Tula State University (Tula, Russia):

O. I. Boriskin, Dr. Eng., Prof., Head of the Dept. of Instrumental and Metrological Systems, Director of Polytechnic Institute
E. V. Larkin, Dr. Eng., Prof., Head of the Dept. “Robotechnics and Production Automation”, e-mail: elarkin@mail.ru
G. V. Markova, Dr. Eng., Prof., Head of the Dept. “Metal Physics and Material Science”

Tula State Pedagogic University (Tula, Russia):
A. N. Privalov, Dr. Eng., Prof., e-mail: privalov.61@mail.ru

A part of the additive technology of creating metal components, namely, laser heating and melting of fine powder particles in a 3D-printer is considered. It is shown, that technological equipment operation optimization is impossible without developing of a mathematical model of metal particles heating and melting. An approach based on the formation and solution of the heat equation with boundary conditions, that take into account the spherical shape of the particle, the energy distribution in the laser beam transverse section and the mutual spatial position of the particle and the laser beam, is used as the basic concept of modeling. It is noted, that for the evaluation of the structure of formed component, such an approach is quite redundant, moreover the algorithm of integrating the partial diff erential equation has a high computational complexity. To simplify the analysis, the original micro-model has been transformed into heating and melting macro-models, in which the temperature distribution over the particle volume is assumed as a constant, and the external effect on the particle is considered as heat transfer through the ball surface, at the top end, from laser beam to the particle, and at the bottom end, from particle to an environment. For the macro-model, the diagrams of particle temperature and accumulated internal energy increase in time, are obtained. The conclusion about the possibility of dividing the space around the particle into zones: complete and incomplete melting, as well as a zone of insufficient heating for melting, is made. It is shown, that the presence of such zones leads to the friability of the structure of the parts formed with use a 3D printer.

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