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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">cheb</journal-id><journal-title-group><journal-title xml:lang="ru">Чебышевский сборник</journal-title><trans-title-group xml:lang="en"><trans-title>Chebyshevskii Sbornik</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-8383</issn><publisher><publisher-name>Tula State Lev Tolstoy  Pedagogical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22405/2226-8383-2022-23-2-191-200</article-id><article-id custom-type="elpub" pub-id-type="custom">cheb-1280</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>История математики и приложений</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Сomputer science</subject></subj-group></article-categories><title-group><article-title>Математические модели внедрения стального шарообразного индентора в титановый сплав при трении в биологических смазочных средах</article-title><trans-title-group xml:lang="en"><trans-title>Research of the influence of biological lubricants on the tribological properties of the steel - titanium alloy friction pair</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>Стрельникова</surname><given-names>Ангелина Анатольевна</given-names></name><name name-style="western" xml:lang="en"><surname>Strelnikova</surname><given-names>Angelina Anatolyevna</given-names></name></name-alternatives><bio xml:lang="ru"><p>аспирант</p></bio><bio xml:lang="en"><p>postgraduate student</p></bio><email xlink:type="simple">strelnikova.angelina@bk.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>Бреки</surname><given-names>Александр Джалюльевич</given-names></name><name name-style="western" xml:lang="en"><surname>Breki</surname><given-names>Alexander Dzhalyulevich</given-names></name></name-alternatives><bio xml:lang="ru"><p>доктор технических наук, доцент</p></bio><bio xml:lang="en"><p>doctor of technical sciences, associate professor</p></bio><email xlink:type="simple">albreki@yandex.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>Скотникова</surname><given-names>Маргарита Александровна</given-names></name><name name-style="western" xml:lang="en"><surname>Skotnikova</surname><given-names>Margarita Aleksandrovna</given-names></name></name-alternatives><bio xml:lang="ru"><p>доктор технических наук, профессор</p></bio><bio xml:lang="en"><p>doctor of technical sciences, professor</p></bio><email xlink:type="simple">albreki@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Плотников</surname><given-names>Дмитрий Георгиевич</given-names></name><name name-style="western" xml:lang="en"><surname>Plotnikov</surname><given-names>Dmitry Georgievich</given-names></name></name-alternatives><bio xml:lang="ru"><p>кандидат технических наук, доцент</p></bio><bio xml:lang="en"><p>candidate of technical sciences, associate professor</p></bio><email xlink:type="simple">albreki@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Подгурскас</surname><given-names>Юозас</given-names></name><name name-style="western" xml:lang="en"><surname>Padgurskas</surname><given-names>Juozas</given-names></name></name-alternatives><bio xml:lang="ru"><p>доктор технических наук, профессор</p></bio><bio xml:lang="en"><p>doctor of technical sciences, professor</p></bio><email xlink:type="simple">juozas.padgurskas@asu.lt</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гвоздев</surname><given-names>Александр Евгеньевич</given-names></name><name name-style="western" xml:lang="en"><surname>Gvozdev</surname><given-names>Alexander Evgenievich</given-names></name></name-alternatives><bio xml:lang="ru"><p>доктор технических наук, профессор</p></bio><bio xml:lang="en"><p>doctor of engineering, professor</p></bio><email xlink:type="simple">gwozdew.alexandr2013@yandex.ru</email><xref ref-type="aff" rid="aff-4"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кузовлева</surname><given-names>Ольга Владимировна</given-names></name><name name-style="western" xml:lang="en"><surname>Kuzovleva</surname><given-names>Olga Vladimirovna</given-names></name></name-alternatives><bio xml:lang="ru"><p>кандидат технических наук, доцент</p></bio><bio xml:lang="en"><p>candidate of technical sciences, associate professor</p></bio><email xlink:type="simple">kusovleva@yandex.ru</email><xref ref-type="aff" rid="aff-5"/></contrib></contrib-group><aff-alternatives id="aff-1"><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><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>St. Petersburg Polytechnic University of Peter the Great</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Университет Александраса Стулгинскиса</institution><country>Литва</country></aff><aff xml:lang="en"><institution>Alesandras Stulginskis University</institution><country>Lithuania</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>Тульский государственный педагогический университет им. Л.Н. Толстого</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tula State Lev Tolstoy Pedagogical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-5"><aff xml:lang="ru"><institution>Российский государственный университет правосудия</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Russian State University of Justice</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>08</day><month>07</month><year>2022</year></pub-date><volume>23</volume><issue>2</issue><fpage>191</fpage><lpage>200</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Стрельникова А.А., Бреки А.Д., Скотникова М.А., Плотников Д.Г., Подгурскас Ю., Гвоздев А.Е., Кузовлева О.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Стрельникова А.А., Бреки А.Д., Скотникова М.А., Плотников Д.Г., Подгурскас Ю., Гвоздев А.Е., Кузовлева О.В.</copyright-holder><copyright-holder xml:lang="en">Strelnikova A.A., Breki A.D., Skotnikova M.A., Plotnikov D.G., Padgurskas J., Gvozdev A.E., Kuzovleva O.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.chebsbornik.ru/jour/article/view/1280">https://www.chebsbornik.ru/jour/article/view/1280</self-uri><abstract><p>В работе приведены результаты исследования влияния биологических смазочных сред на трибологические свойства пары трения «сталь – титановый сплав». Трибологические испытания проводились при вдавливании (царапании) на пути трения 2 мм с увеличениемнагрузки от 0,030 до 10 Н на приборе MicroIndentation Tester CSM. Исследования проводили при различных условиях: сухое трение, с гиалуроновой кислотой и с биологическим маслом. Установлено, что смазочные среды биологического происхождения создают граничные смазочные слои на поверхностях трения и способны уменьшать изнашивание вследствие микрорезания. Реализована разработка и экспериментальная проверка математической модели, выражающей зависимость глубины внедрения от пути трения и других параметров.</p></abstract><trans-abstract xml:lang="en"><p>The paper presents the results of a study of the influence of biological lubricants on the tribological properties of the friction pair "steel - titanium alloy". Tribological tests were carried out with indentation (scratching) on a friction path of 2 mm with an increase in load from 0.030 to 10 N on a Micro Indentation Tester CSM. The studies were carried out under various conditions: dry rubbing, with hyaluronic acid and with biological oil. It was found that lubricating media of biological origin create boundary lubricating layers on friction surfaces and are able to reduce wear due to microcutting. The development and experimental verification of a mathematical model expressing the dependence of the penetration depth on the friction path and other parameters has been implemented.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>биологические смазочные среды</kwd><kwd>высокотемпературная деформация</kwd><kwd>титановый сплав</kwd><kwd>трибологические свойства.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>biological lubricating media</kwd><kwd>titanium alloy</kwd><kwd>high-temperature deformation</kwd><kwd>tribological properties.</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование проведено в рамках гранта по программе Erasmus на обучение в весеннем семестре 2020 года. Авторы выражают благодарность сотрудникам Университета Витаутаса Великого за помощь в проведении эксперимента.</funding-statement><funding-statement xml:lang="en">The research was carried out within the framework of a grant under the Erasmus program for training in the spring semester of 2020. The authors are grateful to the staff of Vytautas Magnus University for their help in carrying out the experiment.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Tomoyuki Kaya. Recent developments in Research, production and application of titanium in Japan / Kaya Tomoyuki // Ti-2007. Science and technology. Proceedings of the 11th World conference on titanium. Kyoto. Japan. 2007. pp. 49–56.</mixed-citation><mixed-citation xml:lang="en">Tomoyuki Kaya. 2007, “Recent developments in Research, production and application of titanium in Japan”, Ti-2007. 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Mathematical Simulation of the Sliding Friction of Silicon Carbide in an Aqueous Medium // Russian Metallurgy (Metally)this link is disabled, 2021, 2021(4), стр. 507–511.</mixed-citation><mixed-citation xml:lang="en">Breki A.D., Chulkin S.G., Gvozdev A.E., Kolmakov A.G., Kuzovleva O.V. 2021, “Empirical Mathematical Model for the Wear Kinetics of Porous Gas-Thermal Coatings”, Russian Metallurgy (Metally), 4, pp. 496–500.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Breki, A.D., Chulkin, S.G., Gvozdev, A.E., Kolmakov, A.G., Kuzovleva, O.V. Empirical Mathematical Model for the Wear Kinetics of Porous Gas-Thermal Coatings // Russian Metallurgy (Metally)this link is disabled, 2021, 2021(4), стр. 496–500.</mixed-citation><mixed-citation xml:lang="en">Breki, A.D., Chulkin, S.G., Gvozdev, A.E., Kolmakov, A.G., Kuzovleva, O.V. 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