Analytical Solution of the Non-Stationary Heat Conduction Problem in Thin-Walled Products during the Additive Manufacturing Process

Abstract

The work is devoted to the development of a model for calculating transient quasiperiodic temperature fields arising in the direct deposition process of thin walls with various configurations. The model allows calculating the temperature field, thermal cycles, temperature gradients, and the cooling rate in the wall during the direct deposition process at any time. The temperature field in the deposited wall is determined based on the analytical solution of the non-stationary heat conduction equation for a moving heat source, taking into account heat transfer to the environment. Heat accumulation and temperature change are calculated based on the superposition principle of transient temperature fields resulting from the heat source action at each pass. The proposed method for calculating temperature fields describes the heat-transfer process and heat accumulation in the wall with satisfactory accuracy. This was confirmed by comparisons with experimental thermocouple data. It takes into account the size of the wall and the substrate, the change in power from layer to layer, the pause time between passes, and the heat-source trajectory. In addition, this calculation method is easy to adapt to various additive manufacturing processes that use both laser and arc heat sources.

An Extended Analytical Solution of the Non-Stationary Heat Conduction Problem in Multi-Track Thick-Walled Products during the Additive Manufacturing Process

“…To take into account the removed mass of the substrate, heat sinks of the corresponding energy are introduced. One of the variants of this approach is described in [ 38 ].…”

“…The objective of this work is to develop a simple and fast but, at the same time, reliable method for calculating transient three-dimensional temperature fields in the AM process of multi-track thick-walled products. This work is a continuation of a previous work [ 38 ], where the heat conduction problem was solved for single-pass thin-walled products. The developed calculation scheme assumes its further inclusion in the optimization system for selecting the technological parameters.…”

“…To take into account the removed mass of the substrate, heat sinks of the corresponding energy are introduced. One of the variants of this approach is described in [38]. the side parts of a substrate that are outside the wall construction area are removed (Figure 4).…”

“…To take into account the removed mass of the substrate, heat sinks of the corresponding energy are introduced. One of the variants of this approach is described in [38]. The second approach consists in replacing the real horizontal substrate with a vertical substrate (rib), the section of which coincides with the wall section.…”

Laser Remelting Process Simulation and Optimization for Additive Manufacturing of Nickel-Based Super Alloys

“…Numerical models for the simulation of laser welding and AM processes are characterized by the model domain, heat source definition, material properties, and the governing equations for heat transfer and fluid flow. The length scale of the model domain ranges from less than a millimeter for the analysis of melt pool dynamics [ 5 ] to several centimeters or even meters where the development of the temperature field on the part scale is of interest [ 6 ]. For melt pool modeling of a single welding track, the symmetry of the process permits consideration of only one half of the track within the domain, in order to reduce computational costs [ 7 , 8 ].…”