An electromagnetic model is proposed to compute translational motion eddy current in a conductive plate. The eddy currents are due to the movement of the plate in a dc magnetic field created by a PM inductor. Firstly, the magnetic field due to the PMs is computed in 3D where the iron yokes influence is considered thanks to the method of images. Then, the motional eddy currents are computed such that the edge effects are correctly taken into account through an iterative procedure which uses magnetic images. The computations are very fast and the obtained results are close to those issued from 3D FE method and from experiments.
This paper presents a simple and accurate 3D analytical expressions to compute the force and torque of an axial flux magnetic couplings (AFMC) based on the equivalent magnetic charges and the images method. The proposed model is formulated and solved in a 3D Cartesian coordinate system by considering the assumption of linearization around the mean radius. Firstly, the magnetic flux density due to the cubic permanent magnets (PM), of one side of the magnetic coupling, is computed in 3D considering the magnetic end effects where the iron yokes influence is considered thanks to the images method. Secondly, the force and the torque among the magnets located in the opposite sides are obtained using the analogy between the electrostatic and magnetostatic forces. The derived analytical expressions depend directly on the geometrical and physical parameters of the AFMC. The analytical results are compared to those obtained with finite element simulation and experimental measurements.
Purpose This paper aims to propose a new 3D electromagnetic model to compute translational motion eddy current in the conducting plate of a novel linear permanent magnet (PM) induction heater. The movement of the plate in a DC magnetic field created by a PM inductor generates induced currents that are at the origin of a heating power by Joule effect. These topologies have strong magnetic end effects. The analytical model developed in this work takes into account the finite length extremity effects of the conducting plate and the reaction field because of induced currents. Design/methodology/approach The developed model is based on the combination of the sub-domain’s method and the image’s theory. First, the magnetic field expressions because of the PMs are obtained by solving the three-dimensional Maxwell equations by the method of separation of variables, using a magnetic scalar potential formulation and a magnetic field strength formulation. Then, the motional eddy currents are computed using the Ampere law, and the finite length extremity effects of the conducting plate are taken into account using the image’s method. To analyze the accuracy of the proposed model, the obtained results are compared to those obtained from 3D finite element model (FEM) and from experimental tests performed on a prototype. Findings The results show that the developed analytical model is very accurate, even for geometries where the edge effects are very strong. It allows directly taking into account the finite length extremity effects (the transverse edge effects) of the conducting plate and the reaction field because of induced currents without the need of any correction factor. The proposed model also presents an important reduction in computation time compared to 3D finite element simulation, allowing fast analysis of linear PM induction heater. Practical implications The proposed electromagnetic analytical model can be used as a quick and accurate design tool for translational motion PM induction heater devices. Originality/value A new 3D analytical electromagnetic model, to find the induced power in the conducting plate of a novel translational motion induction heater has been developed. The studied heating device has a finite length and a finite width, which create edge effects that are not easily considered in calculation. The novelty of the presented method is the accurate 3D analytical model, which allows finding the real power heating and real distribution of the induced currents in the conducting plate without the need to use correction factor. The proposed model also takes into account the reaction field because of induced currents. In addition, the developed model improves an important reduction in the computation time compared with 3D FEM simulation.
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