Экономика и право. XXI век2076-282810.24412/2076-2828-2026-1-115-120OtherЧисленное моделирование в процессе селективного лазерного плавления: анализ температурного поля с движущимся источником теплаNumerical simulation of selective laser melting: temperature field analysis with a moving heat sourceНгуенТуан ЛонгNguyenTuan Longkqvn.nguyenlong@gmail.comНайХтет АунгNayHtet Aungnayhtet70714@gmail.comgraduate student, Moscow Aviation Institute (MAI), Moscow, Russiaаспирант, Московский авиационный институт (МАИ), Москва, Россияgraduate student, Moscow Aviation Institute (MAI), Moscow, Russiaаспирант, Московский авиационный институт (МАИ), Москва, Россия2503202611151200403202621032026

В последние годы технологии 3D-печати металлических изделий активно развиваются, особенно метод селективного лазерного плавления (СЛП), где движущийся лазерный источник тепла создает сложное температурное поле, влияющее на качество продукции. В данной статье представлен численно-аналитический метод расчета температурного поля в полубесконечном пространстве под воздействием движущегося источника тепла. Метод основан на принципе суперпозиции и функции влияния с применением численной аппроксимации на языке программирования Python. Рассчитаны примеры для случаев прямолинейного и сложного движения, демонстрирующие распределение температуры во времени и пространстве. Результаты обеспечивают основу для оптимизации параметров технологии СЛП, минимизации термических напряжений и дефектов.

In recent years, 3D printing technologies for metal products have been actively developing, especially the selective laser melting (SLM) method, where a moving laser heat source creates a complex temperature field that affects product quality. This article presents a numerical and analytical method for calculating the temperature field in a semi-infinite space under the influence of a moving heat source. The method is based on the principle of superposition and the influence function using numerical approximation in the Python programming language. Examples are calculated for cases of rectilinear and complex motion, demonstrating the temperature distribution in time and space. The results provide the basis for optimizing the parameters of SLM technology, minimizing thermal stresses and defects.

3D-печатьселективное лазерное плавлениеаддитивное производствососредоточенная нагрузкадвижущаяся нагрузкатепловой потокфункция влияния3D printingselective laser meltingadditive manufacturingconcentrated loadmoving loadheat flowinfluence functionGibson I., Rosen D.W., Stucker B. Additive Manufacturing Technologies. Springer, 2010.DebRoy T. et al. Additive manufacturing of metallic components – Process, structure and properties // Progress in Materials Science. 2018. Vol. 92. P. 112-224.Khairallah S.A. et al. Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones // Acta Materialia. 2016. Vol. 108. P. 36-45.Gusarov A.V., Smurov I. Modeling the interaction of laser radiation with powder bed at selective laser melting // Physics Procedia. 2010. Vol. 5. P. 381-394.King W.E. et al. Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges // Applied Physics Reviews. 2015. Vol. 2. No. 4. P. 041304.Yadroitsev I. et al. Single track formation in selective laser melting of metal powders // Journal of Materials Processing Technology. 2010. Vol. 210. No. 12. P. 1624-1631.Aboulkhair N.T. et al. Reducing porosity in AlSi10Mg parts processed by selective laser melting // Additive Manufacturing. 2014. Vol. 1-4. P. 77-86.Rosenthal D. The theory of moving sources of heat and its application to metal treatments // Transactions of the ASME. 1946. Vol. 68. P. 849-866.Eagar T.W., Tsai N.S. Temperature fields produced by traveling distributed heat sources // Welding Journal. 1983. Vol. 62. No. 12. P. 346s-355s.Komanduri R., Hou Z.B. Thermal analysis of the laser surface transformation hardening process // International Journal of Heat and Mass Transfer. 2001. Vol. 44. No. 15. P. 2845-2862.Tian Y., Shin Y.C. Thermal modeling for laser machining microscale glass substrates // Journal of Manufacturing Science and Engineering. 2006. Vol. 128. No. 2. P. 425-434.Peyre P. et al. Analytical and numerical modelling of the direct metal deposition laser process // Journal of Physics D: Applied Physics. 2008. Vol. 41. No. 2. P. 025403.Gusarov A.V. et al. Modelling of radiation transfer in metallic powders at laser treatment // International Journal of Heat and Mass Transfer. 2005. Vol. 48. No. 16. P. 3423-3434.Mercelis P., Kruth J.P. Residual stresses in selective laser sintering and selective laser melting // Rapid Prototyping Journal. 2006. Vol. 12. No. 5. P. 254-265.Carslaw H.S., Jaeger J.C. Conduction of Heat in Solids. Oxford University Press, 1959.Luikov A.V. Analytical Heat Diffusion Theory. Academic Press, 1968.Nowacki W. Thermoelasticity. Pergamon Press, 1962.Boley B.A., Weiner J.H. Theory of Thermal Stresses. Wiley, 1960.Melan E., Parkus H. Wärmespannungen infolge stationärer Temperaturfelder. Springer, 1953.Kovalenko A.D. Thermoelasticity: Basic Theory and Applications. Wolters-Noordhoff, 1969.Noda N. et al. Thermal Stresses. Taylor & Francis, 2003.Gibson I., Rosen D.W., Stucker B. Additive Manufacturing Technologies. Springer, 2010.DebRoy T. et al. Additive manufacturing of metallic components – Process, structure and properties // Progress in Materials Science. 2018. Vol. 92. P. 112-224.Khairallah S.A. et al. Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones // Acta Materialia. 2016. Vol. 108. P. 36-45.Gusarov A.V., Smurov I. Modeling the interaction of laser radiation with powder bed at selective laser melting // Physics Procedia. 2010. Vol. 5. P. 381-394.King W.E. et al. Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges // Applied Physics Reviews. 2015. Vol. 2.No. 4. P. 041304.Yadroitsev I. et al. Single track formation in selective laser melting of metal powders // Journal of Materials Processing Technology. 2010. Vol. 210.No. 12. P. 1624-1631.Aboulkhair N.T. et al. Reducing porosity in AlSi10Mg parts processed by selective laser melting // Additive Manufacturing. 2014. Vol. 1-4. P. 77-86.Rosenthal D. The theory of moving sources of heat and its application to metal treatments // Transactions of the ASME. 1946. Vol. 68. P. 849-866.Eagar T.W., Tsai N.S. Temperature fields produced by traveling distributed heat sources // Welding Journal. 1983. Vol. 62.No. 12. P. 346s-355s.Komanduri R., Hou Z.B. Thermal analysis of the laser surface transformation hardening process // International Journal of Heat and Mass Transfer. 2001. Vol. 44.No. 15. P. 2845-2862.Tian Y., Shin Y.C. Thermal modeling for laser machining microscale glass substrates // Journal of Manufacturing Science and Engineering. 2006. Vol. 128.No. 2. P. 425-434.Peyre P. et al. Analytical and numerical modeling of the direct metal deposition laser process // Journal of Physics D: Applied Physics. 2008. Vol. 41.No. 2. P. 025403.Gusarov A.V. et al. Modeling of radiation transfer in metallic powders at laser treatment // International Journal of Heat and Mass Transfer. 2005. Vol. 48.No. 16. P. 3423-3434.Mercelis P., Kruth J.P. Residual stresses in selective laser sintering and selective laser melting // Rapid Prototyping Journal. 2006. Vol. 12.No. 5. P. 254-265.Carslaw H.S., Jaeger J.C. Conduction of Heat in Solids. Oxford University Press, 1959.Luikov A.V. Analytical Heat Diffusion Theory. Academic Press, 1968.Nowacki W. Thermoelasticity. Pergamon Press, 1962.Boley B.A., Weiner J.H. Theory of Thermal Stresses. Wiley, 1960.Melan E., Parkus H. Wärmespannungen infolge stationärer Temperaturfelder. Springer, 1953.Kovalenko A.D. Thermoelasticity: Basic Theory and Applications. Wolters-Noordhoff, 1969.Noda N. et al. Thermal Stresses. Taylor & Francis, 2003.