rus
Issue #3/2022
A. S. Boreysho, G. T. Dzhgamadze, A. A. Moiseev, A. B. Savin, P. G. Smirnov
Multilevel Modeling Operational Processes of Selective Laser Melting
Multilevel Modeling Operational Processes of Selective Laser Melting
DOI: 10.22184/1993-7296.FRos.2022.16.3.212.219
Selective laser melting (SLM) is a promising area in additive processes. The problem of controlling the microstructure and quality of the final product obtained by the SLS method is solved by selecting the melting modes using the experimental search or numerical modeling. As of today, a multilevel simulation method for SLS processes has been developed that is considered in this paper.
Selective laser melting (SLM) is a promising area in additive processes. The problem of controlling the microstructure and quality of the final product obtained by the SLS method is solved by selecting the melting modes using the experimental search or numerical modeling. As of today, a multilevel simulation method for SLS processes has been developed that is considered in this paper.
Теги: digital twin mathematical model mesoscale modeling microscale modeling multilevel modeling selective laser melting математическая модель мезоуровневое моделирование микроуровневое моделирование многоуровневое моделирование селективное лазерное сплавление
Multilevel Modeling Operational Processes of Selective Laser Melting
Multilevel Simulation of Selective Laser Melting Operational Processes
A. S. Boreysho 1, 2, G. T. Dzhgamadze 1, A. A. Moiseev 2, A. V. Savin 1, 2, P. G. Smirnov 2
Lazer Systems Joint Stock Company,
Saint-Petersburg, Russia
VOENMEKH Ustinov Baltic State Technical University, Saint-Petersburg, Russia
Selective laser melting (SLM) is a promising area in additive processes. The problem of controlling the microstructure and quality of the final product obtained by the SLS method is solved by selecting the melting modes using the experimental search or numerical modeling. As of today, a multilevel simulation method for SLS processes has been developed that is considered in this paper.
Keywords: selective laser melting, mathematical model, microscale modeling, mesoscale modeling, multilevel modeling, digital twin
Received: 08.04.2022
Accepted: 20.04.2022
INTRODUCTION
The layer-by-layer production technology of three-dimensional physical objects has become widespread. The method that is the fusion of metal powder microparticles using the high-power laser radiation as a heat source, is called the selective laser melting technology (SLM) [1]. It allows to make almost finished products with extremely comprehensive geometry, including those with the internal channels and cavities. Figure 1 shows the examples of products made using the SLM-machine M250 [2].
One of the SLM technology problems is that the layers of satisfactory quality for each specific metal or alloy are generated only in a narrow range of laser processing modes. An experimental search for such modes is extremely labor-consuming, while the numerical simulation reduces the labor costs for their selection [3]. An analysis of publications devoted to the numerical modeling allows to conclude that the multiscale modeling method is necessary. There are three scales of numerical modeling for SLM process: microscale, mesoscale, and macroscale (Fig. 2). The macroscale is designed for describing the thermal and stress-strain behavior in the product scale, the mesoscale is designed for a generalized description of the SLM processes in the scale of the typical structural element of the product, the microscale is designed for a detailed description of the SLM hydrodynamic and thermophysical processes in the scale of the melt pool.
The development of a digital twin that includes both autonomous preliminary and operational modeling of processes at various levels, shall significantly reduce the preparation time for additive manufacturing and ensure the high quality of the products.
MICROSCALE
It describes interaction of the laser radiation with metal powders near the melt pool. It is a combination of influences and phenomena of various nature:
Descriptions of the mechanisms of these phenomena are used as the basis for the microscale mathematical model that is the coupledcontinuum mechanics equations with variable properties. It consists of the constitutive equation, the continuity equation, the motion equation, and the energy equation [4].
The microscale mathematical model can be implemented as a part of packages designed for the hydrodynamics modeling, with additions that describe the variable medium properties. Figure 3 shows the modeling results for a double laser radiation pass over a layer of metal powder. It can be seen that the melt pool is thickened at the beginning of each pass, the recess is formed at the end of the pass, and lack of fusion is obtained between the passes. By adjusting the laser processing mode parameters, it is possible to achieve complete particle penetration.
At present, special attention is also paid to inclusion of the description of the following comprehensive hydrodynamic phenomena in the mathematical model:
A simulation experiment based on a microscale model (Fig. 4) allows to formulate a hypothesis relating to the formation mechanism of finely dispersed solid particles:
The numerical implementation of the mathematical model is supplemented by a spattering model that includes the particle escape of the base material and molten metal. The liquid phase is replaced by a spherical particle with equivalent mass, while keeping the speed, direction of movement, temperature, and other parameters. For this purpose, a conversion from “Volume of fluid” to “Discrete Particle Modeling” (VOF-to-DPM) is used.
MESOSCALE
This scale provides a general description of the SLM process hydrodynamics and thermal physics in a scale that is intermediate between the scales of the melt pool and the entire product. The mesoscale model is based on the heat conduction equation with inclusion of the heat sources and losses and the porosity dynamic equation. Low computational costs compared to the microscale model are related to the following assumptions made:
the medium is considered as a continuous medium with variable properties, and the physical parameters included in the heat conduction equation depend on temperature and / or porosity.
The thermal conductivity coefficient used includes the thermal conductivity of a solid material, the frame and radiant thermal conductivity of a porous material [5];
theenergy transfer due to the molten metal convection is considered by selecting the efficient thermal conductivity of the liquid phase.
In order to describe the laser radiation interaction with a metal powder as a part of a mesoscale model, it is necessary to determine the effective parameters and establish their dependence on temperature and / or porosity, i. e., the model needs to be calibrated. Calibration can be performed on the basis of both experimental studies and microscale modeling.
The thermal conductivity of the liquid phase is calibrated, since the model does not directly provide calculation of the molten metal convection. The laser processing mode parameters and the powder material specifications are equal in both models. The peak temperature in the center of the melt pool is used as a calibration validity criterion (Fig. 5).
An important role in the product growth by the SLM method is played by the scanning strategy that affects the value of residual porosity and residual stresses. By using the mesoscale model, several options of scanning strategies for a product in the form of a rectangular trapezoid are studied (Fig. 6).
The simulation results show that in the case of such a problem formulation, the availability or absence of the laser spot idle motions does not significantly affect the final product condition. It was confirmed experimentally (Fig. 6). In some cases, residual porosity is observed in the calculations (Fig. 7).
The computational costs for the SLM workflow modeling are increased with the product size and transition from 2D to 3D modeling. Consequently, the computational time is also increased. Therefore, such models require parallel and distributed implementation using the computing clusters and / or capabilities of the multi-core graphics cards (GPUs). This leads to a more comprehensive implementation task based on the parallel software platforms. Therefore, it is rather promising to use the GPU for the mesoscale model implementation.
The paper [6] considers implementation of the numerical solution for the heat conduction equation by iterative methods using the GPU in two ways, such as an iterative method (over-relaxation method) and a strategy based on the elimination method for a tridiagonal matrix. The elimination method is fundamentally consistent, however, if it is used in relation to the entire system. If the system is split into the spatial coordinates (alternating direction implicit method), then it is possible to use elimination for a separate beam in the direction of each coordinate, and launch the number of flows equal to the number of such beams. The result is an efficient algorithm that outperforms the simple iterative method in speed, but is applicable only for the special-type matrices.
CONCLUSION
Numerical simulation is an efficient tool for determining the laser processing modes in the SLM process. The analysis of publications allows to conclude that there is a transition to a multiscale modeling methodology that includes the micro-, meso-, and macroscales. The scales are classified according to the spatial scale: from the melt pool to the entire product. All scales are interconnected: the meso- and macro-problems must be solved simultaneously, and the micro-problem is solved in advance and is used for the mesoscale model calibration. The creation of such a digital twin makes it possible to describe all essential SLM processes and becomes an important element of the production preparation process for testing the process modes of grown products.
REFERENCES
Gordeev G. A., Krivilev M. D., Ankudinov V. E. Computer simulation of selective laser melting of fine-grained metallic powders. Computational Continuum Mechanics. 2017; 10 (3): 293–312. DOI: 10.7242/1999–6691/2017.10.3.23.
Istomina N., Karyakina L. Science and business in the market of laser technologies. Photonics Russia. 2018; 12–6 (74):542–548. DOI: 10.22184/1993-7296.2018.12.6.542.548.
Bogdanovich V. I., Giorbelidze M. G., Sotov A. V., Pronichev N. D., Smelov V. G., Agapovichev A. V. Mathematical modeling of powder melting process in selective laser melting technology. News of the Samara Research Center of the Russian Academy of Sciences. 2017; 19(4): 2–3.
Boreysho A. S., Dzhgamadze G. T., Zybina V. V. Moiseev A. A., Savin A. V., Smirnov P. G., Smolentsev S. S., Timofeev V. A., Tretyak P. S. Microscale modeling of thermophysical and hydrodynamic processes of selective laser melting. Thermophysics of high temperatures. 2022; 60(1):1–7. DOI: 10.31857/S0040364422010148.
Dobrego K. V., ZHdanok S. A. Physics of filtration combustion of gases. – Minsk: Institute of Heat and Mass Transfer. A. V. Lykov NASB. 2002; 203 p. ISBN 985-6456-29-0.
Smirnov P. G., Tretyak P. S., Dzhgamadze G. T. Parallel implementation of the implicit method and the splitting method for the numerical solution of the heat equation on a graphics accelerator. Young people. Technic. Cosmos: Proceedings of the XII All-Russian Youth Scientific and Technical Conference Baltic State Technical University. Saint-Petersburg. 2019; 1: 171–179. ISBN: 978-5-94652-672-2.
CONTRIBUTION BY THE MEMBERS OF THE TEAM OF AUTHORS
Boreysho A. S. – concept of simulation in the frame of whole SLM technology realization. Savin A. V. – supervisor, development of the methodology of multilevel modeling. Smirnov P. G. – software implementation of iterative methods on a graphics accelerator. Moiseev A. A. – development and software implementation of the micro-level model. Dzhgamadze G. T. – development and software implementation of the meso-level model.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest. All authors took part in writing the article and supplemented the manuscript in part of their work.
ABOUT THE AUTHORS
Boreysho Anatoliy Sergeevich, D. Sc. of Engineering Sciences, professor, Scientific supervisor, Timeline of Laser Systems JSC, https://www.lsystems.ru, Strelna, St. Petersburg; Head of the I1 department, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, Boreysho@lsystems.ru, St. Petersburg, Russia.
Savin Andrey Valerevich, D. Sc. of Engineering Sciences, professor, Chief Researcher, Timeline of Laser Systems JSC, https://www.lsystems.ru, Strelna, St. Petersburg; lecturer of the I1 Department, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, izooandrey@inbox.ru, St. Petersburg, Russia.
WoS ResearcherID: V‑2255-2018
Smirnov Petr Gennadevich, Engineer of the 1st category, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, petr.s.8314@mail.ru, St. Petersburg, Russia.
WoS ResearcherID: V‑8450-2018
Moiseev Andrey Andreevich, Engineer of the 1st category, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, terminalmashine@gmail.com, St. Petersburg, Russia.
Dzhgamadze Gvantsa Tengizovna, Engineer of the 2nd category, DgvancaT96@mail.ru, Timeline of Laser Systems JSC, https://www.lsystems.ru, Strelna, St. Petersburg, Russia.
Multilevel Simulation of Selective Laser Melting Operational Processes
A. S. Boreysho 1, 2, G. T. Dzhgamadze 1, A. A. Moiseev 2, A. V. Savin 1, 2, P. G. Smirnov 2
Lazer Systems Joint Stock Company,
Saint-Petersburg, Russia
VOENMEKH Ustinov Baltic State Technical University, Saint-Petersburg, Russia
Selective laser melting (SLM) is a promising area in additive processes. The problem of controlling the microstructure and quality of the final product obtained by the SLS method is solved by selecting the melting modes using the experimental search or numerical modeling. As of today, a multilevel simulation method for SLS processes has been developed that is considered in this paper.
Keywords: selective laser melting, mathematical model, microscale modeling, mesoscale modeling, multilevel modeling, digital twin
Received: 08.04.2022
Accepted: 20.04.2022
INTRODUCTION
The layer-by-layer production technology of three-dimensional physical objects has become widespread. The method that is the fusion of metal powder microparticles using the high-power laser radiation as a heat source, is called the selective laser melting technology (SLM) [1]. It allows to make almost finished products with extremely comprehensive geometry, including those with the internal channels and cavities. Figure 1 shows the examples of products made using the SLM-machine M250 [2].
One of the SLM technology problems is that the layers of satisfactory quality for each specific metal or alloy are generated only in a narrow range of laser processing modes. An experimental search for such modes is extremely labor-consuming, while the numerical simulation reduces the labor costs for their selection [3]. An analysis of publications devoted to the numerical modeling allows to conclude that the multiscale modeling method is necessary. There are three scales of numerical modeling for SLM process: microscale, mesoscale, and macroscale (Fig. 2). The macroscale is designed for describing the thermal and stress-strain behavior in the product scale, the mesoscale is designed for a generalized description of the SLM processes in the scale of the typical structural element of the product, the microscale is designed for a detailed description of the SLM hydrodynamic and thermophysical processes in the scale of the melt pool.
The development of a digital twin that includes both autonomous preliminary and operational modeling of processes at various levels, shall significantly reduce the preparation time for additive manufacturing and ensure the high quality of the products.
MICROSCALE
It describes interaction of the laser radiation with metal powders near the melt pool. It is a combination of influences and phenomena of various nature:
- gravity force and buoyancy;
- surface tension force;
- Marangoni effect;
- reaction force of metal vapors;
- thermodynamics of phase changes;
- conductive heat transfer;
- convection heat transfer;
- radiation.
Descriptions of the mechanisms of these phenomena are used as the basis for the microscale mathematical model that is the coupledcontinuum mechanics equations with variable properties. It consists of the constitutive equation, the continuity equation, the motion equation, and the energy equation [4].
The microscale mathematical model can be implemented as a part of packages designed for the hydrodynamics modeling, with additions that describe the variable medium properties. Figure 3 shows the modeling results for a double laser radiation pass over a layer of metal powder. It can be seen that the melt pool is thickened at the beginning of each pass, the recess is formed at the end of the pass, and lack of fusion is obtained between the passes. By adjusting the laser processing mode parameters, it is possible to achieve complete particle penetration.
At present, special attention is also paid to inclusion of the description of the following comprehensive hydrodynamic phenomena in the mathematical model:
- cavitation;
- generation of cumulative jets;
- detachment of the liquid phase fragments;
- occurrence of finely dispersed metal particles
A simulation experiment based on a microscale model (Fig. 4) allows to formulate a hypothesis relating to the formation mechanism of finely dispersed solid particles:
- A convection induced by the Marangoni forces occurs in the melt pool: the liquid flows out from the high-temperature center (from the area with low surface tension) to the periphery near the pool surface.
- The fluid flowing from the centerapproaches the solid boundaries and splashes out while generating the cumulative jets due to the inertial effects.
- The cumulative jets disintegrate under the influence of capillary instability. The temperature field of cumulative jets has a typical form: the top area becomes cool faster than the bridge. The Marangoni forces lead to the material movement from the bridge to the top area. This accelerates the bridge disruption.
- Further, the isolated liquid fragment that is gradually cooling and solidifying, is moved under its own inertia, moving away from the base material and forming a solid particle.
The numerical implementation of the mathematical model is supplemented by a spattering model that includes the particle escape of the base material and molten metal. The liquid phase is replaced by a spherical particle with equivalent mass, while keeping the speed, direction of movement, temperature, and other parameters. For this purpose, a conversion from “Volume of fluid” to “Discrete Particle Modeling” (VOF-to-DPM) is used.
MESOSCALE
This scale provides a general description of the SLM process hydrodynamics and thermal physics in a scale that is intermediate between the scales of the melt pool and the entire product. The mesoscale model is based on the heat conduction equation with inclusion of the heat sources and losses and the porosity dynamic equation. Low computational costs compared to the microscale model are related to the following assumptions made:
the medium is considered as a continuous medium with variable properties, and the physical parameters included in the heat conduction equation depend on temperature and / or porosity.
The thermal conductivity coefficient used includes the thermal conductivity of a solid material, the frame and radiant thermal conductivity of a porous material [5];
theenergy transfer due to the molten metal convection is considered by selecting the efficient thermal conductivity of the liquid phase.
In order to describe the laser radiation interaction with a metal powder as a part of a mesoscale model, it is necessary to determine the effective parameters and establish their dependence on temperature and / or porosity, i. e., the model needs to be calibrated. Calibration can be performed on the basis of both experimental studies and microscale modeling.
The thermal conductivity of the liquid phase is calibrated, since the model does not directly provide calculation of the molten metal convection. The laser processing mode parameters and the powder material specifications are equal in both models. The peak temperature in the center of the melt pool is used as a calibration validity criterion (Fig. 5).
An important role in the product growth by the SLM method is played by the scanning strategy that affects the value of residual porosity and residual stresses. By using the mesoscale model, several options of scanning strategies for a product in the form of a rectangular trapezoid are studied (Fig. 6).
The simulation results show that in the case of such a problem formulation, the availability or absence of the laser spot idle motions does not significantly affect the final product condition. It was confirmed experimentally (Fig. 6). In some cases, residual porosity is observed in the calculations (Fig. 7).
The computational costs for the SLM workflow modeling are increased with the product size and transition from 2D to 3D modeling. Consequently, the computational time is also increased. Therefore, such models require parallel and distributed implementation using the computing clusters and / or capabilities of the multi-core graphics cards (GPUs). This leads to a more comprehensive implementation task based on the parallel software platforms. Therefore, it is rather promising to use the GPU for the mesoscale model implementation.
The paper [6] considers implementation of the numerical solution for the heat conduction equation by iterative methods using the GPU in two ways, such as an iterative method (over-relaxation method) and a strategy based on the elimination method for a tridiagonal matrix. The elimination method is fundamentally consistent, however, if it is used in relation to the entire system. If the system is split into the spatial coordinates (alternating direction implicit method), then it is possible to use elimination for a separate beam in the direction of each coordinate, and launch the number of flows equal to the number of such beams. The result is an efficient algorithm that outperforms the simple iterative method in speed, but is applicable only for the special-type matrices.
CONCLUSION
Numerical simulation is an efficient tool for determining the laser processing modes in the SLM process. The analysis of publications allows to conclude that there is a transition to a multiscale modeling methodology that includes the micro-, meso-, and macroscales. The scales are classified according to the spatial scale: from the melt pool to the entire product. All scales are interconnected: the meso- and macro-problems must be solved simultaneously, and the micro-problem is solved in advance and is used for the mesoscale model calibration. The creation of such a digital twin makes it possible to describe all essential SLM processes and becomes an important element of the production preparation process for testing the process modes of grown products.
REFERENCES
Gordeev G. A., Krivilev M. D., Ankudinov V. E. Computer simulation of selective laser melting of fine-grained metallic powders. Computational Continuum Mechanics. 2017; 10 (3): 293–312. DOI: 10.7242/1999–6691/2017.10.3.23.
Istomina N., Karyakina L. Science and business in the market of laser technologies. Photonics Russia. 2018; 12–6 (74):542–548. DOI: 10.22184/1993-7296.2018.12.6.542.548.
Bogdanovich V. I., Giorbelidze M. G., Sotov A. V., Pronichev N. D., Smelov V. G., Agapovichev A. V. Mathematical modeling of powder melting process in selective laser melting technology. News of the Samara Research Center of the Russian Academy of Sciences. 2017; 19(4): 2–3.
Boreysho A. S., Dzhgamadze G. T., Zybina V. V. Moiseev A. A., Savin A. V., Smirnov P. G., Smolentsev S. S., Timofeev V. A., Tretyak P. S. Microscale modeling of thermophysical and hydrodynamic processes of selective laser melting. Thermophysics of high temperatures. 2022; 60(1):1–7. DOI: 10.31857/S0040364422010148.
Dobrego K. V., ZHdanok S. A. Physics of filtration combustion of gases. – Minsk: Institute of Heat and Mass Transfer. A. V. Lykov NASB. 2002; 203 p. ISBN 985-6456-29-0.
Smirnov P. G., Tretyak P. S., Dzhgamadze G. T. Parallel implementation of the implicit method and the splitting method for the numerical solution of the heat equation on a graphics accelerator. Young people. Technic. Cosmos: Proceedings of the XII All-Russian Youth Scientific and Technical Conference Baltic State Technical University. Saint-Petersburg. 2019; 1: 171–179. ISBN: 978-5-94652-672-2.
CONTRIBUTION BY THE MEMBERS OF THE TEAM OF AUTHORS
Boreysho A. S. – concept of simulation in the frame of whole SLM technology realization. Savin A. V. – supervisor, development of the methodology of multilevel modeling. Smirnov P. G. – software implementation of iterative methods on a graphics accelerator. Moiseev A. A. – development and software implementation of the micro-level model. Dzhgamadze G. T. – development and software implementation of the meso-level model.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest. All authors took part in writing the article and supplemented the manuscript in part of their work.
ABOUT THE AUTHORS
Boreysho Anatoliy Sergeevich, D. Sc. of Engineering Sciences, professor, Scientific supervisor, Timeline of Laser Systems JSC, https://www.lsystems.ru, Strelna, St. Petersburg; Head of the I1 department, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, Boreysho@lsystems.ru, St. Petersburg, Russia.
Savin Andrey Valerevich, D. Sc. of Engineering Sciences, professor, Chief Researcher, Timeline of Laser Systems JSC, https://www.lsystems.ru, Strelna, St. Petersburg; lecturer of the I1 Department, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, izooandrey@inbox.ru, St. Petersburg, Russia.
WoS ResearcherID: V‑2255-2018
Smirnov Petr Gennadevich, Engineer of the 1st category, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, petr.s.8314@mail.ru, St. Petersburg, Russia.
WoS ResearcherID: V‑8450-2018
Moiseev Andrey Andreevich, Engineer of the 1st category, Baltic State Technical University “VOENMEH” named after D. F. Ustinov, terminalmashine@gmail.com, St. Petersburg, Russia.
Dzhgamadze Gvantsa Tengizovna, Engineer of the 2nd category, DgvancaT96@mail.ru, Timeline of Laser Systems JSC, https://www.lsystems.ru, Strelna, St. Petersburg, Russia.
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