{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T22:58:56Z","timestamp":1774997936365,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T00:00:00Z","timestamp":1672272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Ministry of Science and Higher Education","award":["0212\/SBAD\/0568"],"award-info":[{"award-number":["0212\/SBAD\/0568"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The paper presents a field model of coupled phenomena occurring in an axisymmetric magnetorheological brake. The coupling between transient fluid dynamics and electromagnetic and thermal fields as well as mechanical equilibrium equations is taken into account. The magnetic field in the studied brake is of an excited hybrid manner, i.e., by the permanent magnets (PMs) and current Is in the excitation winding. The finite element method and a step-by-step algorithm have been implemented in the proposed field model of coupled phenomena in the considered brake. The nonlinearity of the magnetic circuit and rheological properties of a magnetorheological fluid (MR fluid) as well as the influence of temperature on the properties of materials have been taken into account. To solve equations of the obtained field model, the Newton\u2013Raphson method and the coupled block over-relaxation method have been implemented. The elaborated algorithm has been successfully used in the analysis of the phenomena in the considered magnetorheological brake. The accuracy of the developed model and its usefulness have been verified by a comparative analysis of the results of simulation and laboratory tests carried out for the developed prototype of the studied brake.<\/jats:p>","DOI":"10.3390\/s23010358","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T03:19:46Z","timestamp":1672370386000},"page":"358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Coupled Field Analysis of Phenomena in Hybrid Excited Magnetorheological Fluid Brake"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5569-9574","authenticated-orcid":false,"given":"Wojciech","family":"Szelag","sequence":"first","affiliation":[{"name":"Institute of Electrical Engineering and Electronics, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5427-059X","authenticated-orcid":false,"given":"Cezary","family":"Jedryczka","sequence":"additional","affiliation":[{"name":"Institute of Electrical Engineering and Electronics, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adam","family":"Myszkowski","sequence":"additional","affiliation":[{"name":"Institute of Mechanical Technology, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4906-469X","authenticated-orcid":false,"given":"Rafal M.","family":"Wojciechowski","sequence":"additional","affiliation":[{"name":"Institute of Electrical Engineering and Electronics, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,29]]},"reference":[{"key":"ref_1","unstructured":"Piech, Z., and Szelag, W. 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