Toolpath Design for Additive Manufacturing using Graph Theory

Cheng, Puikei

doi:https://doi.org/10.21985/n2-2028-ne65

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Toolpath Design for Additive Manufacturing using Graph Theory

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Metal Additive manufacturing (AM) processes build 3D objects by heating and consolidating material in a point-by-point manner. Unlike traditional manufacturing methods, AM allows the material properties of each point in the build to vary by controlling process conditions locally. The process parameters can be considered as inputs to the AM system, whereas the resulting thermal, microstructural, or property distributions can be considered as outputs to the AM system. Characterizing how AM inputs affect AM outputs is a forward problem. On the contrary, process parameter design involves solving the backward, or inverse, problem. AM presents the opportunity for extremely flexible design, but it also greatly increases the complexity of the search for the optimal set of process parameters. The toolpath is a key process parameter in AM. Different toolpaths produce drastically different microstructural distributions and mechanical properties in the resultant build. However, unlike process parameters like laser power and velocity, toolpaths are discrete variables. In addition, the set of toolpaths is mathematically unstructured. Mathematical structure on a set are additional features associated with the set, such as element order or similarity. Without structure, there is no sense of how different elements on that set relate to each other. Both the forward and backward problems become computationally-expensive, combinatorial search problems. We therefore start by systematically generating toolpaths and thermal simulation data, which will enable our search for structure within those two data sets. We find that Hamiltonian path algorithms can enumerate a broad array of toolpaths on any given discretized geometry using only two assumptions: (1) each subvolume in the geometry is activated exactly once, and (2) toolpaths are space- and time-continuous so that the search space is finite. The enumerated toolpaths serve as the input to finite element thermal simulations that output thermal histories. With the generated toolpath and thermal data, we search for relationships within and between the two data sets. First, we try a feature-based approach, which reduces toolpath information into a vector of internal structure and reduces thermal data into solidification cooling rate (SCR) statistics. Multivariate linear regression shows strong correlation between input and output data features. However, the features do not represent each data instance uniquely and do not account for spatial information in the multi-dimensional data. Hence, we develop a metric-based approach to address those issues. Metrics are distance functions, which can be used to represent dissimilarity. This approach also structures the input and output spaces so that system stability between the two spaces can be estimated by comparing corresponding pairwise distances. Many optimization algorithms require system stability. We find that the AM system exhibits high instability when the input and output spaces are modeled by two standard image comparison metrics. Deep learning is a promising direction for structuring and regularizing the toolpath design problem. We show preliminary work on using Artificial Neural Networks and Convolutional Neural Networks to predict SCR distribution from toolpath data. However, more work is needed before algorithmic toolpath design is practical on an industrial level.

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