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

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 wire-based 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.

Numerical 3D simulation of wire deposition process to predict distortion of parts

In the work, on the basis of the analysis of publications, existing approaches to the numerical modeling of additive processes of product formation are shown. The work itself is devoted to the study of the influence of parameters of the process of surfacing wire materials on the formation of residual deformations in parts. A mathematical formulation of the non-stationary thermomechanical problem is presented, and algorithms for solving the problem using the technology of birth and death of finite elements in the ANSYS package are described. Verification of the model created by the finite element was carried out on the basis of data from the experiment on surfacing a multilayer sample. The effect on the level of residual warping of the following process parameters was studied: the exposure time before the next layer was deposited; the motion path of the burner; ambient temperature. It is shown that the change in ambient temperature is the most effective way to reduce the residual distortions of the form.