Received August 10, 2020, accepted August 26, 2020, date of publication August 31, 2020, date of current version September 11, 2020. Digital Object Identifier 10.1109/ACCESS.2020.3020258 Coupled Circuit and Magnetic Model for a Transverse Flux Permanent Magnet Linear Motor DONGSHAN FU 1 , (Member, IEEE), JINLIN GONG 2 , (Member, IEEE), YANLIANG XU 2 , FREDERIC GILLON 3 , AND NICOLAS BRACIKOWSKI 4 1 Jiangsu Province Laboratory of Mining Electric and Automation, China University of Mining and Technology, Xuzhou 221008, China 2 School of Electrical Engineering, Shandong University, Jinan 250061, China 3 Ecole Centrale de Lille, Engineering School of Arts et Métiers ParisTech, University of Lille, 59000 Lille, France 4 IREENA Laboratory, University of Nantes, 44600 Saint-Nazaire, France Corresponding author: Yanliang Xu (xuyanliang@sdu.edu.cn) This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant 2020QN66. ABSTRACT In this paper, a strong coupling between magnetic and electric phenomena is provided allowing to have an accurate and high-speed coupled model. A coupled circuit and magnetic model for an E-core transverse flux permanent magnet linear motor (TFPMLM) is proposed, which has an advantage linked to reducing time computing more than ten times when compared to 3-D finite-element model (FEM). Firstly, a multi-plane flexible-mesh nonlinear equivalent magnetic network (EMN) model is proposed to improve the computation efficiency as well as the high precision of the magnetic model. And a new method to define the converged iterative process is presented to further decrease the computing time. Secondly, the magnetic circuit and electric circuit are normalized into a solution matrix by introducing controlled sources and discretization methods which forms the coupled model. Then, the magnetic flux in the magnetic circuits and the current in the electric circuits are obtained simultaneously for each time step. The characteristics such as the air-gap flux density distribution, output thrust force waveforms and the phase currents are analyzed by the proposed coupled model. The modeling approach is approved by comparison with the 3-D FEM model. Finally, the proposed model is validated through the experimental setup with the machine prototype. INDEX TERMS Coupled model, electric circuit, equivalent magnetic network (EMN), linear motor, transverse flux. I. INTRODUCTION Transverse-flux permanent magnet linear motor (TFPMLM) is being focused more and more in recent years, due to the advantages of high acceleration, high operating life, high force density, high fault-tolerant ability, and decoupling between electric loading and magnetic loading [1]. And the growing interest in linear motor systems requires new design approaches which take into account the drive and motor design at the same time. Coupled circuit and magnetic model efficiency and precision is very important for the design of electric machine systems [2], [3]. However, TFPMLM nor- mally suffers from the complex structure resulting from the 3-D magnetic circuit, which is usually analyzed using 3-D The associate editor coordinating the review of this manuscript and approving it for publication was Atif Iqbal . FEM with time-consuming problem [4]. A coupled circuit and magnetic model of TFPMLM need to deal with two parts: magnetic part and coupled circuit part. For the mag- netic part, an efficient and accurate motor analysis model is required. For the coupled circuit part, proper coupling method is another key to achieving an accurate and useful model. Linear motors have many mechanical asymmetries that induce dissymmetry magnetic and electric phenomena it is why the modelling is especially difficult. There are some motor analysis models already used for analysis and design of TFPMLM. The analytical method [5] is adopted only in preliminary design and in understanding relationships between the parameters with brief time but low precision. Schwarz-Christoffel (SC) conformal mapping technique is another analytical method that is used to resolve the air gap field distribution and can consider the slotting 159274 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020