Computer-Aided Design 127 (2020) 102852 Contents lists available at ScienceDirect Computer-Aided Design journal homepage: www.elsevier.com/locate/cad Fabricated shape estimation for additive manufacturing processes with uncertainty Svyatoslav Korneev ∗ , Ziyan Wang, Vaidyanathan Thiagarajan, Saigopal Nelaturi Palo Alto Research Center (PARC), 3333 Coyote Hill Road, Palo Alto, CA 94304, United States of America article info Article history: Received 27 March 2020 Accepted 16 April 2020 Keywords: Additive manufacturing Multiphysics Shape estimation Machine learning Visualization abstract We present an approach to map Additive Manufacturing (AM) process parameters and a given tool path to a representation of the as-manufactured shape that captures machine-specific manufacturing uncertainty. Multi-physics models that capture the deposition process at the smallest manufacturing scale are solved to accurately simulate local material accumulation. A surrogate model for the multiphysics simulation is used to practically simulate the material accumulation by locally varying the spatial distribution of material along the tool path. This generates a training set representing a variational class of as-manufactured shapes. Machine specific manufacturing uncertainty is then represented as a 3D kernel obtained by deconvolving the simulated as-printed shape with the tool path. This kernel provides a good estimate of the probability of local material accumulation independent of the chosen part and tool-path. Convolution of the kernel with a tool-path combined with an appropriate super-level-set of the resulting field provides a computationally efficient way to estimate the as-manufactured shape of AM parts. The efficiency results from the highly parallelized implementation of convolution on the GPU. We demonstrate high-resolution shape estimation and visualization of as-printed parts constructed using this approach. We validate the method using data generated by simulating a build process for droplet-based AM, by performing model order reduction of a system of partial differential equations for the 3D Navier–Stokes multiphase flows coupled with heat-transfer and phase change. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Motivation Uncertainties in any manufacturing process lead to deviations between nominal designs and their fabricated counterparts. Nom- inally designed shape and material layout is invariably altered in an AM process, and shape variations can lead to undesirable effects such as (unintentional) porosity and surface roughness. These in turn can lead to long-term performance degradation due to residual stresses, fatigue failure mechanisms such as crack initiation [1–3], or can negatively affect bulk mechanical proper- ties [4]. Metal parts designed for high stress applications should be fully dense with smooth surfaces to minimize the possibility of failure in service [5]. While such properties are achievable in machining, the geometric complexity achievable using AM enables manufacturing functional high performance lightweight parts that may be impossible to fabricate otherwise. This feature of metal AM motivates the need to understand the relationship ∗ Corresponding author. E-mail addresses: skorneev@parc.com (S. Korneev), ziyanw@stanford.edu (Z. Wang), vaidyana@parc.com (V. Thiagarajan), nelaturi@parc.com (S. Nelaturi). between a nominal design and its corresponding variational class of shapes arising due to the combination of chosen AM process parameters and manufacturing error. Although we focus the dis- cussion in this paper to select metal AM processes, we observe that similar issues arise in polymer AM as well. The intricate relationship between AM process parameters and fabricated part properties has received significant attention [6–9], mostly by fabricating parts and either studying their microstruc- ture [10] or by mechanical testing to determine (anisotropic) material properties [11]. For metal AM, microstructural details such as grain morphology, grain texture, and phase identification for Powder Bed Fusion and Direct Energy Deposition processes are studied using LOM and SEM microstructure imaging. The ori- entation of the columnar grains seen in these processes are highly influenced by a combination of the scan strategy and applied energy to induce material phase changes key to the AM process. Experimental analysis to map process parameters to particular manufacturing-driven structural and material variation is done in a case-by-case manner for each material and process combination in metal AM processes. Due to the availability of several AM technologies, applications, and testing strategies, a rich body of literature exists for AM metallurgy and processing science [4]. https://doi.org/10.1016/j.cad.2020.102852 0010-4485/© 2020 Elsevier Ltd. All rights reserved.