SIM-AM 2023

Temperature-based Trajectory Optimization with Mixed-integer Programming for Layered Geometries in WAAM

  • Schmidt, Johannes (BTU Cottbus - Senftenberg)
  • Fügenschuh, Armin (BTU Cottbus - Senftenberg)

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In wire-arc additive manufacturing (WAAM), a wire is molten by an electrical or laser arc and deposited droplet-by-droplet to construct the desired workpiece given as a set of two-dimensional layers. The weld source can move freely over a substrate plate, processing each layer, but there is also the possibility of moving without welding. The main issue with this manufacturing technique is the temperature distribution within the workpiece since the large thermal gradients caused by the welding process can cause thermal stress, leading to strain or even cracks. Thus, it is desirable to control the temperature of the workpiece during the process by planning the trajectory of the weld source carefully. We consider the problem of finding a trajectory of the moving weld source for a given two-dimensional layer of arbitrary geometry that maximizes the quality of the part. As a measure of the quality, the part's distortion is used. The resulting optimization problem is formulated as a mixed-integer PDE-constrained problem, consisting of two main parts in its constraints: the computation of a detailed temperature distribution and the generation of a feasible trajectory. Both aspects are coupled by the heat source term in the heat equation. For the first part, the two-dimensional heat equation with a Robin boundary is incorporated, taking heat conduction and thermal radiation into account. It is discretized depending on the underlying geometry using domain decomposition. The latter part is formulated as a Split delivery vehicle routing problem, a special version of a well-known combinatorial optimization problem. Therein, a fleet of homogeneous vehicles must serve a set of customers to satisfy their demand under technical restrictions, while the total demand per customer can be split up to different vehicles. This novel approach allows the computation of a global optimal weld source trajectory regarding different objectives. After linearization, the model is solved using the state-of-the-art numerical solver IBM CPLEX. Its performance is examined by several computational studies and the effect of different objective functions regarding the computation time is discussed.