期刊
OPTIMIZATION AND ENGINEERING
卷 22, 期 2, 页码 913-974出版社
SPRINGER
DOI: 10.1007/s11081-020-09552-5
关键词
Mixed-integer linear programming; Heat transmission; Additive manufacturing; Centroidal Voronoi tesselation; Geometric optimization; Eikonal equation
类别
资金
- Projekt DEAL
This study focuses on two mathematical problems related to the layer-wise production process of a workpiece. The first problem involves automatically constructing a honeycomb structure using Lloyd's algorithm and Voronoi tessellation. The second problem is to find an optimal tool path through mixed-integer linear programming to ensure minimal production time and high quality of the workpiece.
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 with manufactured workpieces.
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