Roberto Petry Homrich

Single layer cylindrical and helicoidal coil with voids between successive turns electromagnetic field calculation to be used in superconductor current limiter simulator for design purpose

A very accurate mathematical method, named helicoidal method, to calculate the flux density vector B produced by the current circulating in the resistive single-phase superconductor electrical current limiter (RSCL) coils, at any point of the its whole space, using the Biot-Savarts Law is presented in this paper. It is very important to remember that these coils are single layer concentric cylindrical coils with voids (free space) between its neighbor turns which turns present helicoidal form. The calculation of the vector B, at any point of the space of the coils, is used in the dynamic simulation of the RSCL for design and operation purposes, but it is also used to calculate the self-inductance of each electrical current limiter coil and the mutual inductance between each pair of coils, which are necessary to determine the equivalent impedance of the RSCL. To verify the proposed method accuracy the self-inductance of three different coils, made with copper wire, are calculated, measured and the results are compared.

Simplified Mathematical Modeling for an Electromagnetic Forming System with Flat Spiral Coil as Actuator

This study presents mathematical modeling and calculation procedure for problems of electromagnetic forming of thin circular metal sheets using a flat spiral coil as actuator. The methodbased on the Biot-Savart Law focuses specifically on the calculation of the electromagnetic field generated by the flat coil and analysis of the circuit that models the electromagnetic forming system to the initial time, before the plastic deformation of the sheet. The solution of magnetic induction integral equations is performed by numerical methods specifically with the use of Matlab® software, providing important information that serves as feedback for system design. Free bulging experiments were performed to demonstrate a good relationship with the mathematical model predictions for electrical discharge current in the coil and induced currents in the metal sheet, behavior of the transient electromagnetic force between coil and workpiece, and distribution of magnetic field, electromagnetic density force along the coil.

Fast single layer cylindrical and helicoidal coil with voids between turns electromagnetic field calculation to be used in superconducting current limiter simulator for design purpose

This paper presents a mathematical method to quickly calculate the flux density vector B produced by the current circulating in a resistive single-phase superconducting electrical current limiter (RSCL), at any point of its whole space, using the Biot-Savarts Law. As the calculation using the exact form of the turns of each coil (single layer cylindrical coil with helicoidal form presenting voids (free space) between neighbor turns) is computationally very cumbersome to be used in a RSCL dynamic simulator, it is proposed in this paper to substitute the real coil, only for the subject of the calculation, by an imaginary coil formed by plane closed circular turns with the same number of turns, the same height and radius as the real coil. Each turn of the imaginary coil is placed exactly in the medium position between successive turns of the actual coil and will carry the same current. The coil self-inductance is also calculated to verify the accuracy of the proposed method.

An Analysis of Electromagnetic Sheet Metal Forming Process

Electromagnetic forming (EMF) is a high-speed forming process that uses energy density of a pulsed magnetic field to deform metallic workpieces. This paper presents a method to calculate the electromagnetic force in thin flat plates using a flat spiral coil as an actuator. The method is based on the Biot-Savart law, and the solution of magnetic induction integral equations is performed inside Matlab® by a numerical method based on discretizing the EMF system in a system of ordinary differential equations that couple the electric and magnetic phenomena. Free bulging experiments and a comparison with Ansoft Maxwell® software are presented demonstrating a good correlation with the proposed implementation.