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

Abstract

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.

Multiphysics simulation of laser–material interaction during laser powder depositon

“…Both width and depth of fusion reveal a good correlation with R 2 >0.95 with a slight underestimation of z max (slope< 1) and slight overestimation of w max (slope>1). The comparison of the results for different laser powers was Ambient temperature T 0 293 K -Latent heat of fusion L f 247·10 3 J/(kg) [35] Latent heat of vaporization L v 6.25·10 5 J/kg [36] Specific heat, solid C pS 502 J/(kg·K) [31] Specific heat, liquid C pL 620 J/(kg·K) [35] Specific heat, vapor C pv 747.14 J/(kg·K) [31] Density, liquid ρ l 6350 kg/m 3 [28] Density, solid ρ s 7500 kg/m 3 [28] Liquid-state thermal conductivity k l 43 W/(m·K) [37] Solid-state thermal conductivity k s 40 W/(m·K) - [38] obtained for constant laser scanning speed of 2 mm/s and mass flow of 2.5 g/min as shown in Fig. 6.…”

“…Interactions between laser, substrate, and powder as well as powder-substrate interactions have also been implemented [12]. In general, due to the physical complexity of the involved physical phenomena, the early models were simplified by ignoring some of the phenomena, e.g., heat convection [13], melting of the substrate material [14], radiation losses from the liquid pool [15,16], or fluid flow in the liquid pool [17], which did not allow for accurate prediction of the shape of melt pool. In particular, the nonconsideration of the phenomena occurring at the liquid/gas interface should not be omitted as Marangoni flow induced by surface tension gradients, which is known to be largely responsible for the broadening of the top of the melt pool [18,19].…”

Modelling of additive manufacturing processes: a review and classification

“…More specifically, modelling of surface roughness is presented in [78] (analytically) and in [79] (numerically). Modelling of topology and dimensional accuracy takes place in [80][81][82][83][84] using analytical, in [85,86] analytical-numerical, in [17][18][19]32,79,[87][88][89][90][91][92][93][94] numerical, whereas in [95] those issues have been empirically modelled utilizing artificial neural networks (ANN). Modelling of the mechanical properties and microstructure has been conducted in [80,81] using analytical, in [86,96] analyticalnumerical and in [94,[97][98][99][100][101] using numerical approaches.…”

“…Scanner speed, stand-off distance, diameter ratio of the clad to powder stream for Gaussian mode distribution [84] Layer/melt pool dimensions Laser power, powder mass flux [85] Shapes of manufactured structures, thermal loads [86] Local temperature history, track profile, microstructure scale [87] Spreading, cooling and solidification processes of droplets Substrate velocity [88] Thickness of the deposition layer, the depth of the molten pool, the penetration of the substrate or previous deposited layer Scanning speed, powder feeding rate, input electric current [89] Residual stresses, distortion High speed machining post-process [90] Thermal modelling, residual stresses, thermal distortions…”

Melt pool temperature modeling and control for Laser Metal Deposition processes

“…Although there are several process models available in the literature [4][5][6], they are not suitable for online temperature control because of insufficient information for model computation or excessive model complexity. Therefore, an empirical model structure is employed in this paper.…”