OPTILAS: Numerical Optimization as a Key Tool for the Improvement of Advanced Multi-Beam Laser Welding Techniques

Multi-beam laser welding is an advanced welding technique which can successfully prevent hot cracking, cf. [3], [4]. In order to guarantee that this technique prevents the initiation of hot cracks in the solid-liquid region, it is important to choose the positions, sizes, and powers of the additional heat sources suitably, e.g. optimally if an appropriate objective function can be established. In case of inappropriate choices for these parameters, hot cracking can even be enhanced. Until now these quantities are generally chosen by trial and error. This paper aims towards the simulation and optimization of multi-beam laser welding in order to demonstrate the potential of numerical optimization for the further improvement of this welding technique. For this purpose a constrained nonlinear programming problem is formulated which provides a solution for the hot cracking problem by minimizing the accumulated transverse strain, i.e. the opening displacement, in the solid-liquid region. This approach is based on the so-called strip expansion technique, cf. [6]. For the objective function investigated in this paper it is sufficient to take into account a stationary temperature field in a moving reference frame. It is described by a partial differential equation for which it is possible to find a semi-analytical solution in terms of Bessel functions. Their computation is very time consuming and should be performed in parallel. If an optimization of the process is desired the amount of computation increases even more. This is due to the fact that, in addition to the solution of the partial differential equation, certain sensitivities must be computed in each loop of the optimization iteration, i.e., partial derivatives of the simulation output with respect to the optimization parameters.