scaling factors have a greater impact on the final topology optimization structure, and an ideal topology structure can be obtained with an appropriate scaling factor. Finally, some problems in the optimization process are analyzed and indicate that appropriate mesh density should be chose for component with void structure in order to achieve good optimization results.

Self-piercing riveting (SPR) has become a highly promising new method for connecting dissimilar materials in multi-material vehicle bodies, while the joint’s forming quality which largely affects its connection performance lacks sufficient research. This study conducted a detailed numerical investigation on the forming quality of carbon-fiber-reinforced polymer (CFRP)/aluminum alloy (Al) SPR joint and proposed a novel multi-objective optimization strategy. First, the finite element (FE) model of CFRP/Al SPR joint forming was established and then verified to monitor the forming process. Second, based on FE numerical simulation, the action laws of rivet length and die structural parameters (die depth, die gap, and die radius) on the joint’s forming quality indicators (bottom thickness and interlock value) were systematically studied to reveal the joint’s forming characteristics. Finally, taking the rivet length and die structural parameters as design variables and the above forming quality indicators as optimization objectives, a hybrid Taguchi–Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method was proposed to conduct the multi-objective optimization of the joint’s forming quality. According to the outcomes, the bottom thickness and interlock value of the joint were respectively increased by 10.18% and 34.17% compared with the baseline design, achieving a good multi-objective optimization of the joint’s forming quality, which provides an effective new method for efficiently predicting and improving the forming quality of the CFRP/Al SPR joint.

The present paper introduces a sequential topology optimization method for multi-material structure design. In the proposed method, the moving morphable component (MMC) method and the solid isotropic material with penalization (SIMP) method are performed in sequence to achieve multi-material structure optimization. First, the structural topology is obtained using the MMC method, and then the material layout of the determined structural topology is optimized using the SIMP method. The connection between MMC method and SIMP method is established through components mapping elements, where changes in the material layout within these elements do not affect the external structural topology. The proposed method effectively combines the advantages of two optimization methods, enabling the achievement of an explicit external structural topology and greater freedom in internal multi-material layouts, while remaining easy to implement. The key MATLAB codes for the proposed method are provided in the paper. Finally, the feasibility of the proposed method is verified through some numerical examples.