Laser beam welding analytical model when using wobble strategy

Abstract

This article presents a model for estimating the thermal gradient, bead geometry, and microstructure in the laser welding process when the Wobble strategy is used. This method combines the main feed motion with a secondary high-frequency orbital motion of the laser beam introduced by a galvanometer. The model is developed from an analytical approach and it is particularised to the case of the Wobble strategy through the implementation of two corrective factors. To this end, a two-step analytical model is presented. First, from Carslaw-Jaeger's theory, the thermal field of the upper face of the plates is modelled, allowing the width of the generated weld bead to be determined. The developed model includes the effect of the Wobble strategy as well as the initial transient regime. In a second step, the internal movement of the molten material within the melt-pool is modelled by means of the concepts of monopoles, dipoles, and quadrupoles. Finally, the microstructure calculation is also implemented based on the previously estimated thermal gradient.The model has been experimentally validated in Inconel 718 Nickel-based alloy plates welding, using different process parameters and measuring the resulting bead section and microstructure. Errors below 0.05 mm and 0.3 mm are obtained regarding the bead width and depth, respectively, and differences below 10% are obtained between the estimated cooling rate by the model and experimental measurements. Finally, the estimated values of the Secondary Dendrite Arm Spacing parameters are below 1 μm of error in all tested cases.