Basis of the Lattice Boltzmann Method for Additive Manufacturing
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ORIGINAL PAPER
Basis of the Lattice Boltzmann Method for Additive Manufacturing Alberto Cattenone1 · Simone Morganti2 · Ferdinando Auricchio1 Received: 21 January 2019 / Accepted: 7 June 2019 © CIMNE, Barcelona, Spain 2019
Abstract Additive manufacturing (or 3D printing) is constantly growing as an innovative process for the production of complex-shape components. Among the seven recognized 3D printing technologies, powder bed fusion (PBF) covers a very important role for the production of structurally functional components starting from different metal powder. However, being PBF a production process involving very high thermal gradients, non-negligible deformations and residual stresses may affect the 3D printed component. One of the characterizing aspects of PBF is the evolution of the melt pool and the heat exchange with the surrounding solid powder. In literature many attempts to simulate melt pool evolution have been carried out, however the only approaches leading to interesting results rely on the lattice Boltzmann method. In this work, starting from the Boltzmann’s equation, we derive the lattice Boltzmann equation and we introduce the needed assumptions in order to recover the lattice Boltzmann method. Finally, we apply the lattice Boltzmann method to study some interesting problems related to powder bed fusion process, including droplets wetting, thermal convection and solid–liquid phase change.
1 Introduction Additive manufacturing (AM) technology (also often indicated as 3D printing) is defined by the American Society for Testing and Materials (ASTM) as the process of joining materials to make objects from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies, such as traditional machining [3]. The main advantage of AM is the possibility to manage very complex geometries, reducing the waste of material and energy. Among AM techniques, in this paper, we focus on metal Powder Bed Fusion (PBF). At the beginning of a PBF process, a layer of metal powder is deposited on the building plate, then a high-power heat source is used to melt selectively the powder. Right after the passage of the heat source, * Alberto Cattenone [email protected] Simone Morganti [email protected] Ferdinando Auricchio [email protected] 1
Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
Department of Electrical, Computer, and Biomedical Engineering, University of Pavia, Via Ferrata 5, 27100 Pavia, Italy
2
the melted material starts to cool down until a complete resolidification. Once the heat source is removed, the roller pushes a new layer of material on the top of the previous one, then the process restarts until the final shape of the component is obtained. A distinctive element among different PBF techniques lies in the type of heat source adopted to melt the powder: a laser beam in Selective Laser Melting (SLM), an electron beam in Electron Beam Melting (EBM). PBF is used in several areas, including bio
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