CW LASER MACHINING OF HARD CERAMICS .2. EFFECTS OF MULTIPLE REFLECTIONS

Beam guiding effects during laser machining of ceramics due to multiple reflections in the groove are analyzed theoretically for two extreme cases-purely specular and purely diffuse reflections. Specular reflections are valid for materials that have a smooth surface during laser evaporation (small optical roughness as compared to the laser wavelength). For such cases the material surface is divided into a number of rectangular patches using a bicubic surface representation method. The net radiative flux for these patch elements is obtained by ray tracing methods. The resulting radiative flux due to specular reflections is combined with the three-dimensional conduction equation governing conduction losses into the medium, and the resulting groove shape and depth are found through an iterative procedure. Diffuse reflections are valid for materials that have a very rough surface during material removal. To address beam coupling due to diffuse reflections, irradiation calculations employing view factor theory were combined with the three-dimensional conduction model. Considering multiple reflections results in an increased effective absorptivity and deeper grooves, accompanied by a flatter profile near the centerline and steeper slopes in the other parts of the groove cross-section. For the tested set of parameters, material removal rates are increased by up to 40% by specular reflections, and up to 70% by diffuse reflections. Experiments with hot-pressed silicon nitride ceramic showed increased beam coupling for deeper grooves (high power and/or slow scanning speeds) as predicted by considering multiple reflections. The agreement between theoretical calculations and experimental data for material removal rate and groove shape was good, if multiple reflections were assumed to be diffuse.