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

Dmitrii Mukin,Gleb Turichin,Ekaterina Valdaytseva,Artur Vildanov

doi:10.3390/ma14237291

Abstract

An analytical model has been developed for calculating three-dimensional transient temperature fields arising in the direct deposition process to study the thermal behavior of multi-track walls with various configurations. The model allows the calculation of all characteristics of the temperature fields (thermal cycles, cooling rates, temperature gradients) in the wall during the direct deposition process at any time. The solution of the non-stationary heat conduction equation for a moving heat source is used to determine the temperature field in the deposited wall, taking into account heat transfer to the environment. The method considers the size of the wall and the substrate, the change in power from layer to layer, the change in the cladding speed, the interpass dwell time (pause time), and the heat source trajectory. Experiments on the deposition of multi-track block samples are carried out, as a result of which the values of the temperatures are obtained at fixed points. The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. It is confirmed by comparisons with experimental thermocouple data. The relative difference in the interlayer temperature does not exceed 15%.

Highlights

In the direct energy deposition (DED) process, a heat source is used to form a melt pool on the surface of a solid metal substrate
The thermophysical properties of the filler material and substrate are constant and temperature-independent; Heat flux distribution of the heat source qh is presented as a surface normally distributed heat source; Heat transfer occurs according to Newton’s law; Phase transition is not considered;
The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. This model is based on the obtained three-dimensional solution of the non-stationary heat conduction equation for a moving distributed heat source, considering convective heat transfer to the environment

Summary

Introduction

In the DED process, a heat source is used to form a melt pool on the surface of a solid metal substrate. The filler material is fed into the melt pool, which causes it to melt. There are various direct deposition technologies, differing in the type of heat source used and the filler material used. Technologies using laser and metal powder are well-developed and widespread. A laser, electron beam, and arc can be used when using filler wire. When using a laser or electron beam, the wire is usually fed from the side, which imposes corresponding restrictions on the product shape [6]. The process of using an electric arc as a heat source is similar to fusion welding [7]

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