Time-Stepping FEM-Based Multi-Level Coupling of Magnetic Field–Electric Circuit and Mechanical Structural Deformation Models Dedicated to the Analysis of Electromagnetic Actuators

The present paper introduced a framework for multi-level coupling transient electromagnetic fields (EMF) and mechanical structural dynamics based on the finite element method (FEM). This framework was dedicated to predicting, with better accuracy, the wave magnetic force density for obtaining the mechanical deformation occurring in electromagnetic actuators (EMAs). The first-level EMF transient model coupling is related to the magnetic field equations that are strongly coupled with the electric circuit input voltage equations. This is done by considering the magnetic saturation through the Newton–Raphson (N–R) method. The time-stepping solution of the EMF model resulted in the magnetic force densities being computed from the Lorentz force (LZ) expressions, based on the space–time variation of the induced eddy current. For the second coupling level, the EMF model was sequentially coupled with the mechanical structural deformation equations (MDef) through the local magnetic force density to achieve minimal material dynamic displacement and deformation. The developed multi-physics EMF–MDef time-stepping (FEM) model tools were implemented using the Matlab software