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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">fwj</journal-id><journal-title-group><journal-title xml:lang="ru">Трение и и износ</journal-title><trans-title-group xml:lang="en"><trans-title>Title in english</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0000-0000</issn><issn pub-type="epub">0000-0000</issn><publisher><publisher-name>AGU</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.32864/0202-4977-2024-45-3-262-274</article-id><article-id custom-type="elpub" pub-id-type="custom">fwj-48</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Расчетно-аналитическое прогнозирование износа покрытий при трибологических испытаниях на основе моделей контактно-усталостного разрушения</article-title><trans-title-group xml:lang="en"><trans-title>Calculation and Analytical Prediction of Coating Wear During Tribological Tests Based on Models of Contact Fatigue Failure</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кудряков</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kudryakov</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>пл. Ростовского Стрелкового Полка Народного Ополчения, 2, г. Ростов-на-Дону 344038, Россия</p><p>пл. Гагарина, 1, г. Ростов-на-Дону 344003, Россия</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don 344038, Russia</p><p>Gagarin square, 1, Rostov-on-Don 344000, Russia</p></bio><email xlink:type="simple">kudryakov@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Колесников</surname><given-names>В. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Kolesnikov</surname><given-names>V. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>пл. Ростовского Стрелкового Полка Народного Ополчения, 2, г. Ростов-на-Дону 344038, Россия</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don 344038, Russia</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ковалева</surname><given-names>И. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Kavaliova</surname><given-names>I. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Кирова, 32а, г. Гомель 246050, Беларусь</p></bio><bio xml:lang="en"><p>Kirov st., 32a, Gomel 246050, Belarus</p></bio><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Колесников</surname><given-names>И. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kolesnikov</surname><given-names>I. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>пл. Ростовского Стрелкового Полка Народного Ополчения, 2, г. Ростов-на-Дону 344038, Россия</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don 344038, Russia</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мантуров</surname><given-names>Д. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Manturov</surname><given-names>D. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>пл. Ростовского Стрелкового Полка Народного Ополчения, 2, г. Ростов-на-Дону 344038, Россия</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don 344038, Russia</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Ростовский государственный университет путей сообщения; Донской государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Rostov State Transport University; Don State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Ростовский государственный университет путей сообщения</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Rostov State Transport University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Институт механики металлополимерных систем им. В.А. Белого НАН Беларуси</institution><country>Беларусь</country></aff><aff xml:lang="en"><institution>V.A. Belyi Metal-Polymer Research Institute of National Academy of Sciences of Belarus</institution><country>Belarus</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>27</day><month>09</month><year>2026</year></pub-date><volume>45</volume><issue>3</issue><fpage>262</fpage><lpage>274</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; AGU, 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">AGU</copyright-holder><copyright-holder xml:lang="en">AGU</copyright-holder><license xlink:href="https://fwj.ejournal.by/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://fwj.ejournal.by/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://fwj.ejournal.by/jour/article/view/48">https://fwj.ejournal.by/jour/article/view/48</self-uri><abstract><p>В работе рассмотрены условия трибологических испытаний стальных образцов с нитридными ионно-плазменными покрытиями. Предложена расчётно-аналитическая модель для количественной оценки параметров контакта и изнашивания при испытаниях на трение скольжения: размера контактной площадки, глубины контактного сближения, глубины пластической зоны, напряжений в покрытии, предела усталости, критической толщины покрытия, исключающей его прогиб. Показано, что покрытия, с толщиной выше критической, реализуют свой потенциал физико-механических и трибологических свойств независимо от подложки. При недостаточной толщине покрытия результат трибологических испытаний определяется поведением системы «покрытие—подложка» — высокотвёрдое нитридное покрытие на пластичной стальной подложке испытывает прогиб и преждевременное хрупкое разрушение. Для оценки износа покрытий в этом случае рекомендовано использование моделей усталостного разрушения с построением кривой усталости Велера и определением предела усталости на основе теории Муроками-Эндо. Реализация рекомендованного подхода выполнена для исследованных нитридных покрытий с использованием базы собственных экспериментальных данных.</p></abstract><trans-abstract xml:lang="en"><p>The work examines the conditions of tribological tests of steel samples with nitride ion-plasma coatings. A calculation and analytical model is proposed for quantitative assessment of contact and wear parameters during sliding friction tests: the size of the contact area, the depth of contact approach, the depth of the plastic zone, stresses in the coating, fatigue limit, and the critical thickness of the coating, which excludes its deflection. It has been shown that coatings with a thickness above critical realize their potential for physical, mechanical and tribological properties regardless of the substrate. If the coating thickness is insufficient, the result of tribological tests is determined by the behavior of the “coating-substrate” system — a high-hard nitride coating on a ductile steel substrate experiences deflection and premature brittle failure. To assess the wear of coatings in this case, it is recommended to use fatigue failure models with construction of the Wöhler fatigue curve and determination of the fatigue limit based on the Murokami-Endo theory. The implementation of the recommended approach was carried out for the studied nitride coatings using a database of our own experimental data.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>ионно-плазменная технология</kwd><kwd>нитридные покрытия</kwd><kwd>физико-механические свойства</kwd><kwd>трибология</kwd><kwd>износостойкость</kwd><kwd>трение скольжения</kwd><kwd>механика контактного разрушения</kwd><kwd>усталость</kwd></kwd-group><kwd-group xml:lang="en"><kwd>ion plasma technology</kwd><kwd>nitride coatings</kwd><kwd>physical and mechanical properties</kwd><kwd>tribology</kwd><kwd>wear resistance</kwd><kwd>sliding friction</kwd><kwd>contact fracture mechanics</kwd><kwd>fatigue</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Мышкин Н.К., Петроковец М.И. Трение, смаз-ка, износ. 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