Simulation of melt film dynamics in laser fusion cutting using a boundary layer approximation

Abstract

Process inherent instabilities in the dynamics of the thin melt film during laser fusion cutting reduce the quality of the cut surface with regards to mean profile height and angular tolerance. To enhance the process understanding and to identify and evaluate quality improvement measures, a 3D model of the melt film dynamics is developed and applied to experimental results from literature. To cope with the multi-scale character of the mathematical task, model reduction techniques are applied: the underlying transport equations are mapped to a conformal coordinate system and subjected to a scaling analysis. By using a perturbation series, the most significant contributions to the equations of motion are selected. An integral boundary layer approximation reduces the dimension of the numerical task to a two-dimensional problem that can be solved with very low computational effort. The resulting simulation is able to reflect the dynamics at a spatial resolution below Δx≤25μm and a temporal resolution below Δt≤2.5μs within a reasonable calculation time of a few days for a cut length of L=10mm and a cut thickness of a=3mm. Known correlations between process parameters and quality features are reproduced by this simulation. Results show that a concurrent improvement of mean profile height and angular tolerance cannot be obtained by straightforward measures like changing the beam profile from tophat to Gaussian and vice-versa. Future work will be focused on the extension of this model with regards to surface tension and evaporation.