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Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing

  • We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this, we employ Lloyd’s algorithm in two different realizations. For computing the incorporated Voronoi tesselation we consider the use of a Delaunay triangulation or alternatively, the eikonal equation. We compare and modify these approaches with the aim of combining their respective advantages. Then in the second task, to find an optimal tool path guaranteeing minimal production time and high quality of the workpiece, a mixed-integer linear programming problem is derived. The model takes thermal conduction and radiation during the process into account and aims to minimize temperature gradients inside the material. Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. The results are compared withWe consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this, we employ Lloyd’s algorithm in two different realizations. For computing the incorporated Voronoi tesselation we consider the use of a Delaunay triangulation or alternatively, the eikonal equation. We compare and modify these approaches with the aim of combining their respective advantages. Then in the second task, to find an optimal tool path guaranteeing minimal production time and high quality of the workpiece, a mixed-integer linear programming problem is derived. The model takes thermal conduction and radiation during the process into account and aims to minimize temperature gradients inside the material. Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. The results are compared with manufactured workpieces.show moreshow less

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Metadaten
Author: Martin Bähr, Johannes BuhlORCiD, Georg RadowGND, Johannes Schmidt, Markus BambachGND, Michael BreußGND, Armin FügenschuhORCiD
DOI:https://doi.org/10.1007/s11081-020-09552-5
ISSN:1573-2924
Title of the source (English):Optimization and Engineering
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2021
Tag:Additive manufacturing; Centroidal Voronoi tesselation; Eikonal equation; Geometric optimization; Heat transmission; Mixed-integer linear programming
Volume/Year:22
Issue number:2
First Page:913
Last Page:974
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Angewandte Mathematik
Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Ingenieurmathematik und Numerik der Optimierung
Fakultät 3 Maschinenbau, Elektro- und Energiesysteme / FG Hybride Fertigung
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