This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON ENERGY CONVERSION 1 Hybrid Finite-Element–Boundary Element Analysis of a Single-Sided Sheet Rotor Linear Induction Motor Layth Qaseer and Razzak Marzouk Abstract—A hybrid ﬁnite-element–boundary element method is adopted for the analysis of linear induction machines (LIM) in Cartesian coordinates. A mathematical boundary is deﬁned ar- bitrarily in free space to enclose the system. Finite-element for- mulation is applied for the interior region and boundary integral formulation is applied on the boundary using the response func- tion excited by a transverse line current. The electromagnetic ﬁeld problem is solved for the magnetic vector potential, from which all performance calculations such as air gap power, propulsion force, and levitation force can be obtained. It provides an accurate anal- ysis of the LIM in unbounded free space which can be used as a fast evaluation method to approach the proper design. The accu- racy of the method is veriﬁed through experimental results in the existing literature. The comparison with ﬁnite element method is also explored. Index Terms—Electromagnetic ﬁelds, hybrid ﬁnite-element– boundary element method (FEM-BEM), linear motors, modeling. I. INTRODUCTION T HE increasing need for an improvement in transport sys- tems early in the last century put a considerable amount of effort into the development of design, changing the topol- ogy, and methods of analysis. Linear induction motors are used for conveyor systems, magnetically levitated trains, projectile launchers, material handling, and as people movers. These applications need machines that can produce large forces, operate at high speeds, and can be controlled precisely to meet performance requirements. The various designs of linear machines include single-sided, double-sided, transverse ﬂux induction machines, synchronous, and hybrid linear motors [1]. Single-sided linear induction mo- tors have been widely used due to their simplicity and low construction cost but they suffer from low efﬁciency and exis- tence of end effects [2]. Many researches have been conducted on various conﬁgurations of stator and rotor with their inﬂuence on the design of such motors [2]–[11]. The speed control of linear induction motors has also been paid a considerable atten- tion [12], [13]. Analysis of linear motors has been carried out using both analytical and numerical techniques. For the analyt- ical methods, several papers were published as in [8]–[10], [14] Manuscript received April 30, 2013; revised August 19, 2013; accepted November 14, 2013. Paper no. TEC-00254-2013. L. Qaseer is with the Department of Biomedical Engineering, University of Baghdad, Baghdad, Iraq (e-mail: laythqaseer@yahoo.com). R. Marzouk is with the Department of Electrical Engineering, University of Baghdad, Baghdad, Iraq (e-mail: marzoukrz@yahoo.com). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/TEC.2013.2292057 and [15]. Numerical techniques adopted ﬁnite-element method (FEM) in 2-D and 3-D as in [2]–[8] and [16]. The hybrid method makes use of the advantages of both FEM and boundary-element method (BEM) techniques for the anal- ysis of unbounded ﬁeld problems. It gives more freedom in the choice of mathematical boundaries; therefore, the interior region to which FEM technique is applied becomes smaller [17]. Inte- gral equations derived on the boundary are used as constraints for the FEM analysis. Nonlinear regions can be represented in the hybrid method by using ﬁnite elements [18]. Investigation of the hybrid method for the solution of electromagnetic launchers using two examples compared with their analytical solutions is presented in [19]. Pichon and Razek [20] introduced a hybrid ﬁ- nite element–boundary element method (FEM-BEM) coupling method for the computation of axial forces on the rotor of a tubular linear induction motor using the Maxwell stress tensor technique. The method provides an accurate analysis of the ﬁeld distribution in the motor; however; the analysis is useful only for axisymmetric induction devices. Advantages of the hybrid method can be summarized as follows: 1) Nonlinear materials can be dealt with using FEM discretization. 2) Inﬁnite boundaries can be replaced by ﬁnite boundaries, and suitable boundary relations can be derived and in- troduced as constraints for the equations representing the interior region. 3) Comparable results can be obtained with a smaller number of unknowns in comparison with the general FEM. The main objective of this paper is to present an accurate and fast simulation method that can be used for design studies and performance parameter computation of a sheet rotor linear induction machine (LIM) unbacked by iron, where there is no return path for the ﬂux, in unbounded Cartesian coordinates, based on a hybrid FEM-BEM. Using this method enables the machine designer to draw a large amount of information in addition to the distribution of the electromagnetic ﬁelds inside the machine. For example, the starting and rated speed torques, losses, the effect of changing the number of poles, changing the frequency, increasing air gap and changing the materials used in the rotor, moreover the design study of changing machine parameters helps the designer to select the proper parameters of the machine that ﬁt the design requirements for variable frequency operation. We acknowledge that the complete numerical solution of a ﬂat linear induction motor using this method has not been pub- lished before. The results obtained by this approach are exam- ined against measured performance parameters of a single-sided 0885-8969 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.