Modelling of heat and mass transfer in the laser cladding during direct metal deposition

A physical and mathematical model has been proposed for computing the thermal state and shape of the individual deposited track at the laser powder cladding. A three-dimensional statement of the two-phase problem of Stefan type with curved moving boundaries is considered. One of the boundaries is the melting-crystallization boundary, and the other is the boundary of the deposited layer, where the conservation laws are written from the condition of the inflow of the additional mass and energy. To describe the track shape the equation of kinematic compatibility of the points of a surface is used, the motion of which occurs at the expense of the mass of powder particles supplied to the radiation spot. An explicit finite difference scheme on a rectangular nonuniform grid is used for numerical solution of equations. The computations are carried out by through computation without an explicit identification of curved boundaries by using a modification of the immersed boundary method. The computational results are presented for the thermal state and the shape of the surface of the forming individual track depending on physical parameters: the substrate initial temperature, laser radiation intensity, scanning speed, powder feeding rate, etc.