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.

中文翻译：

---

考虑横向边缘效应的改进的平面感应加热器3D电磁分析模型

目的

本文旨在提出一种新的3D电磁模型，以计算新型线性永磁体（PM）感应加热器的导电板中的平移运动涡流。平板在PM感应器产生的DC磁场中的运动会产生感应电流，该感应电流通过焦耳效应在加热功率的起点。这些拓扑具有强大的磁效应。在这项工作中开发的分析模型考虑了由于感应电流而导致的导电板的有限长度末端效应和反应场。

设计/方法/方法

所开发的模型基于子域方法和图像理论的结合。首先，使用磁标量势公式和磁场强度公式，通过变量分离方法求解三维麦克斯韦方程，获得了由于PM引起的磁场表达式。然后，使用安培定律计算运动涡流，并使用图像方法考虑导电板的有限长度末端效应。为了分析所提出模型的准确性，将获得的结果与从3D有限元模型（FEM）以及在原型上进行的实验测试获得的结果进行比较。

发现

结果表明，即使对于边缘效应非常强的几何形状，所开发的分析模型也非常准确。由于感应电流，它可以直接考虑导电板的有限长度末端效应（横向边缘效应）和反应场，而无需任何校正因子。与3D有限元模拟相比，所提出的模型还显着减少了计算时间，从而可以快速分析线性PM感应加热器。

实际影响

所提出的电磁分析模型可以用作平移运动永磁感应加热器设备的快速准确的设计工具。

创意/价值

已经开发了一种新的3D分析电磁模型，以在新型平移运动感应加热器的导电板上找到感应功率。所研究的加热装置具有有限的长度和有限的宽度，这会产生在计算中不容易考虑的边缘效应。所提出的方法的新颖之处在于精确的3D分析模型，该模型允许在不使用校正因子的情况下找到导电板中的实际功率加热和感应电流的实际分布。所提出的模型还考虑了由于感应电流引起的反应场。此外，与3D FEM仿真相比，开发的模型大大缩短了计算时间。