Calculating temperature field and single track bead shape in laser cladding with Marangoni flow using Rosenthal's solution
The laser cladding process is mainly determined by the applied powder flux, the laser beam intensity, and the feed rate as well as by the strongly interacting influences of heat flow, free surface shape, and surface tension gradient driven (Marangoni) flow in the melt pool. Convection due to superheating may be responsible for undesired dilution of the bead with the substrate material. A quasi-stationary state temperature field is calculated by means of Rosenthal's solution, assuming some low energy surface shape for the liquid head of a single track bead. This shape is analytically described with free parameters which have to be determined from the powder flux and the feed rate and by fitting iteratively the temperature condition at the border line between the melted part of the bead and the substrate. The Marangoni flow essentially modifies the primary surface heat source density caused by the laser beam and the impinging preheated powder particles and, therefore, has a large influence on heat transfer and temperature gradients in the melt pool, particularly on its surface. Hence the temperature field, the fluid flow velocity at the melt pool surface and the unknown parameters of the bead geometry have to be calculated iteratively in a selfconsistent manner. The simulation is to visualize the origin of various possible failures during the cladding process and of the resulting lacks in the quality of treatment such as insufficient heating of the melt pool, poor bonding between substrate and bead, or too large a dilution of the bead with the substrate material. It is the aim of the present approach to get a tool for applications in manufacturing which is able to calculate the temperature field in laser cladding within a time much shorter than that usually required in computing thermocapillary flow by means of the Finite Element Method.