Mathematical modelling of complex heat exchange while developing SLM laser technologies

Mathematica modeling, numerical technique and program complexes


Аuthors

Lebedkin I. F.1*, Molotkov A. A.2**, Tretiyakova O. N.***

1. Research Institute “ESTO”, 5, Georgievsky Avenue, build. 1, Moscow, Zelenograd, 124460, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: ivan_leb@mail.ru
**e-mail: karacerr@gmail.com
***e-mail: tretiyakova_olga@mail.ru

Abstract

An important task of development and research in the field of additive technology is mathematical models developing. A large number of changing parameters, such as laser power, speed, the bulk layer thickness, laser spot diameter, etc.) makes the process of the machine optimal operation mode selecting time consuming and expensive. Besides, various designs of created objects require creation mode of their own. Application of mathematical modeling can significantly reduce research and production costs. In this case, we start solving a simplified problem of heating the body by a mobile heat source, which is a Gaussian beam of radiation, with account for the phase transitions in the material. Calculations are presented in two versions, using third-party software that makes the calculation by the finite element method, and using its own software that performs calculation by the explicit finite difference scheme. The obtained results were compared to the results of other studies. A qualitative matching of the results was observed. The results discrepancy is caused mainly by the assumptions made while the model developing. In the future, it is necessary to account for the medium dispersion and particles movement during the process. As revealed by the experiments, the air flows movement and of the material evaporation from the surface exert a significant impact on the result as well. Strong restrictions on the spatial and temporal steps can be tried to circumvent using implicit methods with the property of absolute stability. The mathematical model and numerical computation method upgrading continues.

Keywords:

mathematical model, Gaussian beam, laser, heat equation, phase transitions, numerical solution

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