MATHEMATICAL MODELING FOR APPLICATIONS THE SELECTIVE LASER MELTING PROCESS IN 3D PRINTING

Abstract

This paper provides an overview of the physical processes occurring during selective laser melting of metal powders, as well as an overview of methods for mathematically modeling these processes. The key physical processes that must be taken into account for an adequate modeling of selective laser melting of metal powders are identified. A general physical and mathematical model is formulated to solve the problem of selective laser melting of metal powders. The assumptions and constraints adopted for the formulated physical model are presented. The governing equations describing heat transfer processes, liquid metal dynamics, and the shape of the free surface are considered. The initial and boundary conditions are presented. Taking into account the requirements for mathematical models, a numerical algorithm for solving the governing equations has been developed, based on a three-layer implicit scheme with second-order accuracy in time integration, third-order counter-current approximation of convective terms, and second-order central difference approximation of diffusion terms. The pressure and velocity fields in the Navier-Stokes equations were coupled using the artificial compressibility method, modified for the calculation of unsteady problems. The system of initial equations was numerically integrated using the finite volume method. The system of linear algebraic equations of the implicit scheme was solved using the well-known generalized misfit minimization (GMRES) method with an incomplete LU decomposition of the total system matrix as preconditioning.

Numerical simulations of the transient processes of selective laser melting of metal powders have yielded a temperature field distribution in the computational domain, highlighting the liquidus zone. Dependences of the width and depth of the molten pool on the laser velocity and the laser spot diameter have been plotted.