Mathematical modelling of a laser drilling problem

Abstract

Laser Drilling has been around for more than half a decade and has many applications in several industries today. Previous works have used different methods to model the 1D laser drilling problem, such as the Finite Element Method. In recent times, new methods such as various mesh-free methods have been developed to solve not only the 1D laser drilling problem, but 2D and 3D laser drilling problem as well. This work uses the Finite Volume Method coupled with an implicit scheme to perform mathematical modelling of the 1D laser drilling problem, to predict the motion of the moving boundary. The developed model is able to illustrate the effect of 2 parameters, 𝛼 and 𝛽, on the speed of laser drilling, as well as determine the temperature at various points on the metal along the laser drilling axis. In this work, the parameter 𝛼 is defined such that it correlates to the energy supplied by the laser and parameter 𝛽 is definedsuch that it correlates to the vaporization temperature of the metal. It was found that increasing the parameter 𝛼 leads to an increase in the laser drilling speed, while increasing 𝛽 leads to a decrease in the laser drilling speed.