# A Numerical Investigation of Laser Beam Welding of Stainless Steel Sheets with a Gap
## 3 Beam Shape Optimization  
Using a sufficiently coarse mesh is a possibility for reducing computational costs and thus getting results faster, which is of paramount importance when applying any CFD model to a real-world application scenario and using it for optimizing many process parameters. To avoid unphysical results due to the coarseness of the mesh, careful calibration and validation have been performed (see Section 2.2). In the course of the CUSTODIAN project, a methodology was developed to increase the quality of a welded seam proposed by an industry partner. The quality requirements set for the welded seams are summarized in Table 2 and schematically illustrated in Figure 8.  
In this Section, an optimization approach is presented, where the addition of a secondary beam and its effect on the final weld bead geometry are studied. The advantages of a dual beam approach and the effect on material properties and quality criteria have \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value Range** & **Reference in Figure 8** \\ \hline total penetration & \textgreater{}50\% of bead length & - \\ min. weld width at interface & \textgreater{}0.67 mm & (a) \\ lack of penetration & \textless{}0.2 mm & (b) \\ incompletely filled groove & \textless{}0.2 mm & (c) \\ excessive penetration & \textless{}0.4 mm & (d) \\ excess weld metal & \textless{}0.4 mm & (e) \\ undercut & \textless{}0.1 mm & (f) \\ root concavity & \textless{}0.2 mm & (g) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Weld quality requirements as defined by the industry partner. Figure 8: Quality requirements. Sub-Figures (**a–g**) are described in detail in Table 2.  
been numerically investigated using commercial CFD software by [PERSON] et al. [31]. One advantage of using a secondary beam superimposed on the primary beam is the possibility of in-situ pre-heating or post-heating without the need for additional scans. The effects of laser based pre-heating and post-heating have previously been investigated by [PERSON] et al. [32]. The starting point was an elliptical beam that covered the whole of the melt pool with the aim of introducing more energy and thus fixing some of the issues. In the course of the project, this shape was changed to a rectangle due to its easier technical feasibility within the chosen beam shaping approach. Different energy distributions, sizes (length and width of rectangle) and positions relative to the primary beam (offset) have been tested using the simulation model to iteratively find the optimal beam shape for each experimental condition. At first, the influences of the parameters on the weld seam were investigated by testing some extreme values of each relevant parameter. The insights thus gained were used to iteratively tune the secondary beam parameters to fulfill all quality criteria listed in Table 2. The final improvements were reached through the use of a secondary beam with the aforementioned rectangular shape with varying parameters for width, length and power density, depending on the experimental conditions. As post-heating did not seem to be strongly correlated with the resulting weld bead geometry, the secondary beam was shifted, so that the optical axis of the primary beam coincided with the tailing edge of the secondary beam, while maintaining symmetry transversely to the scan direction. For the purpose of improving the weld bead quality, transient effects on very small scales were neglected and thus the coarse mesh previously adopted in the calibration was employed here. It was possible to simulate a process like those described in Section 2.2 by including an optimized secondary beam for under 12 h in an off-the-shelf \"AMD Ryzen 7 2700\" eight-core processor. This allowed for testing many different secondary beam shapes and sizes in differing conditions--varying scan speed, laser power and gap widths--in a fairly short amount of time.