Discovery of Spatter Constitutive Models in Additive Manufacturing Using Machine Learning

TL;DR

This work addresses spatter-driven defects in Laser Powder Bed Fusion (LPBF) by building a data-driven framework that combines high-fidelity OpenFOAM simulations with FLOW-3D data to generate a large dataset of melt-pool features and spatter. It employs ensemble ML models (e.g., ExtraTrees, RF, KNN, GB) and polynomial regression to predict melt-pool dimensions and spatter, using process inputs (power, velocity) or melt-pool features, with log-transformations improving nonlinear fits and predictive accuracy. The results show $R^2$ values exceeding 0.95 for melt-pool dimensions and up to 0.97 for some spatter predictions, along with interpretable explicit polynomial equations that relate inputs to outputs, enhancing process insight. The methodology offers a path toward robust, interpretable process control in AM, enabling quality monitoring and defect mitigation by linking processing conditions to melt-pool behavior and spatter dynamics.

Abstract

Additive manufacturing (AM) is a rapidly evolving technology that has attracted applications across a wide range of fields due to its ability to fabricate complex geometries. However, one of the key challenges in AM is achieving consistent print quality. This inconsistency is often attributed to uncontrolled melt pool dynamics, partly caused by spatter which can lead to defects. Therefore, capturing and controlling the evolution of the melt pool is crucial for enhancing process stability and part quality. In this study, we developed a framework to support decision-making towards efficient AM process operations, capable of facilitating quality control and minimizing defects via machine learning (ML) and polynomial symbolic regression models. We implemented experimentally validated computational tools, specifically for laser powder bed fusion (LPBF) processes as a cost-effective approach to collect large datasets. For a dataset consisting of 281 varying process conditions, parameters such as melt pool dimensions (length, width, depth), melt pool geometry (area, volume), and volume indicated as spatter were extracted. Using machine learning (ML) and polynomial symbolic regression models, a high R2 of over 95 % was achieved in predicting the melt pool dimensions and geometry features on both the training and testing datasets, with either process conditions (power and velocity) or melt pool dimensions as the model inputs. In the case of volume indicated as spatter the value of the R2 improved after logarithmic transforming the model inputs, which were either the process conditions or the melt pool dimensions. Among the investigated ML models, the ExtraTree model achieved the highest R2 values of 96.7 % and 87.5 %.

Figures (7)

• Figure 1: Spatter dataset generated using OpenFOAM, a computationally expensive tool, was trained for classification task to differentiate between the two classes. Using the model as an inference, spatter count was predicted on a FLOW-3D, which is 18 times less computationally expensive tool. (a) Datasets consisting of process conditions, melt pool dimensions, geometry, and spatter count were collected from 281 FLOW-3D experiments (b) The process conditions was used as an input to either the ML model or polynomial regression to predict the melt pool dimensions, geometry features and the spatter count (c) The melt pool dimension was used as an input to either the ML model or polynomial regression to predict the spatter count
• Figure 2: Distribution of the extracted parameters from the simulation of LPBF (a) Melt pool length (b) Melt pool width (c) Melt pool depth (d) Volume indicated as spatter (e) Melt pool cross section area (f) Melt pool volume
• Figure 3: A correlation matrix displays the Pearson correlation coefficients between pairs of variables in the process conditions, melt pool dimensions and geometry
• Figure 4: Polynomial regression fitting on the training dataset using either process conditions or melt pool dimension as an input into the model to predict the following (A) Melt pool length prediction using power and velocity as the model input (B) Melt pool width prediction using power and velocity as the model input (C) Melt pool depth prediction using power and velocity as the model input (D) Melt pool top cross sectional area prediction using power and velocity as the model input(E) Melt pool volume prediction using power and velocity as the model input (F) Prediction of volume indicated as spatter using power and velocity as the model input (G) Prediction of volume indicated as spatter using power and velocity as the model input Prediction of volume indicated as spatter using Power, Velocity, and $\log$(Velocity) as the model input (H) Prediction of volume indicated as spatter using length, width and depth as the model input (I) Prediction of volume indicated as spatter using $\log$(length), width, depth, $\log$(width), and $\log$(depth) as the model input
• Figure 5: Polynomial regression fitting for the test dataset (A) Melt pool length prediction using power and velocity as the model input (B) Melt pool width prediction using power and velocity as the model input (C) Melt pool depth prediction using power and velocity as the model input (D) Melt pool top cross sectional area prediction using power and velocity as the model input(E) Melt pool volume prediction using power and velocity as the model input (F) Prediction of volume indicated as spatter using power and velocity as the model input (G) Prediction of volume indicated as spatter using power and velocity as the model input Prediction of volume indicated as spatter using Power, Velocity, and $\log$(Velocity) as the model input (H) Prediction of volume indicated as spatter using length, width and depth as the model input (I) Prediction of volume indicated as spatter using $\log$(length), width, depth, $\log$(width), and $\log$(depth) as the model input