Analytical investigations on geometrical influences on laser drilling

An analytical model for laser drilling is proposed which includes three-dimensional heat conduction in a simplified manner. For that purpose, the heating of the curved surface is locally described by that of a spherical cavity with comparable curvature within an infinite medium. Additionally, the absorption 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 is suitable to study the main aspects of deep drilling such as ablation rates 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 curved surface areas will heat much faster or slower than plane ones which, again, results in local changes of drilling velocity. It is shown that the former is particularly of interest for the description of the resulting hole shape 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 compared with those of three-dimensional numerical simulations. It is shown that the simplified assumptions introduced here are, up to some extent, suitable to explain the final surface shapes for blind holes as well as the experimentally observed dependence of ablation rate on hole depth.