vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университетvmait-79Research ArticleСтатьиМатематическое моделирование термоупругого поведения покрытия с учетом разогрева и износа от тренияMathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wearhttps://orcid.org/0000-0002-5626-1491ЗеленцовВладимир БорисовичZelentsovVladimir Borisovich

Зеленцов Владимир Борисович, руководитель Ресурсного центра коллективного пользования НОЦ «Материалы» Донского государственного технического университета (РФ, 344000, г. Ростов-на-Дону, пл. Гагарина, 1), кандидат физико-математических наук, старший научный сотрудник

Zelentsov Vladimir Borisovich, Head of Center, Scientific Equipment Joint Use Center, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Candidate of Science in Physics and Maths, Senior researcher

vbzelen@gmail.comhttps://orcid.org/0000-0002-5639-274XМитринБорис ИгоревичMitrinBoris Igorevich

Митрин Борис Игоревич, младший научный сотрудник Лаборатории функционально-градиентных и композиционных материалов НОЦ «Материалы» Донского государственного технического университета (РФ, 344000, г. Ростов-на-Дону, пл. Гагарина, 1), кандидат физико-математических наук

Mitrin Boris Igorevich, Junior researcher, Functionally graded and composite materials laboratory, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Candidate of Science in Physics and Maths

bmitrin@dstu.edu.ruhttps://orcid.org/0000-0001-9835-818XЛубягинИгорь АнатольевичLubyaginIgor Anatolyevich

Лубягин Игорь Анатольевич, младший научный сотрудник Лаборатории функционально-градиентных и композиционных материалов НОЦ «Материалы» Донского государственного технического университета (РФ, 344000, г. Ростов-на-Дону, пл. Гагарина, 1)

Lubyagin Igor Anatolyevich, Junior researcher, Functionally graded and composite materials laboratory, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation)

hammavet@gmail.comhttps://orcid.org/0000-0002-2756-5752АйзиковичСергей МихайловичAizikovichSergey Mikhailovich

Айзикович Сергей Михайлович, заведующий Лабораторией функционально-градиентных и композиционных материалов НОЦ «Материалы» Донского государственного технического университета (РФ, 344000, г. Ростов-на-Дону, пл. Гагарина, 1), доктор физико-математических наук, старший научный сотрудник

Aizikovich Sergey Mikhailovich, Head of Laboratory, Functionally graded and composite materials laboratory, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Senior researcher.

saizikovich@gmail.comДонской государственный технический университет (РФ, 344000, г. Ростов-на-Дону, пл. Гагарина, 1)РоссияDon State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation)Russian FederationДонской государственный технический университет (РФ, 344000, г. Ростов-на-Дону, пл. Гагарина, 1)РоссияDon State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation)Russian Federation2017290320231179Copyright © Зеленцов В.Б., Митрин Б.И., Лубягин И.А., Айзикович С.М., 20232023Зеленцов В.Б., Митрин Б.И., Лубягин И.А., Айзикович С.М.Zelentsov V.B., Mitrin B.I., Lubyagin I.A., Aizikovich S.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/79

В работе описывается применение метода интегральных преобразований для решения квазистатической контактной задачи об износе покрытия. Разогрев и износ покрытия от трения происходит при скольжении жёсткого тела по его поверхности. Задача рассматривается в рамках связанной теории термоупругости. Решение задачи построено в виде контурных квадратур обратного преобразования Лапласа. В результате вычисления полученных квадратур, решение записано в виде рядов по полюсам их подынтегральных функций. Проведено исследование полюсов подынтегральных функций решения задачи в зависимости от четырех безразмерных параметров задачи. Подробно изучена зависимость полученных решений в зависимости от безразмерных и размерных параметров задачи. Приведены численные примеры полученных решений — контактных напряжений, смещений, температуры материала покрытия.

This work describes application of the integral transform method to solution of a quasi-static contact problem of the coating wear-out. Frictional heating and wear of the coating occurs during the sliding of a rigid body over its surface. The problem is considered in the framework of the coupled thermoelasticity theory. The solution of the problem is constructed in the form of contour quadratures of the inverse Laplace transformation. After the calculation of the quadratures the solution of the problem is constructed in the form of series over the poles of the integrands. Investigation of the poles of integrands is performed in dependence on four dimensionless parameters of the problem. The solutions obtained are studied in detail with respect to the dimensionless and dimensional parameters of the problem. Numerical examples of the obtained solutions for contact stresses, displacements, temperature and wear of the coating are presented.

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The authors declare that there are no conflicts of interest present.