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An analytical model for the laser drilling of metals with absorption within the vapour

A mathematical model for the laser drilling of metals is given for the cases of constant and pulsed laser sources. Attenuation of the laser beam within the vapour is considered through an averaged absorption coefficient . The experimentally observed logarithmic dependence of the hole depth on the laser energy is predicted theoretically. A singular perturbation technique is used in order to find solutions valid for different regimes of time, namely pre-vaporization and post-vaporization times. Uniformly valid solutions are found for the one-dimensional analysis of the drilling-front position and speed by matching the inner and outer solutions. First-order approximations for the time-dependent hole profile for the various laser source profiles considered are also found. The model is compared with experimental data in the literature for the drilling speed of copper. An additional set of experiments is specifically carried out to allow comparison with the theoretical hole profiles for titanium. The predictions of the model are found to agree well with the experiments.