Electromagnetic riveting process (EMR) is a high-speed impact connection technology with the advantages of fast loading speed, large impact force and stable rivet deformation. In this work, the axisymmetric sequential and loose electromagnetic-structural coupling simulation models were conducted to perform the electromagnetic riveting process of a Ti-6Al-4V titanium rivet, and the parameter analysis of the riveting setup was performed based on the sequential coupled simulation results. In addition, the single-objective optimization problem of punch displacement was conducted using the Hooke–Jeeves algorithm. Based on the adaptive remeshing technology adopted in air meshes, the deformation calculated in the structural field was well transferred to the electromagnetic field in the sequential coupled model. Thus, the sequential coupling simulation results presented higher accuracy on the punch speed and rivet deformation than the loose coupling numerical model. The maximum relative difference of electromagnetic force (EMF) on driver plate and radial displacement in the rivet shaft was 34.86% and 13.43%, respectively. The parameter analysis results showed that the outer diameter and the height of the driver plate had a significant first-order effect on the response of displacement, while the platform height, transition zone height, angle, and transition zone width of the amplifier presented a strong interaction effect. Using the obtained results on the optimal structural parameters, the punch speed was effectively improved from 6.13 to 8.12 m/s with a 32.46% increase. Furthermore, the displacement of the punch increasing from 3.38 to 3.81 mm would lead to an 80.55% increase in the maximum radial displacement of the rivet shaft. This indicated that the deformation of the rivet was efficiently improved by using the optimal rivet model.
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