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Citation information: DOI 10.1109/TMAG.2017.2664063, IEEE Transactions on Magnetics 0487 1 Detent Force Minimization of Permanent Magnet Linear Synchronous Machines using Subdomain Analytical Method considering Auxiliary Teeth Configuration Kyung-Hun Shin 1 , Kyong-Hwan Kim 2 , Keyyong Hong 2 , and Jang-Young Choi 1 1 Dept. of Electrical Engineering, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea 2 Offshore Plant Research Division, Korea Research Institute of Ships and Ocean Engineering, Daejeon 34103, Korea This paper presents electromagnetic modeling and analysis of the detent force in a permanent magnet linear synchronous machine (PMLSM) according to auxiliary teeth configuration. Analytical solutions for magnetic fields generated by permanent magnets (PMs) are derived based on the Maxwell equation in terms of a two-dimensional Cartesian coordinate system. The magnetic vector potential of each subdomain (PM, air-gap, slot, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. Based on the analytical solution, the magnetic force is derived by using the Maxwell stress tensor. All the analytical results were extensively validated using nonlinear finite element analysis and experimental results. Using the proposed method, we investigated the influence of the machine parameters on the detent force. Therefore, the proposed method can be very useful in the initial design and optimization process of PMLSM for detent force analysis. Index Terms— Analytical method, detent force, magnetic field, PMLSM I. INTRODUCTION ERMANENT magnetic linear synchronous machines (PMLSMs) have been widely used in various industrial applications owing to their outstanding performance. However, one of their drawbacks is the generation of detent force caused by the attraction between the permanent magnets (PMs) and the iron core. A large detent force causes thrust ripples and noise, which results in poor positioning accuracy [1]–[3]. Therefore, prediction of the detent force is an important factor to be considered in the design of PMLSMs with slotted-type topologies. An accurate calculation of the magnetic field is critical for the prediction of detent force. Accordingly, magnetic field analysis using the finite element (FE) analysis is preferred. However, this approach is time-consuming and exhibits poor flexibility, especially in the design stage. Our study describes analytical solutions for the magnetic field influenced by the permanent magnet (PM) and the magnetic force calculations are validated by experiments and two-dimensional (2D) FE results. This paper presents electromagnetic modeling and analysis of the detent force in a PMLSM considering slotting, end effect, and auxiliary teeth configuration. The analytical solutions for the calculation of magnetic field distribution are derived by using a subdomain model. Solving the governing equation in all the subdomains and obtaining the field distribution can be carried out by applying the boundary conditions on the interfaces between the subdomains. The analytical results of the magnetic field distribution are validated extensively using the FE analyses. Based on the analytical solutions, the Maxwell stress tensor is used to determine the detent force. The measurement results are compared with the numerical solutions obtained using the nonlinear FE and the analytical model. The predictions are compared with the measured data to confirm the validity of the proposed methods presented in this paper. On the basis of proposed method, we investigated the influence of the design parameters of a PMLSM on the detent force. Therefore, the proposed analytical method can be very useful in the initial design and optimization process of PMLSMs for detent force analysis. II. ELECTROMAGNETIC ANALYSIS OF PMLSM A. Analytical Model The geometric representation of a three phase (18-slot / 10-pole) PMLSM with auxiliary teeth configuration is shown in Fig. 1. The main parameters of this geometry are defined as follows: the height of the mover core y1, height of the PM surface y 2 , inner and outer heights of the slot y 3 and y 5 , respectively, height of the auxiliary teeth y4, and height of the extra slot y 6 . The pole-arc-to-pole-pitch ratio of the PM rotor is  and the number of pole pairs is p. The number of stator slots is Q. The slot opening width is i auxiliary slot width is as, auxiliary teeth width is at, end width is a, and extra end width is e. Owing to the presence of current density in the slots, a magnetic vector potential formulation is used. According to the adopted assumptions [4], the problem is solved with 2D Cartesian coordinates owing to the machine symmetry along its shaft. The magnetic vector potential has only one component along the z-direction and depends only on the x and y coordinates. Except for the iron core and magnets, the permeability of all the materials used in this model is assumed to be equal to that of vacuum ( 0 ). As it can be seen in Fig. 1, the entire domain of the field problem is divided into six types of subdomains: region I (the mover PM subdomain), region II (the air-gap subdomain), region III (the end subdomains), region IV (the extra end slot subdomains), region S (i = 1, 2,…, Q) (the Q stator slot subdomains), and region AS (j = 1, 2) (the j auxiliary slot subdomains). The subdomains I and II have annular shapes. The subdomains III, AS, S, and IV are delimited by the iron core. P Manuscript received November 20, 2016. Corresponding author: Jang-Young Choi (e-mail: choi_jy@cnu.ac.kr) Digital Object Identifier inserted by IEEE