Pulsed Magnetic Field Measurement Outside Finite Length Solenoid: Experimental Results &Mathematical Verification

The paper deals with magnetic field mapping outside a finite length solenoid electromagnet, by an in-house designed and calibrated inductive pick-up or search coil. The search coil is calibrated in a unique methodology based on the azimuthal magnetic field component generated by a straight wire. This unique calibration technique helps us to avoid additional circuitry to integrate the signal obtained from search coil. The methodology proves advantageous in diffusion, implosion studies where the signal frequency changes with dimension and material of experimental job-piece (hollow metal tube). Remedial measures have been taken to avoid electrostatic capacitive pick-up (which eventually exacerbates with integration) keeping measurement simple and accurate. The experimentally measured field values have also been compared with electromagnetic field results obtained from mathematical calculations and finite element based simulations. Two different mathematical approaches have been demonstrated for field computation based on Biot-Savart Law. Both the methods have taken into account the exact geometry of the solenoid, including the inter-turn gaps. The methods use appropriate combination of closed-form mathematical expression and numerical integration techniques and are capable of determining all the vector components of magnetic field anywhere around the finite length solenoid. The mathematical computations are equally significant contributions in the paper especially because exact determination of magnetic fields outside finite length solenoids has not been discussed in sufficient specific details in already existing literature. The mathematical computations, finite element simulations and experimental verification together provide a holistic solution to magnetic field determination problems in pulse power applications that have not been discussed in available literature or books in specific details.

Electromagnetic Expansion and Fragmentation of Hollow Aluminium 5052 Tube

Electromagnetic forming is a high-speed forming technology by which hollow profiles can be compressed or expanded. It is done with a pulsed magnetic field to apply Lorentz’ forces at electrically conductive material. Electromagnetic hollow tube expansion is limited by the fragmentation tendency. This work attempts to use a combination of analytical and computational approach to compute the net tangential stress during tube expansion. A simplified analytical framework to estimate the temporal evolution of plastic stresses present in aluminium alloy AA5052 at low and high applied magnetic pressures is developed based upon dynamic imaging. The time resolved images captured using current synchronised high speed camera record the overall dimensional changes of the tube that is validated by multi-physics simulation of expansion process. Imaging of hollow tube expansions at two selected peak currents has been carried out at various current levels in the range 76 - 160 kA. The direct visualisation of the increase in the tube diameter at two current levels provided a comparison of the developing net tangential stresses in the hollow tube during the undamaged and fragmented expansion. Imaging of tube expansion also facilitates the estimation of the strain rate experienced by the tube and was in the range of ~1700 s-1 to ~1200 s-1. The propensity of fragmentation was found to be due to the level and duration of generated tangential stresses above the yield stress during expansion of the aluminium tubes. Presented study provides a mean of exploiting the enhanced formability of aluminium alloys using electromagnetic forming.