An integrated pseudo-spectral simulation of high-speed discharging at an electromagnetic forming conveying a conductive driver sheet
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An integrated computational methodology is implemented based on a pseudo-spectral solution of governing differential equations in a high-speed discharging of the flat spiral coils, which is used in the electromagnetic-forming systems. Both conductive driver sheet and coil are divided into several peripheral segments. Also, eddy currents induced by each segment are computed as well as the fields generated by each wire of the coil corresponding to defined local source points. The model will be established based on the Chebyshev polynomials to calculate spatial and temporal distributions of the magnetic fields. The Houbolt marching method is applied for the time discretization of the Maxwell equations. By adopting a backward process for implicit boundary conditions and summing up overall components of the magnetic fields at the lower surface, it leads to obtaining an integrated response to the problem. A multiple regression analysis is implemented based on the least square error norm to remove additional equations generated in the spectral discretization. An exponential filtering is used to control aliasing phenomenon due to collocation treatment of the mathematical terms. Validation is carried out by comparisons of the results with other works related in the literature.
KeywordsElectromagnetic forming Pseudo-spectral collocation Maxwell equations Flat spiral coil Impulsive load
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