{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T04:06:40Z","timestamp":1772942800668,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T00:00:00Z","timestamp":1637884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/117921\/2016"],"award-info":[{"award-number":["SFRH\/BD\/117921\/2016"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Instituto de Engenharia Mec\u00e2nica (IDMEC)","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]},{"name":"Instituto de Engenharia Mec\u00e2nica (IDMEC)","award":["PTDC\/EEEIEEL\/4693\/2014 \u2013 HTSISTELEC"],"award-info":[{"award-number":["PTDC\/EEEIEEL\/4693\/2014 \u2013 HTSISTELEC"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Actuators"],"abstract":"<jats:p>This document presents a study on the optimization of the 3D geometry of a horizontal axis radial levitation bearing with zero-field cooled (ZFC) high-temperature superconductor (HTS) bulks in the stator, and radially magnetized permanent magnet (PM) rings in the rotor. The optimization of component dimensions and spacing to minimize the volume or cost concerning only the maximization of the levitation force was previously studied. The guidance force and guiding stability depend on the spacing between PM rings in the rotor and between the rings of HTS bulks in the stator. This new optimization study aims to find the optimum spacing that maximize the guidance force with given HTS bulk and PM ring dimensions while maintaining the minimum required levitation force. Decisions are taken using the non-dominated sorting genetic algorithm (NSGA-II) over 3D finite element analysis (FEA). A simplified electromagnetic model of equivalent relative permeability is used on 3D FEA to reduce numerical processing and optimization time. Experimental prototypes were built to measure magnetic forces and validate appropriate values of equivalent magnetic permeability. An analysis of stable and unstable geometry domains depending on the spacing between rings of HTS bulks and PM rings is also done for two HTS bulk sizes.<\/jats:p>","DOI":"10.3390\/act10120311","type":"journal-article","created":{"date-parts":[[2021,11,28]],"date-time":"2021-11-28T22:19:16Z","timestamp":1638137956000},"page":"311","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimization of the Guiding Stability of a Horizontal Axis HTS ZFC Radial Levitation Bearing"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8872-9207","authenticated-orcid":false,"given":"Ant\u00f3nio J.","family":"Ars\u00e9nio","sequence":"first","affiliation":[{"name":"Instituto de Engenharia Mec\u00e2nica (IDMEC), Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal"},{"name":"Instituto Superior T\u00e9cnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5536-9038","authenticated-orcid":false,"given":"Francisco Ferreira","family":"da Silva","sequence":"additional","affiliation":[{"name":"Instituto de Engenharia Mec\u00e2nica (IDMEC), Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal"},{"name":"Instituto Superior T\u00e9cnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9674-5490","authenticated-orcid":false,"given":"Jo\u00e3o F. P.","family":"Fernandes","sequence":"additional","affiliation":[{"name":"Instituto de Engenharia Mec\u00e2nica (IDMEC), Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal"},{"name":"Instituto Superior T\u00e9cnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7072-5184","authenticated-orcid":false,"given":"Paulo J.","family":"Costa Branco","sequence":"additional","affiliation":[{"name":"Instituto de Engenharia Mec\u00e2nica (IDMEC), Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal"},{"name":"Instituto Superior T\u00e9cnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ars\u00e9nio, A.J., Carvalho, M.V., Cardeira, C., Branco, P.J.C., and Mel\u00edcio, R. (2016, January 25\u201328). Conception of a YBCO superconducting ZFC-magnetic bearing virtual prototype. Proceedings of the IEEE International Power Electronics and Motion Control Conference (PEMC), Varna, Bulgaria.","DOI":"10.1109\/EPEPEMC.2016.7752171"},{"key":"ref_2","first-page":"1","article-title":"Prototype of a Zero-Field-Cooled YBCO Bearing with Continuous Ring Permanent Magnets","volume":"28","author":"Arsenio","year":"2018","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_3","first-page":"1","article-title":"The Critic Liquid\u2013Gas Phase Transition between Liquid Nitrogen and YBCO HTS Bulks: From FEM Modeling to its Experimental Study for ZFC Levitation Devices","volume":"28","author":"Arsenio","year":"2018","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TASC.2021.3066900","article-title":"Thermo-Hydraulic Analysis of a Horizontal HTS ZFC Levitating Bearing Concerning Its Autonomy Safety Service Time","volume":"31","author":"Arsenio","year":"2021","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TASC.2016.2528989","article-title":"Optimization of the Superconducting Linear Magnetic Bearing of a Maglev Vehicle","volume":"26","author":"Queval","year":"2016","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TASC.2020.2964546","article-title":"Optimization of a Horizontal Axis HTS ZFC Levitation Bearing Using Genetic Decision Algorithms over Finite Element Results","volume":"30","author":"Fernandes","year":"2020","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1109\/TASC.2005.849636","article-title":"Superconductively Levitated Transport System\u2014The SupraTrans Project","volume":"15","author":"Schultz","year":"2005","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1109\/TASC.2010.2086034","article-title":"Tests on a Superconductor Linear Magnetic Bearing of a Full-Scale Maglev Vehicle","volume":"21","author":"Sotelo","year":"2011","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1109\/TASC.2006.870013","article-title":"Construction and Performance of HTS Maglev Launch Assist Test Vehicle","volume":"16","author":"Yang","year":"2006","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"di Barba, P., and Palka, R. (2008). Optimization of the HTSC-PM Interaction in Magnetic Bearings by a Multiobjective Design, Intelligent Computer Techniques in Applied Electromagnetics, Springer. Studies in Computational Intelligence.","DOI":"10.1007\/978-3-540-78490-6_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"127","DOI":"10.3233\/JAE-2009-1016","article-title":"Multiobjective design optimization of an excitation arrangement used in superconducting magnetic bearings","volume":"30","author":"May","year":"2009","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Mateev, V., Todorova, M., and Marinova, I. (2018, January 3\u20136). Eddy Current Losses of Coaxial Magnetic Gears. Proceedings of the 2018 XIII International Conference on Electrical Machines (ICEM), Alexandroupoli, Greece.","DOI":"10.1109\/ICELMACH.2018.8506782"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Usman, H., Ikram, J., Alimgeer, K., Yousuf, M., Bukhari, S., and Ro, J.-S. (2021). Analysis and Optimization of Axial Flux Permanent Magnet Machine for Cogging Torque Reduction. Mathematics, 9.","DOI":"10.3390\/math9151738"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Nguyen, H.P., Nguyen, X.B., Bui, T.T., Ueno, S., and Nguyen, Q.D. (2019). Analysis and Control of Slotless Self-Bearing Motor. Actuators, 8.","DOI":"10.3390\/act8030057"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Toh, C.S., and Chen, S.-L. (2016). Design, Modeling and Control of Magnetic Bearings for a Ring-Type Flywheel Energy Storage System. Energies, 9.","DOI":"10.3390\/en9121051"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3761","DOI":"10.1109\/TASC.2007.899108","article-title":"Computer Modeling of Magnetisation in High Temperature Superconductors","volume":"17","author":"Hong","year":"2007","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1103\/PhysRevB.47.915","article-title":"Magnetization of type-II superconductors in the Kim-Anderson model","volume":"47","author":"Yamamoto","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105021","DOI":"10.1088\/0953-2048\/23\/10\/105021","article-title":"Simulation of temperature and magnetic field distribution in superconducting bulk during pulsed field magnetization","volume":"23","author":"Fujishiro","year":"2010","journal-title":"Supercond. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.ssc.2003.09.029","article-title":"Magnetic field dependence on transition temperature Tc in cuprate superconductors","volume":"129","author":"Koo","year":"2004","journal-title":"Solid State Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"015009","DOI":"10.1088\/0953-2048\/25\/1\/015009","article-title":"3D modeling of high-Tc superconductors by finite element software","volume":"25","author":"Zhang","year":"2012","journal-title":"Supercond. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TASC.2021.3057570","article-title":"3D Equivalent Space-Varying Permeability Model of HTS Bulks for Computation of Electromagnetic Forces","volume":"31","author":"Peixoto","year":"2021","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"085001","DOI":"10.1088\/1361-6668\/ab9544","article-title":"Comparison of fast computing methods for ZFC High-temperature superconductors bulks","volume":"33","author":"Fernandes","year":"2020","journal-title":"Supercond. Sci. Technol."},{"key":"ref_23","unstructured":"(2012, January 11). COMSOL Multiphysics 3. Available online: http:\/\/www.comsol.com."}],"container-title":["Actuators"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-0825\/10\/12\/311\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:36:23Z","timestamp":1760168183000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-0825\/10\/12\/311"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,26]]},"references-count":23,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["act10120311"],"URL":"https:\/\/doi.org\/10.3390\/act10120311","relation":{},"ISSN":["2076-0825"],"issn-type":[{"value":"2076-0825","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,26]]}}}