{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T21:13:38Z","timestamp":1776114818788,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,14]],"date-time":"2023-01-14T00:00:00Z","timestamp":1673654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UIDP\/04077\/2020"],"award-info":[{"award-number":["UIDP\/04077\/2020"]}]},{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UIDB\/04077\/2020"],"award-info":[{"award-number":["UIDB\/04077\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>Several aspects must be considered in the design of rolling bearing cages. One of the most important considerations relates to studying and developing a stationary approach for solving problems of heat and mass transfer during convection. In this context, this paper proposes, among other achievements, the development and validation of a model of heat generation that is used, as the basis for an energy-efficient cage design in the context of the roller bearings of axle boxes for rail transport. The forces of interaction of the cage with the bearing parts are determined. The energy-efficient design of the cage is performed with modified friction surfaces in the form of convex contours of the pockets and micro-hollows on the surfaces of the pockets and support rings. On the basis of a flat model, of the interaction between the cage and the bearing parts, the pressure forces on the driving and driven rolling elements in the zone of radial loading are determined. The frictional moment of the bearing has been determined based on the integral design of the cage without taking into account lubrication during the interaction of the cage with the jumpers and with the sides of the basing ring. The calculation of the temperature gradient with standard and improved designs of bearing cages has been performed while taking air blowing into account; results showed a decrease in the average level and growth rate of the bearings\u2019 temperature gradient with an energy-efficient cage design. Based on the obtained results, and on the developed heat generation model, a systematic approach for energy-efficient design of rolling bearing cages is proposed. The proposed approach, as well as the respective developed models, were validated by obtaining and analyzing the experimental results.<\/jats:p>","DOI":"10.3390\/app13021144","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T01:31:15Z","timestamp":1673832675000},"page":"1144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Systematic Approach for Energy-Efficient Design of Rolling Bearing Cages"],"prefix":"10.3390","volume":"13","author":[{"given":"Anatoliy","family":"Gaydamaka","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering Machine Components and Hydropneumatic Systems, National Technical University \u201cKharkiv Polytechnic Institute\u201d, 2, Kyrpychova St., 61002 Kharkiv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0024-5959","authenticated-orcid":false,"given":"Volodymyr","family":"Klitnoi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering Machine Components and Hydropneumatic Systems, National Technical University \u201cKharkiv Polytechnic Institute\u201d, 2, Kyrpychova St., 61002 Kharkiv, Ukraine"}]},{"given":"Sergey","family":"Dobrotvorskiy","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering Technology and Metal-Cutting Machines, National Technical University \u201cKharkiv Polytechnic Institute\u201d, 2, Kyrpychova St., 61002 Kharkiv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8549-4788","authenticated-orcid":false,"given":"Yevheniia","family":"Basova","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering Technology and Metal-Cutting Machines, National Technical University \u201cKharkiv Polytechnic Institute\u201d, 2, Kyrpychova St., 61002 Kharkiv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4417-6115","authenticated-orcid":false,"given":"Dem\u00e9trio","family":"Matos","sequence":"additional","affiliation":[{"name":"School of Design, Polytechnic Institute of C\u00e1vado and Ave, Campus of IPCA, Vila Fresca\u00ednha, S. Martinho, 4750-810 Barcelos, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4917-2474","authenticated-orcid":false,"given":"Jos\u00e9","family":"Machado","sequence":"additional","affiliation":[{"name":"MEtRICs Research Center, Campus of Azur\u00e9m, University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"69","DOI":"10.29354\/diag\/122533","article-title":"On The Problem of Vibration Protection of Rotor Systems with Elastic Adaptive Elements of Quasi-Zero Stiffness","volume":"21","author":"Klitnoi","year":"2020","journal-title":"Diagnostyka"},{"key":"ref_2","first-page":"69","article-title":"Selecting the Method for Pre-tightening Threaded Connections of Heavy Engineering","volume":"305","author":"Gaydamaka","year":"2021","journal-title":"Int. Conf. Reliab. Syst. 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[2nd ed.].","DOI":"10.1007\/3-540-29527-5"}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/13\/2\/1144\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:06:19Z","timestamp":1760119579000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/13\/2\/1144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,14]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["app13021144"],"URL":"https:\/\/doi.org\/10.3390\/app13021144","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,14]]}}}