Analytical heat conduction modelling for shaped laser beams

Conduction mode laser spot welding and laser spot hardening usually employ Gaussian or top-hat-like beam modes. One main requirement of these techniques is the avoidance of overheating in the centre of the laser-material interaction zone. Process flexibility can be improved by spatially and/or temporally shaping the beam, which can enable higher process quality, robustness or speed. A desired spatial beam shape can be achieved by a suitably designed diffractive optical element. However, the prediction of a suitable beam shape for a particular process can be complex. A simplified analytical heat conduction model has been developed that can rapidly calculate the temperature field and cooling behaviour for almost any spatial and temporal beam shape. The potential and limits of the model are demonstrated and discussed by calculating and analysing temperature profiles for several cases of multi-spot welding.