Learning and Predicting Shape Deviations of Smooth and Non-Smooth 3D Geometries Through Mathematical Decomposition of Additive Manufacturing

Yuanxiang Wang, Cesar Ruiz, Qiang Huang

Abstract: In additive manufacturing (AM), final product geometries are often deformed or distorted. The deviations of three-dimensional (3D) shapes from their intended designs can be represented as 2D surfaces in a $\mathbb {R}^{3}$ space, which constitutes a complicated set of data for learning and predicting geometric quality. Patterns of deviation surfaces vary with shape geometries, sizes/volumes, materials, and AM processes. Our previous work has established an engineering-informed convolution framework to learn shape deviation from a small set of training products built with the same material and process. It incorporates the characteristics of the layer-wise shape forming process through a convolution formulation and the size factor for a category of smooth 3D shapes such as domes or cylinders. This study extends this fabrication-aware learning framework to a larger class of products including both smooth and non-smooth surfaces (polyhedral shapes). The key idea of learning heterogeneous deviation surface data under a unified model is to establish the association between the deviation profiles of smooth base shapes and those of non-smooth polyhedral shapes. The association, which is characterized by a novel 3D cookie-cutter function, views polyhedral shapes as being carved out from smooth base shapes. In essence, the AM process of building non-smooth shapes is mathematically decomposed into two steps: additively fabricate smooth base shapes using a convolution learning framework, and then subtract extra materials using a cookie-cutter function. The proposed joint learning framework of shape deviation data reflects this decomposition by adopting a sequential model estimation procedure. The model learning procedure first establishes the convolution model to capture the effects of layer-wise fabrication and sizes, and then estimates the 3D cookie-cutter function to realize geometric differences between smooth and non-smooth shapes. A new Gaussian process model is proposed to consider the spatial correlation among neighboring regions within a 3D shape and across different shapes. The case study demonstrates the feasibility and prospects of prescriptive learning of complex 3D shape deviations in AM and extension to broader engineering surface data. Note to Practitioners —Engineering processes such as 3D printing generate complex shape data in the form of 3D point clouds. Qualification and verification of 3D shapes involves modeling and learning of heterogeneous shape deviation data that are affected by both product geometries and process physics. This study develops an engineering-informed, small-sample machine learning methodology to learn and predict deviations of smooth and non-smooth 3D shapes in a unified modeling framework. The fabrication of a non-smooth 3D shape is mathematically decomposed into the smooth base shape formation and shape difference realization. Both process knowledge and shape geometries are captured in the learning framework. It provides a new data analytical tool for shape engineering in additive manufacturing and beyond.