State-Space Modeling of Weld Bead Geometry in the Gas Metal Arc-Direct Energy Deposition Process Applied to Wire and Arc Additive Manufacturing and Welding Processes

Abstract

One of the main problems of additive manufacturing with electric arc and welding, in general, is the difficulty in controlling or predicting the output variables and their parameters, as well as creating a model that effectively represents the changes in the main variables involved in the system. These changes during the deposition process can promote the formation of splashes, instabilities, and changes in the geometry of the beads, making the analysis of these variables important, as it will be through them that the quality of the deposit and the desired characteristics will be established. Despite the correlation between the variables, they present nonlinear and chaotic behavior. With this, the purpose of this research is mathematical modeling in state space that allows an approximation to the model in state spaces, an approximation of the real values of the process, and a knowledge of the system composed of a set of input, output, and states related to each other by means of first-order differential equations. The model was validated from depositions via a design of experiments with central composite planning monitored with the use of sensors to capture the characteristics of the beads (e.g., molten pool, width, penetration, and height).