Numerical Modeling of Heat Transfer and Material Flow During Wire-Based Electron-Beam Additive Manufacturing
The development of a mathematical model provides an analysis of heat transfer and metal flow during wire-based electron-beam additive manufacturing described. The procedure for solving the heat equation for the metal in the solid phase and the Navier–Stokes equations in the liquid phase, based on the use of the finite-difference method and the predictor–corrector procedure, is described. An algorithm for numerical approximation of the motion of the free surface of the melt, using the concept of the volume of fluid (VOF) is described. The original method for calculating the effect of surface tension forces, based on the numerical calculation of the surface curvature index, is proposed. The results of simulating the melting of a wire element localized above a substrate made of 316L steel are described. Experiments showed the predominant role of surface tension force in the formation of deposited layer and also that metal’s flow has a laminar structure. These results were obtained by simulating a short-time beam exposure (t = 0.1 s) with a power of 6 kW. Thus, even when the wire and the substrate are exposed with a more intense beam than often used in practice, the metal transfer is not characterized by the formation of intense vortex flows. This can simplify the solution of the problem of additive manufacturing modeling in the future.
KeywordsAdditive manufacturing Electron beam Melting Mathematical model Navier–Stokes equations Heat transfer Fluid flow Surface tension
This work was carried out in National Research University “Moscow Power Engineering Institute”; it was supported by grant from the Russian Science Foundation (Project 17-79-20015).
- 1.Zlenko MA, Nagaytsev MV, Dovbysh VM (2015) Additive technologies in mechanical engineering. Manual for Engineers. Moscow: State Science Center of Russia Federal State Unitary Enterprise “NAMI”Google Scholar
- 2.Gibson I, Rosen D, Stucker B (2015) Additive manufacturing technologies. 3D printing, rapid prototyping, and direct digital manufacturing. Springer Science + Business Media, New YorkGoogle Scholar
- 7.Jhavar S, Jain N (2014) Development of Micro-plasma wire deposition process for layered manufacturing. In: Katalinic B (ed) DAAAM International scientific book, pp 239–256Google Scholar
- 10.Taminger KMB, Hafley RA (2003) Electron beam freeform fabrication: a rapid metal deposition process. In: Proceedings of third annual automotive composites conference. Society of Plastic Engineers, Troy, Michigan, USA, pp 9–10Google Scholar
- 11.Zalameda JN, Burke ER, Hafley RA, Taminger KM et al (2013) Thermal imaging for assessment of electron-beam freeform fabrication (EBF3) additive manufacturing deposits. Proc SPIE 8705(87050M):8Google Scholar
- 12.Taminger KM, Domack CS, Zalameda JN, Taminger BL et al (2016) Thermal imaging of the electron beam freeform fabrication process. In: Proceedings of SPIE Commercial + Scientific Sensing and Imaging. Baltimore, MD, United States, Report No. NF1676L-22574Google Scholar
- 13.Noh WF; Woodward P (1976) SLIC (Simple line interface calculation). In: van de Vooren AI, & Zandbergen PJ (ed) Proceedings of 5th international conference of fluid dynamics. Lecture Notes in Physics 59, pp 330–340Google Scholar
- 15.Patankar SV (1980) Numerical Heat transfer and fluid flow. Series in computational methods in mechanics and thermal sciencesGoogle Scholar
- 17.Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics: the finite volume method. Longman Scientific & TechnicalGoogle Scholar