Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution
This study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The solution is based on the Green’s function method, acc...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-03-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/4/650 |
| _version_ | 1797443528884748288 |
|---|---|
| author | Alexander Orekhov Lev Rabinskiy Gregory Fedotenkov |
| author_facet | Alexander Orekhov Lev Rabinskiy Gregory Fedotenkov |
| author_sort | Alexander Orekhov |
| collection | DOAJ |
| description | This study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The solution is based on the Green’s function method, according to which the influence function of a surface-concentrated heat source is found at the first stage. The influence function has axial symmetry and the problem of finding the influence function is axisymmetric. To find the Green’s function, Laplace and Fourier integral transforms are used. The novelty of the obtained analytical solution is that the heat transfer at the free surface of the half-space is taken into account. The Green’s function that was obtained is used to construct an analytical solution to the moving heat-source problem in the integral form. The kernel of the advising integral operator is the constructed Green’s function. The Gaussian distribution is used to calculate integrals on spatial variables analytically. Gaussian law models the distribution of heat flux in the laser beam. As a result, the corresponding integrals on the spatial variables can be calculated analytically. A convenient formula that allows one to study the non-stationary temperature distribution when the heat source moves along arbitrary trajectories is obtained. A numerical, analytical algorithm has been developed and implemented that allows one to determine temperature distribution both on the surface and on the depth of a half-space. For verification purposes, the results were compared with the solution obtained using FEM. |
| first_indexed | 2024-03-09T12:57:22Z |
| format | Article |
| id | doaj.art-eb5e08b2c79b4a04aebc880d23c32fdf |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:57:22Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-eb5e08b2c79b4a04aebc880d23c32fdf2023-11-30T21:58:36ZengMDPI AGSymmetry2073-89942022-03-0114465010.3390/sym14040650Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian DistributionAlexander Orekhov0Lev Rabinskiy1Gregory Fedotenkov2Moscow Aviation Institute, National Research University, 125993 Moscow, RussiaMoscow Aviation Institute, National Research University, 125993 Moscow, RussiaMoscow Aviation Institute, National Research University, 125993 Moscow, RussiaThis study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The solution is based on the Green’s function method, according to which the influence function of a surface-concentrated heat source is found at the first stage. The influence function has axial symmetry and the problem of finding the influence function is axisymmetric. To find the Green’s function, Laplace and Fourier integral transforms are used. The novelty of the obtained analytical solution is that the heat transfer at the free surface of the half-space is taken into account. The Green’s function that was obtained is used to construct an analytical solution to the moving heat-source problem in the integral form. The kernel of the advising integral operator is the constructed Green’s function. The Gaussian distribution is used to calculate integrals on spatial variables analytically. Gaussian law models the distribution of heat flux in the laser beam. As a result, the corresponding integrals on the spatial variables can be calculated analytically. A convenient formula that allows one to study the non-stationary temperature distribution when the heat source moves along arbitrary trajectories is obtained. A numerical, analytical algorithm has been developed and implemented that allows one to determine temperature distribution both on the surface and on the depth of a half-space. For verification purposes, the results were compared with the solution obtained using FEM.https://www.mdpi.com/2073-8994/14/4/6503D printingselective laser meltingadditive manufacturingconcentrated loadmoving loadheat flow |
| spellingShingle | Alexander Orekhov Lev Rabinskiy Gregory Fedotenkov Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution Symmetry 3D printing selective laser melting additive manufacturing concentrated load moving load heat flow |
| title | Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution |
| title_full | Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution |
| title_fullStr | Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution |
| title_full_unstemmed | Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution |
| title_short | Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution |
| title_sort | analytical model of heating an isotropic half space by a moving laser source with a gaussian distribution |
| topic | 3D printing selective laser melting additive manufacturing concentrated load moving load heat flow |
| url | https://www.mdpi.com/2073-8994/14/4/650 |
| work_keys_str_mv | AT alexanderorekhov analyticalmodelofheatinganisotropichalfspacebyamovinglasersourcewithagaussiandistribution AT levrabinskiy analyticalmodelofheatinganisotropichalfspacebyamovinglasersourcewithagaussiandistribution AT gregoryfedotenkov analyticalmodelofheatinganisotropichalfspacebyamovinglasersourcewithagaussiandistribution |