Research Papers

Toward Feedback Control for Additive Manufacturing Processes Via Enriched Analytical Solutions

[+] Author and Article Information
John C. Steuben, Andrew J. Birnbaum, Athanasios P. Iliopoulos

U.S. Naval Research Laboratory,
Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology,
Washington, DC 20375

John G. Michopoulos

Fellow ASME
U.S. Naval Research Laboratory,
Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology,
Washington, DC 20375

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received August 31, 2018; final manuscript received November 20, 2018; published online March 21, 2019. Assoc. Editor: Yan Wang.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Comput. Inf. Sci. Eng 19(3), 031009 (Mar 21, 2019) (8 pages) Paper No: JCISE-18-1225; doi: 10.1115/1.4042105 History: Received August 31, 2018; Revised November 20, 2018

Additive manufacturing (AM) enables the fabrication of objects using successive additions of mass and energy. In this paper, we explore the use of analytic solutions to model the thermal aspects of AM, in an effort to achieve high computational performance and enable “in the loop” use for feedback control of AM processes. It is shown that the utility of existing analytical solutions is limited due to their underlying assumption of a homogeneous semi-infinite domain. These solutions must, therefore, be enriched from their exact form in order to capture the relevant thermal physics associated with AM processes. Such enrichments include the handling of strong nonlinear variations in material properties, finite nonconvex solution domains, behavior of heat sources very near boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) is shown to produce results equivalent to those of numerical methods, which require six orders of magnitude greater computational effort. It is also shown that the EASM's computational performance is sufficient to enable AM process feedback control.

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Grahic Jump Location
Fig. 1

Illustration of AM process and variable definitions

Grahic Jump Location
Fig. 2

Temperature-varying properties of Ti–6Al–4V (UNS R56400) [67,68]. Note the scaling of the vertical axes.

Grahic Jump Location
Fig. 3

Illustration the method of images

Grahic Jump Location
Fig. 4

Illustration of the variation between original and mirror source energy densities

Grahic Jump Location
Fig. 5

Domain for the first test problem, with the heat source path indicated

Grahic Jump Location
Fig. 6

Output of the FEA models versus the exact analytic solution for the first test problem, at t = 0.4 s, for sections at y = 0 (top) and x = 0.005 (bottom)

Grahic Jump Location
Fig. 7

Output of the variable-property FEA models versus the EASM for the first test problem, at t = 0.4 s, for sections at y = 0 (top) and x = 0.005 (bottom)

Grahic Jump Location
Fig. 8

Output of the variable-property FEA versus the EASM for the first test problem, at the origin

Grahic Jump Location
Fig. 9

Domain for the second test problem, with variables illustrated

Grahic Jump Location
Fig. 10

Output of the variable-property FEA model versus the EASM for the second problem, at P

Grahic Jump Location
Fig. 11

Full-field output of the variable-property FEA models versus the final EASM for the second problem, over the subdomain ωvis

Grahic Jump Location
Fig. 12

Full-field output of the mass accretion FEA model (top) versus the EASM (bottom) for the third test problem. Snapshot shortly after the heat source has doubled-back along the major raster direction.

Grahic Jump Location
Fig. 13

Profile generated by the mass accretion EASM model along the section line noted in Fig. 12 for the third test problem



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