3532 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 5, OCTOBER 2011 Experimental and Theoretical Levitation Forces in a Superconducting Bearing for a Real-Scale Maglev System Guilherme Goncalves Sotelo, Daniel Henrique N. Dias, Rubens de Andrade, Jr., Richard Magdalena Stephan, Nuria Del-Valle, Alvaro Sanchez, Carles Navau, and Du-Xing Chen Abstract—A numerical model based on the critical-state ap- proximation and on a magnetic-energy minimization procedure is presented to simulate the levitation of a system composed of two isolated infinitely long superconductors levitating over permanent- magnet guideways. Three different sets of magnetic guideways are simulated and compared with experimental tests of a linear super- conducting magnetic bearing for a prototype of a real magnetic levitation vehicle. In spite of the complexity of the permanent- magnet guideway design, the model serves as a first approach to calculate the vertical levitation force of these superconducting bearings. The measured and calculated force results validate the model applied to study these systems, in addition to some limita- tions caused by simplifications considered in the theoretical model. Index Terms—Magnetic levitation (maglev), superconducting devices. I. I NTRODUCTION S UPERCONDUCTING magnetic bearings (SMBs) repre- sent one of the most important applications of supercon- ductors (SCs). SMBs are almost frictionless even at very high speeds. The second advantage of SMBs is that they are passive. This means that an SMB does not need a complex active control, which makes it a safer device. A rotational SMB can replace the active magnetic bearing in high-speed machines and flywheels [1]–[4]. A linear SMB presents the same ad- Manuscript received January 14, 2011; revised May 19, 2011; accepted May 31, 2011. Date of publication July 22, 2011; date of current version September 28, 2011. This paper was recommended by Associate Editor L. Chiesa. This work was supported in part by Consolider Project NANOSELECT under Grant CSD2007-00041 and in part by Brazilian agencies Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Coordenação de Aperfeiçoamento de Pessoal de Nível Superio (CAPES), and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). G. G. Sotelo is with the Department of Electrical Engineering, Fluminense Federal University, 24210-240 Rio de Janeiro-RJ, Brazil. D. H. N. Dias, R. de Andrade, Jr., and R. M. Stephan are with the Department of Electrical Engineering, Federal University of Rio de Janeiro (UFRJ), 21945- 970 Rio de Janeiro-RJ, Brazil. N. Del-Valle, A. Sanchez, and C. Navau are with the Grup d’Electromagnetisme, Departament de Física, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain. D.-X. Chen is with the Grup d’Electromagnetisme, Departament de Física, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain, and also with the Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, 08010 Barcelona, Spain. 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/TASC.2011.2159114 vantages as the rotational one, and it can be used in magnetic levitation (maglev) vehicles, high-speed tools, and other linear actuators. Frictionless linear SMBs can also be useful for low-speed trams. Steel wheel trams have higher energy efficiency than the pneumatic ones [5] since the rolling resistance of steel is lower. However, steel wheel trams must be heavy to compensate for the loss of adherence from the rails. In this context, the linear SMB could be used to build a frictionless light rail vehicle (LRV) more efficient than a steel wheel tram and even lighter than a pneumatic bus. This maglev LRV has to be propelled by a linear electric motor. Additionally, nowadays, public transportation is one of the main issues in big cities. Millions of people spend several hours along the day just in the way from house to work and vice versa. This situation increases the interest on new public transportation concepts that are less expensive than subways. The Maglev–Cobra proposal [6], [7], which is a supercon- ducting lightweight levitated vehicle with multiple articulated short units, presents a lot of advantages, e.g., low energy consumption, negligible noise emission, small curvature radius (50 m), and capability to ascend ramps of 15%. These prop- erties allow the vehicle to be perfectly adjustable to the city topography and constructed along roads or rivers, channels, and coasts profiles. This technology proposes the use of YBa 2 Cu 3 O 7−δ (YBCO) top-seed melt-textured SC blocks refrigerated by liquid nitro- gen [8], which levitate along a magnetic guideway made of Nd–Fe–B permanent magnets (PMs) and iron. The energy spent for levitation is basically necessary for cooling the YBCO bulks. As these superconducting blocks are located inside cryostats, energy consumption is negligible. Similar projects are also being developed by Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Dresden, Germany [9] and Southwest Jiaotong University, Chengdu, China [10], but with reduced scale models. The design of the magnetic guideway is crucial. The Nd–Fe–B volume must be minimized while maintaining the required conditions of levitation force and lateral stability. This optimization is important to the viability of the project because the rare earth PM rails are a significant part of the system cost. For this reason, many efforts have been carried out to find theoretical models that could help to optimize the design. However, modeling maglev systems is not an easy 1051-8223/$26.00 © 2011 IEEE