Analytical Modeling of the Keyhole Including Multiple Reflections for Analysis of the Influence of Different Laser Intensity Distributions on Keyhole Geometry

An analytical model of the keyhole for deep penetration welding is presented. Based on a pressure and energy equilibrium the initial keyhole radii in different depths are calculated depending on different incident beam intensity distributions. Multiple reflections are included by using a ray tracing method in a second step to improve calculation of the keyhole shape. A Gaussian and a top hat beam profile are used for evaluation and show similar resulting keyhole geometries and different pressure gradients.