1 Department of Mathematics, Technical University of Denmark2 Applied functional analysis, Department of Mathematics, Technical University of Denmark3 Manufacturing Engineering, Department of Mechanical Engineering, Technical University of Denmark4 Department of Mechanical Engineering, Technical University of Denmark5 Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark6 Risø National Laboratory for Sustainable Energy, Technical University of Denmark7 Department of Wind Energy, Technical University of Denmark
This thesis investigates how to apply optimization methods to numerical models of a friction stir welding process. The work is intended as a proof-of-concept using different methods that are applicable to models of high complexity, possibly with high computational cost, and without the possibility for efficient gradient calculation. Thus, the focus is on surrogate optimization methods with the aim of reducing the number of expensive function evaluations, by using a low-fidelity model together with the highfidelity model to be optimized. The methods used here do not require the user to supply gradient information of the high-fidelity model. The optimization schemes are applied to stationary thermal models of differing complexity of the friction stir welding process. The optimization problems considered are based on optimizing the temperature field in the workpiece by finding optimal translational speed and rotational speed of the tool. Besides the deterministic problem a robust optimization problem is considered in which the effects of uncertain material and optimization parameters are taken into account. The objective is to obtain a desired mean response while reducing the standard deviation of the response. Also an optimization problem based on a microstructure model is solved, allowing the hardness distribution in the plate to be optimized. The use of purely thermal models represents a simplification of the real process; nonetheless, it shows the applicability of the optimization methods considered and forms the basis for optimization of more detailed models. Surrogate models of varying complexity, and similarity with the true model, are applied and the effect on the optimization results is discussed. Furthermore, the thesis contributes to the modelling of the heat transfer between the workpiece and the backingplate by solving an inverse modelling problem in which experimental data and a numerical model are used for determining the contact heat transfer coefficient. Different parametrizations of the spatial distribution of the heat transfer coefficient are studied and discussed, and the optimization problem is formulated as a minimization of the difference between measured and calculated temperatures. The magnitude and distribution of the heat transfer coefficient is determined for the available data.
Friction stir welding; Optimization
Main Research Area:
Stolpe, Mathias, Sigmund, Ole, Hattel, Jesper Henri