Authors: Joseph Kubalak, Alfred Wicks, and Chris Williams

J. Mech. Des. May 2021, 143(5): 051701 (15 pages)
https://doi.org/10.1115/1.4048117

Multi-axis (MA) material extrusion (ME) additive manufacturing offers the opportunity to place each deposition path along load paths in 3D space. Such a capability has the potential to address anisotropy concerns presented by conventional (i.e., XY-planar) ME processes, which suffer from poor inter- and intra-layer bonding. With both geometric flexibility and freedom of deposition placement, MA-ME can simultaneously optimize part topology and printing toolpath to maximize part performance relative to any (e.g., 3D) load case. However, there is no existing method for determining the desired 3D material orientations needed for planning deposition paths. This paper introduces a topology optimization (TO) method that simultaneously optimizes for 3D material distribution and orientation. Three parameterizations of the orientation design space are explored: Euler angles, explicit quaternions, and natural quaternions. The parameterizations are compared using two benchmark TO problems and a multi-loaded structure undergoing i) tension and ii) three-point bending. For the evaluated 3D load case, the presented algorithm demonstrates a 38% improvement in compliance over an algorithm that only allowed planar orientation variation. Additionally, natural quaternions reduce computational requirements and consistently produced the most performant designs.

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