Mathematical modeling of the electron-beam wire deposition additive manufacturing by the smoothed particle hydrodynamics method

Abstract

Background: The actual problem for calculating a shape of free surface of the melt when analyzing the processes of wire-based electron-beam surfacing on the substrate, being introduced into additive manufacturing, is the development of adequate mathematical models of heat and mass transfer. The paper proposed a formulation of the problem of melt motion in the framework of the Lagrangian description. The mathematical statement includes the balance equations for mass, momentum and energy, and physical equations for describing heat and mass transfer. Methods: The smoothed particle hydrodynamics method was used for numerical simulation of the process of wirebased electron-beam surfacing on the substrate made from same materials (titanium or steel). A finite-difference analog of the equations is given and the algorithm for solving the problem is implemented. To integrate the discretized equations Verlet method was utilized. Algorithms are implemented in the open software package LAMMPS. Results: The numerical simulation results allow the estimation of non-stationary volume temperature distributions, melt flow velocities and pressures, and characteristics of process. Conclusion: The possibility of applying the developed mathematical model to describe additive production is shown. The comparison of numerical calculations with experimental studies showed good agreement.

Smooth particle hydrodynamics: a meshless approach for structural mechanics

“…The researchers were able to point out the applicability and shortcomings of both methods in their work. Researchers Trushnikov et al 9 proposed a mathematical model for electron-beam wire deposition additive manufacturing. SPH approach was adopted for the simulation of the manufacturing process and results pertaining to temperature distributions, melt flow velocities, and pressures were obtained.…”

Simulation of the multi-beam electron-beam wire-feed additive manufacturing process in a vacuum

“…Recently, researchers have been more likely to use meshless approaches to solve these problems, such as a smoothed particle hydrodynamics method (SPH). However, these studies aim to study the selective laser sintering process or do not consider surface effects or solve the problem in a 2D formulation [9][10][11].…”

Modelling the effect of vibrations on the surface tension of a liquid droplet using meshless methods

“…Так, метод SPH (метод сглаженных частиц) обладает большим потенциалом по производительности [27]. Авторами статьи ранее была проведена работа по моделированию процесса наплавки проволоки с применением метода SPH [28][29][30]. Модель позволяет рассчитывать нестационарные объемные распределения температур, скоростей течения расплава, давлений, форму и размеры расплавленной ванны, форму свободной поверхности расплавленного металла, форму и размеры наплавляемого валика.…”