Modelling the geometry of a moving laser melt pool and deposition track via energy and mass balances

The additive manufacturing technique of laser direct metal deposition allows multiple tracks of full density metallic material to be built to form complex parts for rapid tooling and manufacture. Practical results and theoretical models have shown that the geometries of the tracks are governed by multiple factors. Original work with single layer cladding identified three basic clad profiles but, so far, models of multiple layer, powder-feed deposition have been based on only two of them. At higher powder mass flow rates, experimental results have shown that a layer's width can become greater than the melt pool width at the substrate surface, but previous analytical models have not been able to accommodate this. In this paper, a model based on this third profile is established and experimentally verified. The model concentrates on mathematical analysis of the melt pool and establishes mass and energy balances based on one-dimensional heat conduction to the substrate. Deposition track limits are considered as arcs of circles rather than of ellipses, as used in most established models, reflecting the dominance of surface tension forces in the melt pool, and expressions for elongation of the melt pool with increasing traverse speed are incorporated. Trends in layer width and height with major process parameters are captured and predicted layer dimensions correspond well to the experimental values.