An accelerated analytical method for predicting workpiece velocity and displacement during electromagnetic forming

This paper presents complementary analytical analyses, experiments, and numerical simulations of the elec-tromagnetic tube compression (EMTC) process using a multi-turn axisymmetric coil with a field shaper. In earlier contributions, we proposed an analytical model capable of predicting the magnetic pressure, radial velocity, and radial displacement for EMTC. In the present paper, our understanding of EMTC is expanded with the aid of a modified analytical model, a series of experimental tests with various materials, and 3D coupled electromagnetic- mechanical numerical simulations. First, the analytical model was improved by generating elements across the entire landing area of the field shaper. This modification provided a more accurate induced magnetic pressure in the analytical model. In addition, the experimentally measured coupling coefficients between the coil, field shaper, and workpiece tube were directly incorporated into the analytical model as opposed to utilizing them as correction factors during the magnetic pressure calculation in the previous studies. In the proposed analytical model, at each time increment, the magnetic field geometry is updated in response to the tube deformation. Second, to assess the proposed analytical model, experimental tests with Photon Doppler Velocimetry (PDV) were carried out for three different materials with different thermo-mechanical properties, i.e., Al6061-T6, Cu101, and Cu260 (Brass). Third, to compare the computational cost of the analytical model and to deter-mine the accuracy of the proposed analytical model compared to the existing software packages in the market, a 3D coupled electromagnetic-mechanical finite element model was used. To investigate the influence of discharge energy on tube deformation, all three methods were examined at three different charging energies, i.e., 2.4, 3.6, and 4.8 kJ. Reasonably good agreement between all three approaches validates the ability of the analytical model to accurately capture the deformation velocity and displacement for this complex multi-physics manufacturing process in a computationally cost-effective manner. Such an analytical model can be used as a base model for predicting the impact velocity during electromagnetic pulse welding and crimping processes prior to performing expensive and time-consuming experimental tests or numerical simulations.