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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">10.32864/0202-4977-2024-45-2-171-182</article-id><article-id custom-type="elpub" pub-id-type="custom">fwj-19</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>Инженерные соотношения для расчетно-аналитического прогнозирования износа покрытий при трибологических испытаниях</article-title><trans-title-group xml:lang="en"><trans-title>Engineering Relationships for Computational and Analytical Prediction of Coating Wear During Tribological Tests</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, Ростов-на-Дону 344038</p><p>пл. Гагарина, 1, Ростов-на-Дону 344003</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don, 344038</p><p>Gagarin square 1, Rostov-on-Don, 344000</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, Ростов-на-Дону 344038</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don, 344038</p><p> </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, Ростов-на-Дону 344038</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don, 344038</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>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, Ростов-на-Дону 344038</p></bio><bio xml:lang="en"><p>Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya Sq., 2, Rostov-on-Don, 344038</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>Варавка</surname><given-names>В. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Varavka</surname><given-names>V. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>пл. Гагарина, 1, Ростов-на-Дону 344003</p></bio><bio xml:lang="en"><p>Gagarin square 1, Rostov-on-Don, 344000</p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Ростовский государственный университет путей сообщения;&#13;
Донской государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Rostov State Transport University;&#13;
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>Донской государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Don State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>26</day><month>09</month><year>2026</year></pub-date><volume>45</volume><issue>2</issue><fpage>171</fpage><lpage>182</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/19">https://fwj.ejournal.by/jour/article/view/19</self-uri><abstract><p>В работе поставлена задача определения условий трибологических испытаний покрытий, в которых покрытие реализует свой потенциал физико-механических и трибологических свойств независимо от подложки. Использована стандартная методика трибологических испытаний на машине трения по схеме «штифт-пластина» с круговым движением сферического штифта-индентора. Приведены экспериментальные данные исследования структуры и свойств вакуумных ионно-плазменных нитридных покрытий TiN, TiAlN, CrAlSiN толщиной 0,8—4,0 мкм, нанесённых на пластинчатые стальные образцы, предназначенные для испытаний на машине трения. Процесс изнашивания покрытий рассмотрен с позиций механики контактного разрушения и теорий усталости. Предложена расчётно-аналитическая модель для количественной оценки параметров контакта и изнашивания при испытаниях на трение: размера контактной площадки, глубины контактного сближения, глубины пластической зоны, напряжений в покрытии, предела усталости, критической толщины покрытия, исключающей его прогиб. 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 sets the task of determining the conditions for tribological testing of coatings, in which the coating realizes its potential of physical, mechanical and tribological properties regardless of the substrate. A standard method of tribological testing was used on a friction machine according to the “pin-disk” scheme with a circular motion of a spherical indenter pin. Experimental data are presented on the study of the structure and properties of vacuum ion-plasma nitride coatings TiN, TiAlN, CrAlSiN. The coatings had a thickness of 0.8–4.0 microns and were applied to plate steel samples intended for testing in a friction machine. The wear process of coatings is considered from the perspective of contact fracture mechanics and fatigue theories. A calculation and analytical model is proposed for quantitative assessment of contact and wear parameters during 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; critical thickness of the coating, which excludes its deflection. To assess the wear of coatings in this case, it is recommended to use fatigue failure models with the construction of a Woehler 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 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>сканирующая электронная микроскопия</kwd><kwd>физико-механические свойства</kwd><kwd>трибологические свойства</kwd><kwd>испытания на износостойкость</kwd><kwd>механизмы износа покрытий</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>scanning electron microscopy</kwd><kwd>physical and mechanical properties</kwd><kwd>tribological properties</kwd><kwd>wear resistance tests</kwd><kwd>coating wear mechanisms</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">Белый А.В., Карпенко Г.Д., Мышкин Н.К. 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