<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE root>
<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Frontier Materials &amp; Technologies</journal-id><journal-title-group><journal-title xml:lang="en">Frontier Materials &amp; Technologies</journal-title><trans-title-group xml:lang="ru"><trans-title>Frontier Materials &amp; Technologies</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2782-4039</issn><issn publication-format="electronic">2782-6074</issn><publisher><publisher-name xml:lang="en">Togliatti State University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">1232</article-id><article-id pub-id-type="doi">10.18323/2782-4039-2026-2-76-2</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Mathematical model of a mechatronic system for powder layer formation in additive manufacturing technologies</article-title><trans-title-group xml:lang="ru"><trans-title>Математическая модель мехатронной системы формирования порошкового слоя в аддитивных технологиях</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0006-6865-3579</contrib-id><name-alternatives><name xml:lang="en"><surname>Bogdanov</surname><given-names>Valery M.</given-names></name><name xml:lang="ru"><surname>Богданов</surname><given-names>Валерий Михайлович</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>postgraduate student</p></bio><bio xml:lang="ru"><p>аспирант</p></bio><email>bogdanov.vm@edu.spbstu.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="scopus">57203462180</contrib-id><name-alternatives><name xml:lang="en"><surname>Timofeev</surname><given-names>Andrey Nikolaevich</given-names></name><name xml:lang="ru"><surname>Тимофеев</surname><given-names>Андрей Николаевич</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Doctor of Sciences (Engineering), Professor</p></bio><bio xml:lang="ru"><p>доктор технических наук, профессор</p></bio><email>timofeevan@inbox.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Peter the Great St. Petersburg Polytechnic University (SPbPU)</institution></aff><aff><institution xml:lang="ru">Санкт-Петербургский политехнический университет Петра Великого (СПбПУ)</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2026-06-30" publication-format="electronic"><day>30</day><month>06</month><year>2026</year></pub-date><issue>2</issue><issue-title xml:lang="en">Frontier Materials &amp; Technologies</issue-title><issue-title xml:lang="ru">Frontier Materials &amp; Technologies</issue-title><fpage>23</fpage><lpage>32</lpage><history><date date-type="received" iso-8601-date="2026-06-30"><day>30</day><month>06</month><year>2026</year></date><date date-type="accepted" iso-8601-date="2026-06-30"><day>30</day><month>06</month><year>2026</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2026, Bogdanov V.M., Timofeev A.N.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2026, Богданов В.М., Тимофеев А.Н.</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="en">Bogdanov V.M., Timofeev A.N.</copyright-holder><copyright-holder xml:lang="ru">Богданов В.М., Тимофеев А.Н.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://vektornaukitech.ru/jour/article/view/1232">https://vektornaukitech.ru/jour/article/view/1232</self-uri><abstract xml:lang="en"><p><bold><italic>Abstract:</italic></bold> <bold>Problem.</bold> Increasing the productivity of additive manufacturing (Binder Jetting technology) is limited by the low speed of powder layer deposition while maintaining high geometric accuracy of the products. Traditional systems often lead to defects such as shear deformations, formation of local voids, and interlayer delamination. <bold>Aim.</bold> To develop and study a mathematical model of a mechatronic system for powder layer formation that allows improving the productivity and quality of 3D printing. <bold>Methods.</bold> A comparative analysis of deposition systems (blade, rotating roller, and the proposed mechatronic module) was carried out using analytical modeling and computer simulation in Altair EDEM 2023 and MatLab Simulink software. <bold>Results.</bold> The developed mathematical models describe the dynamics of granular material flows and the dependencies of powder flow rate on the motion parameters of the actuating elements. It was established that the proposed mechatronic system allows achieving a deposition speed of 2800 mm/s with a shear value of 1.98 mm. This is 14 times faster than when using a squeegee (200 mm/s, shear 5 mm) and 3.3 times faster than when using a rotating roller (850 mm/s, shear 2.4 mm), while maintaining Class 7 dimensional accuracy according to GOST 26645-85. <bold>Conclusions.</bold> The resulting mathematical models of granular material flow dynamics can form the basis for the physics of powder layer formation and research in the field of improving the quality of printed products.</p></abstract><trans-abstract xml:lang="ru"><p><bold><italic>Аннотация:</italic></bold><italic> </italic><bold>Проблема. </bold>Повышение производительности аддитивного производства (технология Binder Jetting) ограничено низкой скоростью нанесения порошкового слоя при сохранении высокой геометрической точности изделий. Традиционные системы часто приводят к возникновению дефектов, таких как сдвиговые деформации, образование локальных пустот и межслойная деламинация. <bold>Цель.</bold> Разработать и исследовать математическую модель мехатронной системы формирования порошкового слоя, позволяющую повысить производительность и качество 3D-печати. <bold>Методы.</bold> Проведен сравнительный анализ систем нанесения (пластина, вращающийся ролик и предложенный мехатронный модуль) с использованием аналитического моделирования и компьютерного моделирования в среде Altair EDEM 2023 и MatLab Simulink. <bold>Результаты.</bold> Разработанные математические модели описывают динамику потоков сыпучих сред и зависимости расхода порошка от параметров движения исполнительных органов. Установлено, что предложенная мехатронная система позволяет достичь скорости нанесения 2800 мм/с при величине сдвига 1,98 мм. Это в 14 раз быстрее, чем при использовании прямоугольного ракеля (200 мм/с, сдвиг 5 мм), и в 3,3 раза быстрее, чем при использовании вращающегося ролика (850 мм/с, сдвиг 2,4 мм), при сохранении 7 класса точности размеров ГОСТ 26645-85.<italic> </italic><bold>Выводы.</bold> Полученные математические модели динамики потоков сыпучих сред могут лечь в основу физики формирования порошкового слоя и исследований в области повышения качества печатных изделий.</p></trans-abstract><kwd-group xml:lang="en"><kwd>additive manufacturing</kwd><kwd>mathematical model</kwd><kwd>powder layer formation</kwd><kwd>mechatronic system</kwd><kwd>deposition speed</kwd><kwd>material flow rate</kwd><kwd>rheological properties</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>аддитивное производство</kwd><kwd>математическая модель</kwd><kwd>формирование порошкового слоя</kwd><kwd>мехатронная система</kwd><kwd>скорость нанесения</kwd><kwd>расход материала</kwd><kwd>реологические свойства</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Capozzi L.C., Sivo A., Bassini E. Powder spreading and spreadability in the additive manufacturing of metallic materials: A critical review. Journal of Materials Processing Technology, 2022, vol. 308, article number 117706. DOI: 10.1016/j.jmatprotec.2022.117706.</mixed-citation><mixed-citation xml:lang="ru">Capozzi L.C., Sivo A., Bassini E. Powder spreading and spreadability in the additive manufacturing of metallic materials: A critical review // Journal of Materials Processing Technology. 2022. Vol. 308. Article number 117706. DOI: 10.1016/j.jmatprotec.2022.117706.</mixed-citation></citation-alternatives></ref><ref id="B2"><label>2.</label><citation-alternatives><mixed-citation xml:lang="en">Bogdanov V.M. Influence of roller characteristics on powder layer applying in additive technologies. Frontier Materials &amp; Technologies, 2024, no. 4, pp. 9–18. DOI: 10.18323/2782-4039-2024-4-70-1.</mixed-citation><mixed-citation xml:lang="ru">Богданов В.М. Влияние характеристик ролика на нанесение порошкового слоя в аддитивных технологиях // Frontier Materials &amp; Technologies. 2024. № 4. C. 9–18. DOI: 10.18323/2782-4039-2024-4-70-1.</mixed-citation></citation-alternatives></ref><ref id="B3"><label>3.</label><citation-alternatives><mixed-citation xml:lang="en">Ziaee M., Crane N.B. Binder jetting: A review of process, materials, and methods. Additive Manufacturing, 2019, vol. 28, pp. 781–801. DOI: 10.1016/j.addma.2019.05.031.</mixed-citation><mixed-citation xml:lang="ru">Ziaee M., Crane N.B. Binder jetting: A review of process, materials, and methods // Additive Manufacturing. 2019. Vol. 28. P. 781–801. DOI: 10.1016/j.addma.2019.05.031.</mixed-citation></citation-alternatives></ref><ref id="B4"><label>4.</label><citation-alternatives><mixed-citation xml:lang="en">Avrampos P., Vosniakos G.-C. A review of powder deposition in additive manufacturing by powder bed fusion. Journal of Manufacturing Processes, 2022, vol. 74, pp. 332–352. DOI: 10.1016/j.jmapro.2021.12.021.</mixed-citation><mixed-citation xml:lang="ru">Avrampos P., Vosniakos G.-C. A review of powder deposition in additive manufacturing by powder bed fusion // Journal of Manufacturing Processes. 2022. Vol. 74. P. 332–352. DOI: 10.1016/j.jmapro.2021.12.021.</mixed-citation></citation-alternatives></ref><ref id="B5"><label>5.</label><citation-alternatives><mixed-citation xml:lang="en">Penny R.W., Oropeza D., Weissbach R., Praegla P.M., Meier C., Wall W.A., Hart A.J. Quantitative analysis of thin metal powder layers via transmission X-ray imaging and discrete element simulation: Roller-based spreading approaches. Powder Technology, 2024, vol. 432, article number 119105. DOI: 10.1016/j.powtec.2023.119105.</mixed-citation><mixed-citation xml:lang="ru">Penny R.W., Oropeza D., Weissbach R., Praegla P.M., Meier C., Wall W.A., Hart A.J. Quantitative analysis of thin metal powder layers via transmission X-ray imaging and discrete element simulation: Roller-based spreading approaches // Powder Technology. 2024. Vol. 432. Article number 119105. DOI: 10.1016/j.powtec.2023.119105.</mixed-citation></citation-alternatives></ref><ref id="B6"><label>6.</label><citation-alternatives><mixed-citation xml:lang="en">Shaheen M.Y., Thornton A.R., Luding S., Weinhart T. The influence of material and process parameters on powder spreading in additive manufacturing. Powder Technology, 2021, vol. 383, pp. 564–583. DOI: 10.1016/j.powtec.2021.01.058.</mixed-citation><mixed-citation xml:lang="ru">Shaheen M.Y., Thornton A.R., Luding S., Weinhart T. The influence of material and process parameters on powder spreading in additive manufacturing // Powder Technology. 2021. Vol. 383. P. 564–583. DOI: 10.1016/j.powtec.2021.01.058.</mixed-citation></citation-alternatives></ref><ref id="B7"><label>7.</label><citation-alternatives><mixed-citation xml:lang="en">Ashrafizadeh S.M., Ejtehadi O., Pelletier R., Habibnejad-Korayem M., Haeri S., Stephen Yue. Experimental and numerical investigation of re-coating process parameters on the spreadability of plasma-atomized powder. Powder Technology, 2026, vol. 469, part 2, article number 121851. DOI: 10.1016/j.powtec.2025.121851.</mixed-citation><mixed-citation xml:lang="ru">Ashrafizadeh S.M., Ejtehadi O., Pelletier R., Habibnejad-Korayem M., Haeri S., Stephen Yue. Experimental and numerical investigation of re-coating process parameters on the spreadability of plasma-atomized powder // Powder Technology. 2026. Vol. 469. Part 2. Article number 121851. DOI: 10.1016/j.powtec.2025.121851.</mixed-citation></citation-alternatives></ref><ref id="B8"><label>8.</label><citation-alternatives><mixed-citation xml:lang="en">Weissbach R., Praegla P.M., Wall W.A., Hart A.J., Meier C. Exploration of improved, roller-based spreading strategies for cohesive powders in additive manufacturing via coupled DEM-FEM simulations. Powder Technology, 2024, vol. 443, article number 119956. DOI: 10.1016/j.powtec.2024.119956.</mixed-citation><mixed-citation xml:lang="ru">Weissbach R., Praegla P.M., Wall W.A., Hart A.J., Meier C. Exploration of improved, roller-based spreading strategies for cohesive powders in additive manufacturing via coupled DEM-FEM simulations // Powder Technology. 2024. Vol. 443. Article number 119956. DOI: 10.1016/j.powtec.2024.119956.</mixed-citation></citation-alternatives></ref><ref id="B9"><label>9.</label><citation-alternatives><mixed-citation xml:lang="en">Matveenko V.N., Kirsanov E.A. Structural causes of the non-newtonian behavior of fluid systems. Russian Journal of Physical Chemistry A, 2023, vol. 97, no. 8, pp. 1708–1724. DOI: 10.1134/s0036024423080162.</mixed-citation><mixed-citation xml:lang="ru">Матвеенко В.Н., Кирсанов Е.А. Структурные причины неньютоновского поведения текучих систем // Журнал физической химии. 2023. Т. 97. № 8. С. 1137–1154. DOI: 10.31857/S0044453723080162.</mixed-citation></citation-alternatives></ref><ref id="B10"><label>10.</label><citation-alternatives><mixed-citation xml:lang="en">Pertsev V.T., Ledenev A.A., Usachev S.M., Usachev A.M. Evaluation of rheological properties of building mixes with obtaining additional quantitative characteristics. Condensed Matter and Interphases, 2016, vol. 18, no. 3, pp. 394–401. EDN: WKPQFV.</mixed-citation><mixed-citation xml:lang="ru">Перцев В.Т., Леденев А.А., Усачев С.М., Усачев А.М. Оценка реологических свойств строительных смесей с получением дополнительных количественных характеристик // Конденсированные среды и межфазные границы. 2016. Т. 18. № 3. С. 394–401. EDN: WKPQFV.</mixed-citation></citation-alternatives></ref><ref id="B11"><label>11.</label><citation-alternatives><mixed-citation xml:lang="en">Kulikov S.A., Rudnitskiy F.I., Shumigay V.A., Kulikov Yu.A. Control of properties of core mixes manufactured by Cold-box-amineprocess. Lite I metallurgiya, 2024, no. 3, pp. 51–56. DOI: 10.21122/1683-6065-2024-3-51-56.</mixed-citation><mixed-citation xml:lang="ru">Куликов С.А., Рудницкий Ф.И., Шумигай В.А., Куликов Ю.А. Управление свойствами стержневых смесей, изготовленных по Cold-box-amine-процессу // Литье и металлургия. 2024. № 3. С. 51–56. DOI: 10.21122/1683-6065-2024-3-51-56.</mixed-citation></citation-alternatives></ref><ref id="B12"><label>12.</label><citation-alternatives><mixed-citation xml:lang="en">Arzumanyan M.G. The special features of plastic deformation of non-sintered powder materials. Vestnik Natsionalnogo politekhnicheskogo universiteta Armenii. Mekhanika, mashinovedenie, mashinostroenie, 2023, no. 2, pp. 53–63. DOI: 10.53297/18293387-2023.2-53.</mixed-citation><mixed-citation xml:lang="ru">Арзуманян М.Г. Особенности пластического деформирования неспеченных порошковых материалов // Вестник Национального политехнического университета Армении. Механика, машиноведение, машиностроение. 2023. № 2. С. 53–63. DOI: 10.53297/18293387-2023.2-53.</mixed-citation></citation-alternatives></ref><ref id="B13"><label>13.</label><citation-alternatives><mixed-citation xml:lang="en">Bogdanov V.M., Timofeev A.N. Влияние характеристик нанесения на сдвиг порошкового слоя в аддитивном производстве. Automation and Remote Control, 2025, no. 5, pp. 22–25. EDN: YHFZDO.</mixed-citation><mixed-citation xml:lang="ru">Богданов В.М., Тимофеев А.Н. Влияние характеристик нанесения на сдвиг порошкового слоя в аддитивном производстве // Автоматизация в промышленности. 2025. № 5. С. 22–25. EDN: YHFZDO.</mixed-citation></citation-alternatives></ref><ref id="B14"><label>14.</label><citation-alternatives><mixed-citation xml:lang="en">Maximenko A.L., Olumor I.D., Maidaniuk A.P., Olevsky E.A. Modeling of effect of powder spreading on green body dimensional accuracy in additive manufacturing by binder jetting. Powder Technology, 2021, vol. 385, pp. 60–68. DOI: 10.1016/j.powtec.2021.02.070.</mixed-citation><mixed-citation xml:lang="ru">Maximenko A.L., Olumor I.D., Maidaniuk A.P., Olevsky E.A. Modeling of effect of powder spreading on green body dimensional accuracy in additive manufacturing by binder jetting // Powder Technology. 2021. Vol. 385. P. 60–68. DOI: 10.1016/j.powtec.2021.02.070.</mixed-citation></citation-alternatives></ref><ref id="B15"><label>15.</label><citation-alternatives><mixed-citation xml:lang="en">Lin Wang, Zongyan Zhou, Erlei Li, Haopeng Shen, Aibing Yu. Powder deposition mechanism during powder spreading with different spreader geometries in powder bed fusion additive manufacturing. Powder Technology, 2022, vol. 395, pp. 802–810. DOI: 10.1016/j.powtec.2021.10.017.</mixed-citation><mixed-citation xml:lang="ru">Lin Wang, Zongyan Zhou, Erlei Li, Haopeng Shen, Aibing Yu. Powder deposition mechanism during powder spreading with different spreader geometries in powder bed fusion additive manufacturing // Powder Technology. 2022. Vol. 395. P. 802–810. DOI: 10.1016/j.powtec.2021.10.017.</mixed-citation></citation-alternatives></ref><ref id="B16"><label>16.</label><citation-alternatives><mixed-citation xml:lang="en">Jiangtao Zhang, Ningchang Wang, Xing Chen, Yuanqiang Tan. Particle gradations optimization for powder spreading in additive manufacturing. Materials &amp; Design, 2023, vol. 236, article number 112509. DOI: 10.1016/j.matdes.2023.112509.</mixed-citation><mixed-citation xml:lang="ru">Jiangtao Zhang, Ningchang Wang, Xing Chen, Yuanqiang Tan. Particle gradations optimization for powder spreading in additive manufacturing // Materials &amp; Design. 2023. Vol. 236. Article number 112509. DOI: 10.1016/j.matdes.2023.112509.</mixed-citation></citation-alternatives></ref><ref id="B17"><label>17.</label><citation-alternatives><mixed-citation xml:lang="en">Jiangtao Zhang, Yuanqiang Tan, Xiangwu Xiao, Shengqiang Jiang. Comparison of roller-spreading and blade-spreading processes in powder-bed additive manufacturing by DEM simulations. Particuology, 2022, vol. 66, pp. 48–58. DOI: 10.1016/j.partic.2021.07.005.</mixed-citation><mixed-citation xml:lang="ru">Jiangtao Zhang, Yuanqiang Tan, Xiangwu Xiao, Shengqiang Jiang. Comparison of roller-spreading and blade-spreading processes in powder-bed additive manufacturing by DEM simulations // Particuology. 2022. Vol. 66. P. 48–58. DOI: 10.1016/j.partic.2021.07.005.</mixed-citation></citation-alternatives></ref></ref-list></back></article>
