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In droplet-on-demand liquid metal jetting (DoD-LMJ) additive manufacturing, complex physical interactions govern the droplet characteristics, such as size, velocity, and shape. These droplet characteristics, in turn, determine the functional quality of the printed parts. Hence, to ensure repeatable and reliable part quality it is necessary to monitor and control the droplet characteristics. Existing approaches for in-situ monitoring of droplet behavior in DoD-LMJ rely on high-speed imaging sensors. The resulting high volume of droplet images acquired is computationally demanding to analyze and hinders real-time control of the process. To overcome this challenge, the objective of this work is to use time series data acquired from an in-process millimeter-wave sensor for predicting the size, velocity, and shape characteristics of droplets in DoD-LMJ process. As opposed to high-speed imaging, this sensor produces data-efficient time series signatures that allows rapid, real-time process monitoring. We devise machine learning models that use the millimeter-wave sensor data to predict the droplet characteristics. Specifically, we developed multilayer perceptron-based non-linear autoregressive models to predict the size and velocity of droplets. Likewise, a supervised machine learning model was trained to classify the droplet shape using the frequency spectrum information contained in the millimeter-wave sensor signatures. High-speed imaging data servedmore »as ground truth for model training and validation. These models captured the droplet characteristics with a statistical fidelity exceeding 90%, and vastly outperformed conventional statistical modeling approaches. Thus, this work achieves a practically viable sensing approach for real-time quality monitoring of the DoD-LMJ process, in lieu of the existing data-intensive image-based techniques.

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The objective of this work is to provide experimental validation of the graph theory approach for predicting the thermal history in additively manufactured parts that was recently published in the ASME transactions. In the present paper the graph theory approach is validated with in-situ infrared thermography data in the context of the laser powder bed fusion (LPBF) additive manufacturing process. We realize this objective through the following three tasks. First, two types of test parts (stainless steel) are made in two corresponding build cycles on a Renishaw AM250 LPBF machine. The intent of both builds is to influence the thermal history of the part by changing the cooling time between melting of successive layers, called interlayer cooling time. Second, layer-wise thermal images of the top surface of the part are acquired using an in-situ a priori calibrated infrared camera. Third, the thermal imaging data obtained during the two builds were used to validate the graph theory-predicted surface temperature trends. Furthermore, the surface temperature trends predicted using graph theory are compared with results from finite element analysis. As an example, for one the builds, the graph theory approach accurately predicted the surface temperature trends to within 6% mean absolute percentagemore »error, and approximately 14 Kelvin root mean squared error of the experimental data. Moreover, using the graph theory approach the temperature trends were predicted in less than 26 minutes which is well within the actual build time of 171 minutes.

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The goal of this work is to predict the effect of part geometry and process parameters on the instantaneous spatial distribution of heat, called the heat flux or thermal history, in metal parts as they are being built layer-by-layer using additive manufacturing (AM) processes. In pursuit of this goal, the objective of this work is to develop and verify a graph theory-based approach for predicting the heat flux in metal AM parts. This objective is consequential to overcome the current poor process consistency and part quality in AM. One of the main reasons for poor part quality in metal AM processes is ascribed to the heat flux in the part. For instance, constrained heat flux because of ill-considered part design leads to defects, such as warping and thermal stress-induced cracking. Existing non-proprietary approaches to predict the heat flux in AM at the part-level predominantly use mesh-based finite element analyses that are computationally tortuous — the simulation of a few layers typically requires several hours, if not days. Hence, to alleviate these challenges in metal AM processes, there is a need for efficient computational thermal models to predict the heat flux, and thereby guide part design and selection of processmore »parameters instead of expensive empirical testing. Compared to finite element analysis techniques, the proposed mesh-free graph theory-based approach facilitates layer-by-layer simulation of the heat flux within a few minutes on a desktop computer. To explore these assertions we conducted the following two studies: (1) comparing the heat diffusion trends predicted using the graph theory approach, with finite element analysis and analytical heat transfer calculations based on Green’s functions for an elementary cuboid geometry which is subjected to an impulse heat input in a certain part of its volume, and (2) simulating the layer-by-layer deposition of three part geometries in a laser powder bed fusion metal AM process with: (a) Goldak’s moving heat source finite element method, (b) the proposed graph theory approach, and (c) further comparing the heat flux predictions from the last two approaches with a commercial solution. From the first study we report that the heat flux trend approximated by the graph theory approach is found to be accurate within 5% of the Green’s functions-based analytical solution (in terms of the symmetric mean absolute percentage error). Results from the second study show that the heat flux trends predicted for the AM parts using graph theory approach agrees with finite element analysis with error less than 15%. More pertinently, the computational time for predicting the heat flux was significantly reduced with graph theory, for instance, in one of the AM case studies the time taken to predict the heat flux in a part was less than 3 minutes using the graph theory approach compared to over 3 hours with finite element analysis. While this paper is restricted to theoretical development and verification of the graph theory approach for heat flux prediction, our forthcoming research will focus on experimental validation through in-process sensor-based heat flux measurements.

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Purpose The purpose of this paper is to develop, apply and validate a mesh-free graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process. Design/methodology/approach In this study, the authors develop a novel mesh-free graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti-6Al-4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples. Findings The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error. Research limitations/implications This study uses data from fixed thermocouples when printing thin-wall DED parts. In the future, the authors will incorporate infrared thermal cameramore »data from large parts. Practical implications The DED process is particularly valuable for near-net shape manufacturing, repair and remanufacturing applications. However, DED parts are often afflicted with flaws, such as cracking and distortion. In DED, flaw formation is largely governed by the intensity and spatial distribution of heat in the part during the process, often referred to as the thermal history. Accordingly, fast and accurate thermal models to predict the thermal history are necessary to understand and preclude flaw formation. Originality/value This paper presents a new mesh-free computational thermal modeling approach based on graph theory (network science) and applies it to DED. The approach eschews the tedious and computationally demanding meshing aspect of finite element modeling and allows rapid simulation of the thermal history in additive manufacturing. Although the graph theory has been applied to thermal modeling of laser powder bed fusion (LPBF), there are distinct phenomenological differences between DED and LPBF that necessitate substantial modifications to the graph theory approach.« less

The objective of this work is to predict a type of thermal-induced process failure called recoater crash that occurs frequently during laser powder bed fusion (LPBF) additive manufacturing. Rapid and accurate thermomechanical simulations are valuable for LPBF practitioners to identify and correct potential issues in the part design and processing conditions that may cause recoater crashes. In this work, to predict the likelihood of a recoater crash (recoater contact or impact) we develop and apply a computationally efficient thermomechanical modeling approach based on graph theory. The accuracy and computational efficiency of the approach is demonstrated by comparison with both non-proprietary finite element analysis (Abaqus), and a proprietary LPBF simulation software (Autodesk Netfabb). Based on both numerical (verification) and experimental (validation) studies, the proposed approach is found to be 5 to 6 times faster than the non-proprietary finite element modeling and has the same order of computational time as a commercial simulation software (Netfabb) without sacrificing prediction accuracy.