An Inhomogeneous Model for Laser Welding of Industrial Interest
An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5<...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/15/3357 |
| _version_ | 1797586410298933248 |
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| author | Carmelo Filippo Munafò Annunziata Palumbo Mario Versaci |
| author_facet | Carmelo Filippo Munafò Annunziata Palumbo Mario Versaci |
| author_sort | Carmelo Filippo Munafò |
| collection | DOAJ |
| description | An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>%</mo></mrow></semantics></math></inline-formula> alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer. |
| first_indexed | 2024-03-11T00:22:48Z |
| format | Article |
| id | doaj.art-c3e586e8ec5d4eb8958782fb3132f55c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:22:48Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c3e586e8ec5d4eb8958782fb3132f55c2023-11-18T23:15:35ZengMDPI AGMathematics2227-73902023-07-011115335710.3390/math11153357An Inhomogeneous Model for Laser Welding of Industrial InterestCarmelo Filippo Munafò0Annunziata Palumbo1Mario Versaci2MIFT Department, University of Messina, Viale F. D’Alcontres 31, I-98166 Messina, ItalyMIFT Department, University of Messina, Viale F. D’Alcontres 31, I-98166 Messina, ItalyDICEAM Department, Mediterranea University, Via Zehender (ex Via Graziella Feo di Vito), I-89122 Reggio Calabria, ItalyAn innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>%</mo></mrow></semantics></math></inline-formula> alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer.https://www.mdpi.com/2227-7390/11/15/3357laser weldingheat transferinhomogeneous parabolic modelco-presence of solid–liquid phasesCauchy–Stefan–Boltzmann boundary conditionsGalerkin-FEM approach |
| spellingShingle | Carmelo Filippo Munafò Annunziata Palumbo Mario Versaci An Inhomogeneous Model for Laser Welding of Industrial Interest Mathematics laser welding heat transfer inhomogeneous parabolic model co-presence of solid–liquid phases Cauchy–Stefan–Boltzmann boundary conditions Galerkin-FEM approach |
| title | An Inhomogeneous Model for Laser Welding of Industrial Interest |
| title_full | An Inhomogeneous Model for Laser Welding of Industrial Interest |
| title_fullStr | An Inhomogeneous Model for Laser Welding of Industrial Interest |
| title_full_unstemmed | An Inhomogeneous Model for Laser Welding of Industrial Interest |
| title_short | An Inhomogeneous Model for Laser Welding of Industrial Interest |
| title_sort | inhomogeneous model for laser welding of industrial interest |
| topic | laser welding heat transfer inhomogeneous parabolic model co-presence of solid–liquid phases Cauchy–Stefan–Boltzmann boundary conditions Galerkin-FEM approach |
| url | https://www.mdpi.com/2227-7390/11/15/3357 |
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