Abstract
Common goals of modern production processes are precision and efficiency. Typically, they are conflicting and cannot be optimized at the same time. Multi-objective optimization methods are able to compute a set of good parameters, from which a decision maker can make a choice for practical situations. For complex processes, the use of physical experiments and/or extensive process simulations can be too costly or even unfeasible, so the use of surrogate models based on few simulations is a good alternative.In this work, we present an integrated framework to find optimal process parameters for a laser-based material accumulation process (thermal upsetting) using a combination of meta-heuristic optimization models and finite element simulations. In order to effectively simulate the coupled system of heat equation with solid-liquid phase transitions and melt flow with capillary free surface in three space dimensions for a wide range of process parameters, we introduce a new coupled numerical 3d finite element method. We use a multi-objective optimization method based on surrogate models. Thus, with only few direct simulations necessary, we are able to select Pareto sets of process parameters which can be used to optimize three or six different performance measures.
Highlights
Modern production technologies follow a strategy of continuous improvement and, as part of it, producers permanently strive to deliver components with high quality at the lowest possible cost
The combination of optimization methods with computer simulations where simulations are used to transform input parameters into the relevant performance measures (PMs) is an actual engineering need [19, 24, 27, 29]. This requires evaluating optimization functionals on a large amount of candidate solutions, making it a demanding computational task when the simulations are numerically expensive [16]. This is the case for simulating laser-based material accumulation processes, for which we have developed a suitable new 3d finite element method (FEM), presented and analyzed in detail in [18]
Starting with a general description of our simulation strategy based on physical models for the solid-liquid phase change and the corresponding changes in the geometrical shape of a three-dimensional domain, we presented the details of a new combination of numerical methods to conduct a FEM simulation solving for temperature, evolution of solid-liquid interphase, and the moving boundaries of the time dependent 3d domain, that is capable to deal with various geometric and topological changes which may happen due to a large range of process parameters
Summary
Modern production technologies follow a strategy of continuous improvement and, as part of it, producers permanently strive to deliver components with high quality at the lowest possible cost. For a 2d (or rotationally symmetric) situation with clearly separated melting and solidification times, a direct formulation and discretization of the Stefan condition with a corresponding ALE-formulation could be used during melting [18], but in 3d the situation is definitely more complicated, as an ALE formulation would technically be much more involved, and melting/solidification times are typically not separated, so switching between different methods is not possible The latter is especially the case when process parameters are varied in a wide range, as it will be needed for the solution of our optimization problem. The approximation obtained with this design performs very well when the optimization functional does not have strong oscillations and even better when it is a smooth functional
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