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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">zldm</journal-id><journal-title-group><journal-title xml:lang="ru">Заводская лаборатория. Диагностика материалов</journal-title><trans-title-group xml:lang="en"><trans-title>Industrial laboratory. Diagnostics of materials</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1028-6861</issn><issn pub-type="epub">2588-0187</issn><publisher><publisher-name>ООО «Издательство «ТЕСТ-ЗЛ»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26896/1028-6861-2023-89-9-82-90</article-id><article-id custom-type="elpub" pub-id-type="custom">zldm-2017</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>МАТЕМАТИЧЕСКИЕ МЕТОДЫ ИССЛЕДОВАНИЯ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICAL METHODS OF INVESTIGATION</subject></subj-group></article-categories><title-group><article-title>Применение математических методов для исследования температурно-временных условий процесса фрикционной наплавки при изготовлении функционально-организованных сталеалюминиевых композиций</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical methods in studying temperature-time conditions of the friction surfacing in the manufacture of functionally organized steel-aluminum compositions</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>Захарченко</surname><given-names>В. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Zaharchenko</surname><given-names>V. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Владислав Дмитриевич Захарченко</p><p>105005, Москва, 2-я Бауманская ул., д. 5, стр. 1</p></bio><bio xml:lang="en"><p>Vladislav D. Zaharchenko</p><p>5, 2-ya Baumanskaya, Moscow, 105005</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>Михеев</surname><given-names>Р. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Mikheev</surname><given-names>R. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Роман Сергеевич Михеев</p><p>105005, Москва, 2-я Бауманская ул., д. 5, стр. 1</p></bio><bio xml:lang="en"><p>Roman S. Mikheev</p><p>5, 2-ya Baumanskaya, Moscow, 105005</p></bio><email xlink:type="simple">mikheev.roman@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>Калашников</surname><given-names>И. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Kalashnikov</surname><given-names>I. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Игорь Евгеньевич Калашников</p><p>105005, Москва, 2-я Бауманская ул., д. 5, стр. 1,</p><p>119334, Москва, Ленинский пр-т, д. 49</p></bio><bio xml:lang="en"><p>Igor E. Kalashnikov</p><p>5, 2-ya Baumanskaya, Moscow, 105005,</p><p>49, Leninskii prospekt, Moscow, 119334</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Московский государственный технический университет имени Н. Э. Баумана (национальный исследовательский университет)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Moscow State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Московский государственный технический университет имени Н. Э. Баумана (национальный исследовательский университет);&#13;
Институт металлургии и материаловедения им. А. А. Байкова РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Moscow State Technical University;&#13;
Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>24</day><month>09</month><year>2023</year></pub-date><volume>89</volume><issue>9</issue><fpage>82</fpage><lpage>90</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Захарченко В.Д., Михеев Р.С., Калашников И.Е., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Захарченко В.Д., Михеев Р.С., Калашников И.Е.</copyright-holder><copyright-holder xml:lang="en">Zaharchenko V.D., Mikheev R.S., Kalashnikov I.E.</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.zldm.ru/jour/article/view/2017">https://www.zldm.ru/jour/article/view/2017</self-uri><abstract><p>Разработана математическая модель для исследования температурно-временных условий процесса фрикционной наплавки при изготовлении функционально-организованных сталеалюминиевых композиций и проведена ее валидация. В качестве материала расходуемого стержня при фрикционной наплавке применяли прутки из чистого алюминия марки ER1100. Подложка в форме прямоугольной пластины была изготовлена из качественной стали 20. Геометрическую модель объекта при моделировании процесса фрикционной наплавки в программном комплексе ANSYS 2021R2 задавали в виде стержня и подложки. Исходными данными для проведения расчетов температурно-временных условий процесса фрикционной наплавки в ПК ANSYS являлись: геометрические параметры объекта моделирования; характеристики тепловых нагрузок источника нагрева, зависящие от технологических параметров режима наплавки (скорость осевого вращения стержня, осевое давление, граничные условия объекта моделирования для температурной задачи); вспомогательные параметры, определяющие порядок выполнения расчетов. В качестве параметра тепловых нагрузок источника рассматривали тепловую мощность, возникающую в месте физического контакта вращающегося расходуемого стержня и подложки. Расчет распространения тепла для процесса фрикционной наплавки проводили по схеме с нормально-круговым источником, расположенным на поверхности подложки. Выбранная расчетная схема отражает основную особенность процесса фрикционной наплавки — введение тепла вследствие трения между вращающимся расходуемым стержнем и подложкой. Показано, что за счет учета граничных условий и геометрических особенностей 3D-модели разработанная математическая модель характеризуется удовлетворительной сходимостью и позволяет с неопределенностью не более 5 % определять температуру нагрева стальной подложки при формировании методом наплавки на ее поверхности функциональных алюминиевых покрытий, а также композиционных материалов на их основе.</p></abstract><trans-abstract xml:lang="en"><p>A mathematical model for studying temperature and time conditions of the process of friction surfacing in the manufacture of functionally organized steel-aluminum compositions has been developed and validated. Bars made of pure aluminum grade ER1100 were used as the consumable rod material during friction surfacing. The substrate in the form of a rectangular plate was made of high-quality steel 20. The geometric model of the object when modeling the process of friction surfacing in the ANSYS 2021R2 software package was specified in the form of a rod and a substrate. The initial data for calculating temperature-time conditions of the friction surfacing process are: geometric parameters of the simulation object; characteristics of thermal loads of the heating source which depend on the technological parameters of the surfacing mode (the speed of axial rotation of the rod, axial pressure, boundary conditions of the simulation object for the temperature problem), and auxiliary parameters that determine the order of calculations. The thermal power arising at the point of physical contact between the rotating consumable rod and the substrate was considered a parameter of the source thermal load. The calculation of heat propagation for the friction surfacing process was carried out according to a scheme with a normally circular source located on the substrate surface. The calculation scheme directly reflects the main feature of the friction surfacing process: the introduction of heat due to friction between the rotating consumable rod and the substrate. It is shown that taking into account the boundary conditions and geometric features of the 3D model provide a satisfactory convergence of developed mathematical model and ensure the uncertainty of no more than 5 % in determining the heating temperature of the substrate when forming functional aluminum coatings, as well as composite materials on their base when surfacing them on the surface of steel substrates.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>сталеалюминиевые композиции</kwd><kwd>фрикционная наплавка</kwd><kwd>математическая модель</kwd><kwd>температурно-временные условия</kwd><kwd>тепловая мощность</kwd></kwd-group><kwd-group xml:lang="en"><kwd>steel-aluminum compositions</kwd><kwd>friction surfacing process</kwd><kwd>mathematical model</kwd><kwd>temperature-time conditions</kwd><kwd>thermal power</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">Gandra J., Krohn H., Miranda R. 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