Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing
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Stable honeycomb structures and temperature based trajectory optimization for wire‑arc additive manufacturing Martin Bähr1 · Johannes Buhl1 · Georg Radow1 · Johannes Schmidt1 · Markus Bambach1 · Michael Breuß1 · Armin Fügenschuh1 Received: 20 December 2019 / Revised: 3 April 2020 / Accepted: 13 August 2020 © The Author(s) 2020
Abstract We consider two mathematical problems that are connected and occur in the layerwise 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. Keywords Mixed-integer linear programming · Heat transmission · Additive manufacturing · Centroidal Voronoi tesselation · Geometric optimization · Eikonal equation
1 Introduction Additive manufacturing (AM) processes evolved in the past decades into a notable alternative to classical material-removing production techniques. Especially in the aircraft industry their potential of building components on demand, besides the possibility of reducing weight and material loss, is appreciated (Allen 2006).
* Johannes Schmidt johannes.schmidt@b‑tu.de Extended author information available on the last page of the article
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We consider the AM process called wire-arc additive manufacturing (WAAM). It uses the conventional welding technology to print parts with direct energy deposition. A welding torch fed by wire moves over the workpiece. The wire is molten by an electrical arc using high temperatures, and then the material is deposited in droplets in the proposed area. In this way, the workpiece can be built layer-wise or even subpart-by-subpart, if the geometry is more complex (Nguyen et al. 2018). Although it is desired to weld in a continuous path, most structures can not be handled in this way. So eventually movements of the welding torch without welding, called transition moves, are necessary. Since this may lead to more abrasion and reduced quality, it should be avoided if possible. Given the shape of a workpiece, the problems of (i) finding a good inner structure in terms of functionality and stability and (ii) the best path for printing the desired layer arise. These two consecutive subproblems of s
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