Fast dynamic macro element and finite element 2D coupled model for an electromagnetic launcher study

Purpose - The modelling of the electromagnetic devices with moving objects such as launchers, electrical machines and actuators, necessitates considering the motion. This paper aims to examine this subject.Design methodology approach - This task can be performed by introducing the velocity term in the electromagnetic equation. However, the application of this method leads to a non-symmetrical finite element matrix. This numerical problem can be avoided either by the finite element meshing domain every displacement step or by using special techniques coupled to the finite element method like the moving bound, sliding surface and macro element (ME). The ME solution, based on an analytical model in the air-gap of the devices, is more solicited for its low cost and accuracy by comparison with the other one. This technique keeps unchanged the finite element topology during the simulation, where the motion is taken into account by modification of the ME formula's every displacement.Findings - This paper sought to present a new formula of the ME which is called dynamic ME. This new formula keeps unchanged the finite element topology and the terms of the analytical stiffness matrix too during the movement simulation.Research limitations implications - The developed model is limited to analyzing the 2D devices with moving objects in linear or non-linear case with saturation of the magnetic circuits. Extending the model to consider the 3D effects is the perspective of this work.Originality value - The developed formula is more economical than the classical one.