Modelling the keyhole profile in laser welding through energy balance including the local contribution of multiple reflections through the plasma by ray tracing

Several numerical and analytical methods were developed over the years in the attempt to properly model the keyhole laser welding. Among them, semi-analytical models revealed to be effective and efficient for the calculation of the keyhole geometry. They can take into account the plasma absorption mechanism through inverse Bremsstrahlung, as well as the effects related to the multiple reflection phenomena that the laser beam rays experience in the keyhole cavity, with relatively low computational costs. However, multiple reflections contribution was usually calculated through a very simple average estimation. In this work, a semi-analytical model that employs an iterative ray-tracing technique for the calculation of multiple reflections inside the keyhole is described. The approach can take precisely into account the absorption mechanism for each laser beam ray along its segmented path in the keyhole considering also the commonly neglected-upward oriented reflections. The energy transferred to the molten material due to all the rays hitting the keyhole wall is locally considered for the energy balance and the keyhole is recalculated iteratively until the profile does not significantly deviate from the previous one. The laser beam attenuation due to the plasma plume that develops above the keyhole is also considered, for a CO 2 -laser, investigating different plume height values. A numerical-experimental comparison considering two different laser welding setups is then performed. The results show that both the upward-oriented reflections and the plasma plume damping have noticeable effects on the cavity shape and depth, while the numerical-experimental comparison reveals that the model is able to predict keyhole depths, especially for welding configurations with higher heat input values. • Laser welding keyhole is profiled through a semi-analytical energy balance model. • Upward and downward multiple reflections and plasma damping effects are considered. • Commonly neglected upward reflections have appreciable effects on keyhole geometry. • Plasma plume height can sizably modify the keyhole profile for CO 2 -lasers. • Numerical-experimental comparison shows a properly keyhole depths model prediction.