Analytical investigations on geometrical influences on laser drilling

An analytical model for laser drilling is proposed which includes three-dim ensional heat conduction in a simplified manner. For that purpose, the heat ing of the curved surface is locally described by that of a spherical cavit y with comparable curvature within an infinite medium. Additionally, the ab sorption of laser radiation on the inclined side wall is taken into account . Using these components, it is possible to calculate the evolution of the hole shape from pulse-to-pulse in an iterative way. Therefore, this model i s suitable to study the main aspects of deep drilling such as ablation rate s and hole shapes without the disadvantage of long computational times. As a drilled hole deepens and the walls become steeper, its surface area grows and, thereby, in principle the absorbed intensity drops. This can lead to a considerable reduction of ablation rate. At the same time, extremely curv ed surface areas will heat much faster or slower than plane ones which, aga in, results in local changes of drilling velocity. It is shown that the for mer is particularly of interest for the description of the resulting hole s hape while the latter has a considerable influence on the ablation velocity at the tip of the hole. To verify the analytical model, its results are co mpared with those of three-dimensional numerical simulations. It is shown t hat the simplified assumptions introduced here are, up to some extent, suit able to explain the final surface shapes for blind holes as well as the exp erimentally observed dependence of ablation rate on hole depth.