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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">powder</journal-id><journal-title-group><journal-title xml:lang="ru">Известия вузов. Порошковая металлургия и функциональные покрытия</journal-title><trans-title-group xml:lang="en"><trans-title>Powder Metallurgy аnd Functional Coatings (Izvestiya Vuzov. Poroshkovaya Metallurgiya i Funktsional'nye Pokrytiya)</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1997-308X</issn><issn pub-type="epub">2412-8767</issn><publisher><publisher-name>НИТУ "МИСИС"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17073/1997-308X-2025-1-5-14</article-id><article-id custom-type="elpub" pub-id-type="custom">powder-949</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>Процессы получения и свойства порошков</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Production Processes and Properties of Powders</subject></subj-group></article-categories><title-group><article-title>Влияние передаточного отношения на энергосиловые условия столкновения размольных тел в планетарной мельнице</article-title><trans-title-group xml:lang="en"><trans-title>Influence of gear ratio on the energy-force conditions of grinding body collisions in a planetary mill</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4979-7164</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Аборкин</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Aborkin</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Артемий Витальевич Аборкин – к.т.н., доцент кафедры «Технология машиностроения»</p><p>Россия, 600000, г. Владимир, ул. Горького, 87</p></bio><bio xml:lang="en"><p>Artemiy V. Aborkin – Cand. Sci. (Eng.), Associate Professor of the Department of mechanical engineering technology</p><p>87 Gorky Str., Vladimir 600000, Russia</p></bio><email xlink:type="simple">aborkin@vlsu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5842-9625</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Елкин</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Elkin</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Иванович Елкин – к.т.н., директор Института машиностроения и автомобильного транспорта</p><p>Россия, 600000, г. Владимир, ул. Горького, 87</p></bio><bio xml:lang="en"><p>Aleksey I. Elkin – Cand. Sci. (Eng.), Director of the Institute of Mechanical Engineering and Automobile Transport</p><p>87 Gorky Str., Vladimir 600000, Russia</p></bio><email xlink:type="simple">elkin@vlsu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0000-5757-6922</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рябкова</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Ryabkova</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Варвара Викторовна Рябкова – мл. науч. сотрудник</p><p>Россия, 600000, г. Владимир, ул. Горького, 87</p></bio><bio xml:lang="en"><p>Varvara V. Ryabkova – Junior Researcher</p><p>87 Gorky Str., Vladimir 600000, Russia</p></bio><email xlink:type="simple">VVRyabkova@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0006-0441-5264</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бугаёв</surname><given-names>А. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Bugayov</surname><given-names>A. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Александр Павлович Бугаёв – магистрант</p><p>Россия, 600000, г. Владимир, ул. Горького, 87</p></bio><bio xml:lang="en"><p>Aleksandr P. Bugayov – Postgraduate Student</p><p>87 Gorky Str., Vladimir 600000, Russia</p></bio><email xlink:type="simple">bugaev689@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0008-7021-7156</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бобожанов</surname><given-names>А. Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Bobozhanov</surname><given-names>A. R.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Анис Рахмонович Бобожанов – мл. науч. сотрудник, аспирант </p><p>Россия, 142432, Московская обл., г. Черноголовка, ул. Академика Осипьяна, 8</p></bio><bio xml:lang="en"><p>Anis R. Bobozhanov – Junior Researcher, Graduate Student</p><p>8 Akademika Osip’yan Str., Chernogolovka, Moscow Region 142432, Russia</p></bio><email xlink:type="simple">bobozhanov.anis@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6147-5753</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Алымов</surname><given-names>М. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Alymov</surname><given-names>M. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михаил Иванович Алымов – д.т.н., член-корр. РАН, директор </p><p>Россия, 142432, Московская обл., г. Черноголовка, ул. Академика Осипьяна, 8</p></bio><bio xml:lang="en"><p>Mikhail I. Alymov – Dr. Sci. (Eng.), Corresponding Member of the Russian Academy of Sciences, Director</p><p>8 Akademika Osip’yan Str., Chernogolovka, Moscow Region 142432, Russia</p></bio><email xlink:type="simple">alymov@ism.ac.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Владимирский государственный университет им. А.Г. и Н.Г. Столетовых</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Vladimir State University named after Alexander and Nikolay Stoletovs</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт структурной макрокинетики и проблем материаловедения им. А.Г. Мержанова РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Merzhanov Institute of Structural Macrokinetics and Materials Science of the Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>19</day><month>02</month><year>2025</year></pub-date><volume>19</volume><issue>1</issue><fpage>5</fpage><lpage>14</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; НИТУ "МИСИС", 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">НИТУ "МИСИС"</copyright-holder><copyright-holder xml:lang="en">НИТУ "МИСИС"</copyright-holder><license xlink:href="https://powder.misis.ru/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://powder.misis.ru/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://powder.misis.ru/jour/article/view/949">https://powder.misis.ru/jour/article/view/949</self-uri><abstract><p>Высокоэнергетическая обработка в планетарных мельницах нашла широкое применение для решения задач механического легирования/активации, синтеза композиционных порошковых смесей и переработки стружечных отходов. При этом передача механической энергии в обрабатываемое вещество зависит, в том числе, и от технологических параметров механической обработки, определяющих механику движения размольных тел, а следовательно, и энергосиловые характеристики процесса. Для изучения влияния передаточного отношения на энергосиловые условия механической обработки разработана, численно реализована и валидирована дискретно-элементная модель движения размольных тел в планетарной мельнице. Определены параметры модели, обеспечивающие разумное согласование экспериментальной и расчетной структур мгновенных изображений размольных тел на установившемся режиме работы мельницы. С помощью модели проведены серии численных экспериментов с варьированием передаточного отношения K от 1 до 2. Показано, что увеличение K в указанном диапазоне ведет к изменению характера движения размольных тел с режима перекатывания на перекатывание и свободный полет. Это снижает число столкновений и одновременно обеспечивает рост их силовых характерис­тик. Проведен анализ изменения суммарной потери энергии при столкновениях «тело–тело» и «тело–камера». Установлено, что при изменении K от 1 до 2 повышение суммарной потери энергии при столкновениях в основном происходит за счет увеличения потери энергии при столкновениях пар «тело–тело». Разработанные модели и полученные расчетные оценки влияния передаточного отношения на энергосиловые характеристики столкновений могут быть использованы при разработке рациональной технологии механической обработки в планетарной мельнице.</p></abstract><trans-abstract xml:lang="en"><p>High-energy milling in planetary mills has found widespread application for tasks such as mechanical alloying/activation, synthesis of composite powder mixtures, and recycling of chip waste. The transfer of mechanical energy to the processed material depends, among other factors, on the technological parameters of mechanical processing, which determine the motion of the grinding bodies and, consequently, the energy-force characteristics of the process. To study the effect of the gear ratio on the energy-force conditions of mechanical processing, a discrete element model of grinding body motion in a planetary mill was developed, numerically implemented, and validated. Model parameters were determined to ensure reasonable agreement between the experimental and calculated structures of instantaneous images of grinding body motion in the steady-state operation of the mill. Using the model, a series of numerical experiments were conducted, varying the gear ratio K from 1 to 2. It was shown that increasing K within this range changes the motion pattern of the grinding bodies from a rolling mode to a combination of rolling and free flight. This transition reduces the number of collisions while simultaneously increasing their force characteristics. An analysis of the changes in total energy loss during “body–body” and “body–chamber” collisions was performed. It was established that as K increases from 1 to 2, the total energy loss during collisions primarily increases due to greater energy loss in “body–body” collision pairs. The developed models and the obtained numerical estimates of the effect of the gear ratio on the energy-force characteristics of collisions can be utilized to design optimized mechanical processing technology in planetary mills.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>высокоэнергетический размол</kwd><kwd>метод дискретных элементов</kwd><kwd>энергосиловые характеристики</kwd><kwd>столкновения</kwd><kwd>характер движения размольных тел</kwd></kwd-group><kwd-group xml:lang="en"><kwd>high-energy milling</kwd><kwd>discrete element method</kwd><kwd>energy-force characteristics</kwd><kwd>collisions</kwd><kwd>motion pattern of grinding bodies</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Авторы выражают благодарность проф. А.С. Рогачеву за помощь в организации и проведении экспериментального исследования. Исследование выполнено за счет гранта Российского научного фонда № 23-29-00889, https://rscf.ru/project/23-29-00889/.</funding-statement><funding-statement xml:lang="en">The authors express their gratitude to Prof. A.S. Rogachev for his assistance in organizing and conducting the experimental study. This research was supported by the Russian Science Foundation (grant no. 23-29-00889, https://rscf.ru/project/23-29-00889/).</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">Зырянов В.В. Механохимический синтез сложных оксидов. Успехи химии. 2008;77(2):107–137. https://doi.org/10.1070/RC2008v077n02ABEH003709</mixed-citation><mixed-citation xml:lang="en">Zyryanov V.V. Mechanochemical synthesis of complex oxides. Russian Chemical Reviews. 2008;77(2):105–135. https://doi.org/10.1070/RC2008v077n02ABEH003709</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Michalchuk A.A.L., Boldyreva E.V., Belenguer A.M., Emmerling F., Boldyrev V.V. Tribochemistry, mechanical alloying, mechanochemistry: What is in a name? Frontiers in Chemistry. 2021;9:685789. https://doi.org/10.3389/fchem.2021.685789</mixed-citation><mixed-citation xml:lang="en">Michalchuk A.A.L., Boldyreva E.V., Belenguer A.M., Emmerling F., Boldyrev V.V. Tribochemistry, mechanical alloying, mechanochemistry: What is in a name? Frontiers in Chemistry. 2021;9:685789. https://doi.org/10.3389/fchem.2021.685789</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Лапшин О.В., Болдырева Е.В., Болдырев В.В. Роль смешения и диспергирования в механохими­чес­ком синтезе (обзор). Журнал неорганической химии. 2021;66(3):402–424. https://doi.org/10.31857/S0044457X21030119</mixed-citation><mixed-citation xml:lang="en">Lapshin O.V., Boldyreva E.V., Boldyrev V.V. Role of mixing and milling in mechanochemical synthesis (review). Inorganic Materials and Nanomaterials. 2021;66(3): 433–453. https://doi.org/10.1134/S0036023621030116</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Туманов И.А., Ачкасов А.Ф, Мызь С.А, Болдырева Е.В., Болдырев В.В. Качественно различное влияние сдвиговой и ударной механической нагрузки на механохимическую сокристаллизацию пироксикама и янтарной кислоты. Доклады Академии наук. 2014;457(6): 670–675. https://doi.org/10.7868/S0869565214240141</mixed-citation><mixed-citation xml:lang="en">Tumanov I.A., Achkasov A.F., Мызь Myz S.A., Boldyreva E.V., Boldyrev V.V. Different effect of impact and shear mechanical treatment on mechanochemical cocrystallization of piroxicam and succinic acid. Doklady Chemistry. 2014;457(2):154–159. https://doi.org/10.1134/S0012500814080059</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Suryanarayana C. Mechanical alloying: A critical review. Materials Research Letters. 2022;10(10):619–647. https://doi.org/10.1080/21663831.2022.2075243</mixed-citation><mixed-citation xml:lang="en">Suryanarayana C. Mechanical alloying: A critical review. Materials Research Letters. 2022;10(10):619–647. https://doi.org/10.1080/21663831.2022.2075243</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Рогачёв А.С., Мукасьян А.С. Горение гетерогенных наноструктурных систем (обзор). Физика горения и взрыва. 2010;(3):3–30.</mixed-citation><mixed-citation xml:lang="en">Rogachev A.S., Mukasyan A.S Combustion of heterogeneous nanostructural systems (review). Combustion, Explosion, and Shock Waves. 2010;46(3):243–266. https://doi.org/10.1007/s10573-010-0036-2</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Wei L.K., Bin Abd. Rahim S.Z., Al Bakri Abdullah M.M., Yin A.T.M., Ghazali M.F., Omar M.F., Nemes O., Sandu A.V., Vizureanu P., Abdellah A.E.-h. Producing metal powder from machining chips using ball milling process: A Review. Materials. 2023;16(13):4635. https://doi.org/10.3390/ma16134635</mixed-citation><mixed-citation xml:lang="en">Wei L.K., Bin Abd. Rahim S.Z., Al Bakri Abdullah M.M., Yin A.T.M., Ghazali M.F., Omar M.F., Nemes O., Sandu A.V., Vizureanu P., Abdellah A.E.-h. Producing metal powder from machining chips using ball milling process: A Review. Materials. 2023;16(13):4635. https://doi.org/10.3390/ma16134635</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Burmeister C., Titscher L., Breitung-Faes S., Kwade A. Dry grinding in planetary ball mills: Evaluation of a stressing model. Advanced Powder Technology. 2018;29(1): 191–201. https://doi.org/10.1016/j.apt.2017.11.001</mixed-citation><mixed-citation xml:lang="en">Burmeister C., Titscher L., Breitung-Faes S., Kwade A. Dry grinding in planetary ball mills: Evaluation of a stressing model. Advanced Powder Technology. 2018;29(1): 191–201. https://doi.org/10.1016/j.apt.2017.11.001</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Santhanam P.R., Dreizin E.L. Predicting conditions for scaled-up manufacturing of materials prepared by ball milling. Powder Technology. 2012;221:403–411. https://doi.org/10.1016/j.powtec.2012.01.037</mixed-citation><mixed-citation xml:lang="en">Santhanam P.R., Dreizin E.L. Predicting conditions for scaled-up manufacturing of materials prepared by ball milling. Powder Technology. 2012;221:403–411. https://doi.org/10.1016/j.powtec.2012.01.037</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Rosenkranz S., Breitung-Faes S., Kwade A. Experimental investigations and modelling of the ball motion in plane­tary ball mills. Powder Technology. 2011;212:224–230. https://doi.org/10.1016/j.powtec.2011.05.021</mixed-citation><mixed-citation xml:lang="en">Rosenkranz S., Breitung-Faes S., Kwade A. Experimental investigations and modelling of the ball motion in plane­tary ball mills. Powder Technology. 2011;212:224–230. https://doi.org/10.1016/j.powtec.2011.05.021</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Kozawa T., Fukuyama K., Kushimoto K., Ishihara S., Kano J., Kondo A., Naito M. Effect of ball collision direction on a wet mechanochemical reaction. Scientific Reports. 2021;11(1):210. https://doi.org/10.1038/s41598-020-80342-w</mixed-citation><mixed-citation xml:lang="en">Kozawa T., Fukuyama K., Kushimoto K., Ishihara S., Kano J., Kondo A., Naito M. Effect of ball collision direction on a wet mechanochemical reaction. Scientific Reports. 2021;11(1):210. https://doi.org/10.1038/s41598-020-80342-w</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Rogachev A.S., Moskovskikh D.O., Nepapushev A.A., Sviridova T.A., Vadchenko S.G., Rogachev S.A., Mukasyan A.S. Experimental investigation of milling regimes in planetary ball mill and their influence on structure and reactivity of gasless powder exothermic mixtures. Powder Technology. 2015;274(2):44–52. https://doi.org/10.1016/j.powtec.2015.01.009</mixed-citation><mixed-citation xml:lang="en">Rogachev A.S., Moskovskikh D.O., Nepapushev A.A., Sviridova T.A., Vadchenko S.G., Rogachev S.A., Mukasyan A.S. Experimental investigation of milling regimes in planetary ball mill and their influence on structure and reactivity of gasless powder exothermic mixtures. Powder Technology. 2015;274(2):44–52. https://doi.org/10.1016/j.powtec.2015.01.009</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Mindlin R.D., Deresiewicz H. Elastic spheres in contact under varying oblique force. Journal of Applied Mechanics. 1953;20(3):327–344. https://doi.org/10.1115/1.4010702</mixed-citation><mixed-citation xml:lang="en">Mindlin R.D., Deresiewicz H. Elastic spheres in contact under varying oblique force. Journal of Applied Mechanics. 1953;20(3):327–344. https://doi.org/10.1115/1.4010702</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Aryaei A., Hashemnia K., Jafarpur K. Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts. International Journal of Impact Engineering. 2010;37(10):1037–1044. https://doi.org/10.1016/j.ijimpeng.2010.04.005</mixed-citation><mixed-citation xml:lang="en">Aryaei A., Hashemnia K., Jafarpur K. Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts. International Journal of Impact Engineering. 2010;37(10):1037–1044. https://doi.org/10.1016/j.ijimpeng.2010.04.005</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Hlosta J., Žurovec D., Rozbroj J., Ramírez-Gómez Á., Nečas J., Zegzulka J. Experimental determination of particle–particle restitution coefficient via double pendulum method. Chemical Engineering Research and Design. 2018;135:222–233. https://doi.org/10.1016/j.cherd.2018.05.016</mixed-citation><mixed-citation xml:lang="en">Hlosta J., Žurovec D., Rozbroj J., Ramírez-Gómez Á., Nečas J., Zegzulka J. Experimental determination of particle–particle restitution coefficient via double pendulum method. Chemical Engineering Research and Design. 2018;135:222–233. https://doi.org/10.1016/j.cherd.2018.05.016</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Hlosta J., Jezerská L., Rozbroj J., Žurovec D., Nečas J., Zegzulka J. DEM investigation of the influence of particulate properties and operating conditions on the mixing process in rotary drums: Part 1 – Determination of the DEM parameters and calibration process. Processes. 2020;8(2):222. https://doi.org/10.3390/pr8020222</mixed-citation><mixed-citation xml:lang="en">Hlosta J., Jezerská L., Rozbroj J., Žurovec D., Nečas J., Zegzulka J. DEM investigation of the influence of particulate properties and operating conditions on the mixing process in rotary drums: Part 1 – Determination of the DEM parameters and calibration process. Processes. 2020;8(2):222. https://doi.org/10.3390/pr8020222</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Gusev V.G., Sobolkov A.V., Aborkin A.V. Determination of the coefficient of restitution upon contact of a steel ball with aluminum and steel surfaces. Journal of Physics: Conference Series. 2021;2131(3):032087. https://doi.org/10.1088/1742-6596/2131/3/032087</mixed-citation><mixed-citation xml:lang="en">Gusev V.G., Sobolkov A.V., Aborkin A.V. Determination of the coefficient of restitution upon contact of a steel ball with aluminum and steel surfaces. Journal of Physics: Conference Series. 2021;2131(3):032087. https://doi.org/10.1088/1742-6596/2131/3/032087</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Гусев В.Г., Собольков А.В., Аборкин А.В., Алымов М.И. Моделирование энергосиловых параметров обработки в планетарной мельнице и оценка их влияния на размер частиц композиционного порошка сплав АМг2/графит. Металлы. 2019;(1):27–34.</mixed-citation><mixed-citation xml:lang="en">Gusev V.G., Sobol’kov A.V., Aborkin A.V., Alymov M.I. Simulation of the energy–force parameters of planetary ball mill processing and estimation of their influence on the particle size in an AMg2 alloy/graphite composite powder. Russian Metallurgy (Metally). 2019;(1):24–30. https://doi.org/10.1134/S0036029519010063</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Hirosawa F., Iwasaki T. Dependence of the dissipated ener­gy of particles on the sizes and numbers of particles and balls in a planetary ball mill. Chemical Engineering Research and Design. 2021;167:84–95. https://doi.org/10.1016/j.cherd.2020.12.024</mixed-citation><mixed-citation xml:lang="en">Hirosawa F., Iwasaki T. Dependence of the dissipated ener­gy of particles on the sizes and numbers of particles and balls in a planetary ball mill. Chemical Engineering Research and Design. 2021;167:84–95. https://doi.org/10.1016/j.cherd.2020.12.024</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Capece M., Davé R.N., Bilgili E. On the origin of non-linear breakage kinetics in dry milling. Powder Techno­logy. 2015;272:189–203. https://doi.org/10.1016/j.powtec.2014.11.040</mixed-citation><mixed-citation xml:lang="en">Capece M., Davé R.N., Bilgili E. On the origin of non-linear breakage kinetics in dry milling. Powder Techno­logy. 2015;272:189–203. https://doi.org/10.1016/j.powtec.2014.11.040</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>
