Dynamic model of solenoids under impact excitation, including motion and eddy currents

Modeling of solenoids activated from a DC source (impact excitation) is difficult because of the coupling of a nonlinear magnetic system, which indicates eddy currents, with a mechanical system that involves a time-varying gap. While the finite-element method in two dimensions has been successfully implemented to solve this complex problem, the large number of successive iterations involved makes it inconvenient when repeated design trials are made, for instance, during optimization. It is shown that the problem geometry, including eddy currents, can be satisfactorily approximated using only one dimension. The resulting set of equations is solved using the finite-difference method. Comparisons with test data and with two-dimensional finite-element calculations are conclusive. The proposed model can be used for the assessment of any solenoid, including fast-acting devices. The resulting algorithm converges rapidly, a desirable feature during a design process where many runs are necessary