Functional Models with Spatially Varying Coefficients for Fast Prediction of Temperature History for Wire-based Metal Additive Manufacturing

Wire-based metal additive manufacturing is a promising technique for fabricating large-scale structural components across various industrial sectors. Using robot-assisted deposition, these technologies offer relatively low equipment cost for fast fabrication on large areas. However, high operating temperatures and heat accumulation create significant thermal stresses, causing distortion and roughness in deposited layers. Precise thermal history prediction is essential for achieving proper deposition process planning and control. Typically, finite element method (FEM) simulations are used to solve large PDEs for thermal analysis. However, these methods are computationally prohibitive for large parts, making them unsuited the effective automation of the deposition process. In this paper, we develop a functional regression model as a surrogate for thermal history prediction during single layer, single track deposition. The interaction between prediction features is modeled using tensor-product basis. Thermal history heterogeneity along weld cross-sections are modeled using Gaussian Process-based varying coefficients. We studied the effect of track geometry on the FEM results, the accuracy of the proposed surrogate methodology for predictions of the thermal history profile for each geometry and discuss its applicability to help automate process planning and control in large-scale metal additive manufacturing.