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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">10.32864/0202-4977-2025-46-6-544-551</article-id><article-id custom-type="elpub" pub-id-type="custom">fwj-101</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>Особенности контактного взаимодействия и трехмерное напряженно-деформированное состояние системы для испытаний на фрикционно-механическую усталость</article-title><trans-title-group xml:lang="en"><trans-title>Features of Contact Interaction and Three-Dimensional Stress-Strain State of the System for Friction-Mechanical Fatigue Testing</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>Щербаков</surname><given-names>С. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Sherbakov</surname><given-names>S. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Академическая, 12, г. Минск 220072</p></bio><bio xml:lang="en"><p>Akademicheskaya str., 12, Minsk 220072</p></bio><email xlink:type="simple">sherbakovss@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>Климкович</surname><given-names>Н. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Klimkovich</surname><given-names>N. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Академическая, 12, г. Минск 220072</p></bio><bio xml:lang="en"><p>Akademicheskaya str., 12, Minsk 220072</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Подгайская</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Podgayskaya</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Академическая, 12, г. Минск 220072</p></bio><bio xml:lang="en"><p>Akademicheskaya str., 12, Minsk 220072</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Полещук</surname><given-names>М. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Polestchuk</surname><given-names>M. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Академическая, 12, г. Минск 220072</p></bio><bio xml:lang="en"><p>Akademicheskaya str., 12, Minsk 220072</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Боровков</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Borovkov</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Политехническая, д. 29 литера Б, г. Санкт-Петербург 195251</p></bio><bio xml:lang="en"><p>Polytechnicheskaya str.,29 B, St. Petersburg 195251</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>Карчевская</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Karchevskaia</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Политехническая, д. 29 литера Б, г. Санкт-Петербург 195251</p></bio><bio xml:lang="en"><p>Polytechnicheskaya str.,29 B, St. Petersburg 195251</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>Новокшенов</surname><given-names>А. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Novokshenov</surname><given-names>A. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Политехническая, д. 29 литера Б, г. Санкт-Петербург 195251</p></bio><bio xml:lang="en"><p>Polytechnicheskaya str.,29 B, St. Petersburg 195251</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>Матвеева</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Matveeva</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ул. Политехническая, д. 29 литера Б, г. Санкт-Петербург 195251</p></bio><bio xml:lang="en"><p>Polytechnicheskaya str.,29 B, St. Petersburg 195251</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Объединенный институт машиностроения НАН Беларуси</institution><country>Беларусь</country></aff><aff xml:lang="en"><institution>he Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus</institution><country>Belarus</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Санкт-Петербургский политехнический университет Петра Великого</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Peter the Great St.Petersburg Polytechnic University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>30</day><month>09</month><year>2026</year></pub-date><volume>46</volume><issue>6</issue><fpage>544</fpage><lpage>551</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/101">https://fwj.ejournal.by/jour/article/view/101</self-uri><abstract><p>Цель исследования — определение методом конечных элементов напряженно-деформированного состояния и характеристик контактного взаимодействия при различных режимах нагружения системы вкладыш—вал, используемой для исследований материалов при работе в условиях фрикционно-механической усталости. В ходе исследования рассмотрены случаи нагружения системы различными соотношениями контактной (FN), приложенной ко вкладышу, и изгибающей (Fb), приложенной к валу, силами. Верификация полученных результатов проводилась при помощи балочной теории и теории контактного взаимодействия. По результатам исследования было показано, что в зависимости от направления и величины изгибающего нагружения возможно формирование поверхности контакта трех различных форм: прямоугольной, эллиптической и разделённой на две части. Кроме того, найдены оптимальные соотношения нагрузок, минимизирующие интенсивность напряжений: во вкладыше при сонаправленных Fb и FN для соотношения FN/Fb = 20—50 (например, при FN = –500 Н, Fb = –25 Н), в вале при разнонаправленных Fb и FN для соотношения FN/Fb = 20 (например, при FN = –500 Н, Fb = 25 Н). Таким образом, представленный подход к моделированию объёмной повреждаемости пары трения, один из элементов которой нагружен неконтактной нагрузкой, даёт возможность решать задачи оптимизации и управления повреждаемостью сложных технических систем за счёт изменения граничных условий без дорогостоящего изменения конструкции и материалов.</p></abstract><trans-abstract xml:lang="en"><p>The purpose of the study is to determine by finite element method the stress-strain state and behavior of the contact interactions characteristics under various loading conditions of the liner-shaft system, which is used for materials research when operating under conditions of frictional and mechanical fatigue. The cases of loading the system with different ratios of contact forces applied to the liner and bending forces applied to the shaft are considered. The verification of the obtained results is carried out using beam theory and contact theory. According to the results of the study, it is shown that depending on the direction and magnitude of the bending load, it is possible to form contact area of three different shapes: rectangular, elliptical and divided into two parts. Furthermore, optimal load ratios minimizing the von Mises stresses were identified: in the liner with co-directed Fb and FN at a ratio of FN/Fb = 20—50 (e.g., at FN = 500 N, Fb = 25 N); in the shaft with oppositely directed Fb and FN at a ratio of FN/ Fb = 20 (e.g., at FN = 500 N, Fb = 25 N). Thus, the presented approach to modeling volumetric damage in a friction pair, one element of which is loaded by a non-contact force, provides an opportunity to solve optimization and damage management problems for complex technical systems by controlling boundary conditions without costly design or material changes.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>трёхмерное численное моделирование</kwd><kwd>объёмное напряженно-деформированное состояние</kwd><kwd>метод конечных элементов</kwd><kwd>система вкладыш—вал</kwd><kwd>контактное взаимодействие</kwd></kwd-group><kwd-group xml:lang="en"><kwd>three-dimensional numerical modeling</kwd><kwd>volumetric stress-strain state</kwd><kwd>finite element method</kwd><kwd>liner-shaft system</kwd><kwd>contact interaction</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">Popov V.L. Contact Mechanics and Friction. — Berlin: Springer Berlin Heidelberg. — 2010</mixed-citation><mixed-citation xml:lang="en">Popov V.L. Contact Mechanics and Friction. — Berlin: Springer Berlin Heidelberg. — 2010</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Goryacheva I.G. Contact Mechanics in Tribology. — Springer Science &amp; Business Media. — 2013</mixed-citation><mixed-citation xml:lang="en">Goryacheva I.G. Contact Mechanics in Tribology. — Springer Science &amp; Business Media. — 2013</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Sosnovskiy L.A., Sherbakov S.S., Khonsari M.M., and Bogdanovich A.V. From Fatigue and Tribology to Tribo-Fatigue // Int. J. Materials and Structural Integrity. — 2021 (14), no. 2/3/4, 164—237. https://doi.org/10.1504/IJMSI.2021.125815</mixed-citation><mixed-citation xml:lang="en">Sosnovskiy L.A., Sherbakov S.S., Khonsari M.M., and Bogdanovich A.V. From Fatigue and Tribology to Tribo-Fatigue // Int. J. Materials and Structural Integrity. — 2021 (14), no. 2/3/4, 164—237. https://doi.org/10.1504/IJMSI.2021.125815</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Wilson S. and Alpas A. T. Wear Mechanism Maps for Metal Matrix Composites // Wear. — 1997 (212), no. 1, 41—49. https://doi.org/10.1016/S0043-1648(97)00142-7</mixed-citation><mixed-citation xml:lang="en">Wilson S. and Alpas A. T. Wear Mechanism Maps for Metal Matrix Composites // Wear. — 1997 (212), no. 1, 41—49. https://doi.org/10.1016/S0043-1648(97)00142-7</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Lv Q., He W., and Lu Z. Physical Models of Sliding Friction: A Review // Friction. — 2025. https://doi.org/10.26599/FRICT.2025.9441132</mixed-citation><mixed-citation xml:lang="en">Lv Q., He W., and Lu Z. Physical Models of Sliding Friction: A Review // Friction. — 2025. https://doi.org/10.26599/FRICT.2025.9441132</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Berger E.J. Friction Modeling for Dynamic System Simulation //Appl. Mech. Rev. — 2002 (55), no. 6, 535—577. https://doi.org/10.1115/1.1501080</mixed-citation><mixed-citation xml:lang="en">Berger E.J. Friction Modeling for Dynamic System Simulation //Appl. Mech. Rev. — 2002 (55), no. 6, 535—577. https://doi.org/10.1115/1.1501080</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Faulkner A. and Arnell R.D. The Development of a Finite Element Model to Simulate the Sliding Interaction between Two, Three-Dimensional, Elastoplastic, Hemispherical Asperities // Wear. — 2000 (242), no. 1–2, 114—122. https://doi.org/10.1016/S0043-1648(00)00406-3</mixed-citation><mixed-citation xml:lang="en">Faulkner A. and Arnell R.D. The Development of a Finite Element Model to Simulate the Sliding Interaction between Two, Three-Dimensional, Elastoplastic, Hemispherical Asperities // Wear.  —  2000  (242),  no.  1–2,  114—122. https://doi.org/10.1016/S0043-1648(00)00406-3</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Писаренко Г.С., Яковлев А.П., Матвеев В.В. Справочник по сопротивлению материалов. — Киев: Наук. Думка. — 1988</mixed-citation><mixed-citation xml:lang="en">Pisarenko G.S., Yakovlev A.P., Matveev V.V. Spravochnik po soprotivleniyu materialov. — Kiev: Nauk. Dumka. — 1988 (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Испытательный центр SZ-01. Руководство по эксплуатации SZ.000.000 РЭ. — Гомель: НПО Трибофатика. — 2013</mixed-citation><mixed-citation xml:lang="en">Ispytatelnyy centr SZ-01. Rukovodstvo po kspluatacii SZ.000.000 R. — Gomel: NPO Tribofatika, 2013 (in Russian)</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
