0
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

Mem. ASME
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Deckard, C. R. , and Beaman, J. J. , 1987, “ Recent Advances in Selective Laser Sintering,” 14th Conference on Production Research and Technology, Ann Arbor, MI, Oct. 6, pp. 447–452.
Gibson, I. , and Shi, D. , 1997, “ Material Properties and Fabrication Parameters in Selective Laser Sintering Process,” Rapid Prototyping J., 3(4), pp. 129–136. [CrossRef]
Agarwala, M. , Bourell, D. , Beaman, J. , Marcus, H. , and Barlow, J. , 1995, “ Direct Selective Laser Sintering of Metals,” Rapid Prototyping J., 1(1), pp. 26–36. [CrossRef]
Simchi, A. , 2006, “ Direct Laser Sintering of Metal Powders: Mechanism, Kinetics and Microstructural Features,” Mater. Sci. Eng. A, 428(1–2), pp. 148–158. [CrossRef]
Rombouts, M. , Kruth, J. P. , Froyen, L. , and Mercelis, P. , 2006, “ Fundamentals of Selective Laser Melting of Alloyed Steel Powders,” CIRP Ann.-Manuf. Technol., 55(1), pp. 187–192. [CrossRef]
Mumtaz, K. A. , Erasenthiran, P. , and Hopkinson, N. , 2008, “ High Density Selective Laser Melting of Waspaloy®,” J. Mater. Process. Technol., 195(1–3), pp. 77–87. [CrossRef]
Murr, L. E. , Gaytan, S. M. , Ramirez, D. A. , Martinez, E. , Hernandez, J. , Amato, K. N. , Shindo, P. W. , Medina, F. R. , and Wicker, R. B. , 2012, “ Metal Fabrication by Additive Manufacturing Using Laser and Electron Beam Melting Technologies,” J. Mater. Sci. Technol., 28(1), pp. 1–14. [CrossRef]
Cormier, D. , Harrysson, O. , and West, H. , 2004, “ Characterization of H13 Steel Produced Via Electron Beam Melting,” Rapid Prototyping J., 10(1), pp. 35–41. [CrossRef]
Lewis, G. K. , and Schlienger, E. , 2000, “ Practical Considerations and Capabilities for Laser Assisted Direct Metal Deposition,” Mater. Des., 21(4), pp. 417–423. [CrossRef]
Mazumder, J. , Dutta, D. , Kikuchi, N. , and Ghosh, A. , 2000, “ Closed Loop Direct Metal Deposition: Art to Part,” Opt. Lasers Eng., 34(4–6), pp. 397–414. [CrossRef]
Bandyopadhyay, A. , Krishna, B. V. , Xue, W. , and Bose, S. , 2009, “ Application of Laser Engineered Net Shaping (LENS) to Manufacture Porous and Functionally Graded Structures for Load Bearing Implants,” J. Mater. Sci.: Mater. Med., 20(Suppl. 1), pp. 29–34.
Griffith, M. L. , Keicher, D. M. , Atwood, C. L. , Romero, J. A. , Smugeresky, J. E. , Harwell, L. D. , and Greene, D. L. , 1996, “ Free Form Fabrication of Metallic Components Using Laser Engineered Net Shaping (LENS),” Solid Freeform Fabrication Symposium, Austin, TX, Aug. 12, pp. 125–131.
Frazier, W. E. , 2014, “ Metal Additive Manufacturing: A Review,” J. Mater. Eng. Perform., 23(6), pp. 1917–1928. [CrossRef]
Singh, S. , Ramakrishna, S. , and Singh, R. , 2017, “ Material Issues in Additive Manufacturing: A Review,” J. Manuf. Process., 25, pp. 185–200. [CrossRef]
Cooper, K. P. , and Wachter, R. F. , 2014, “ Cyber-Enabled Manufacturing Systems for Additive Manufacturing,” Rapid Prototyping J., 20(5), pp. 355–359. [CrossRef]
Gibson, I. , Rosen, D. , and Stucker, B. , 2015, “ Software Issues for Additive Manufacturing,” Additive Manufacturing Technologies SE–15, Springer, New York, pp. 351–374.
Gao, W. , Zhang, Y. , Ramanujan, D. , Ramani, K. , Chen, Y. , Williams, C. B. , Wang, C. C. , Shin, Y. C. , Zhang, S. , and Zavattieri, P. D. , 2015, “ The Status, Challenges, and Future of Additive Manufacturing in Engineering,” Comput. Aided Des., 69, pp. 65–89. [CrossRef]
Mani, M. , Lane, B. , Feng, S. , Feng, S. , Moylan, S. , and Fesperman, R. , 2015, “ Measurement Science Needs for Real-Time Control of Additive Manufacturing Powder Bed Fusion Processes,” National Institute of Standards and Technology, Gaithersburg, MD, Report No. NISTIR 8036. https://www.nist.gov/publications/measurement-science-needs-real-time-control-additive-manufacturing-powder-bed-fusion
Jacobs, P. F. , 2002, “ A Brief History of Rapid Prototyping & Manufacturing: The Growth Years,” International Conference on Metal Powder Deposition for Rapid Manufacturing, San Antonio, TX, Nov. 3, pp. 5–8.
Ruan, J. , Sparks, T. E. , Fan, Z. , Stroble, J. K. , Panackal, A. , and Liou, F. , 2006, “ A Review of Layer Based Manufacturing Processes for Metals,” Solid Freeform Fabrication Proceedings, D. L. Bourell , R. H. Crawford , J. J. Beaman , K. L. Wood , and H. Marcus , eds., University of Texas, Austin, TX, pp. 233–245.
Toyserkani, E. , Khajepour, A. , and Corbin, S. , 2004, Laser Cladding, CRC Press, Boca Raton, FL.
Zhang, H.-O. , Kong, F.-R. , Wang, G.-L. , and Zeng, L.-F. , 2006, “ Numerical Simulation of Multiphase Transient Field During Plasma Deposition Manufacturing,” J. Appl. Phys., 100(12), p. 123522. [CrossRef]
Chen, T. , and Zhang, Y. , 2006, “ Three-Dimensional Modeling of Selective Laser Sintering of Two-Component Metal Powder Layers,” ASME J. Manuf. Sci. Eng., 128(1), pp. 299–306. [CrossRef]
Alimardani, M. , Toyserkani, E. , and Huissoon, J. P. , 2007, “ Three-Dimensional Numerical Approach for Geometrical Prediction of Multilayer Laser Solid Freeform Fabrication Process,” J. Laser Appl., 19(1), p. 14. [CrossRef]
Lambrakos, S. , and Cooper, K. , 2008, “ An Algorithm for Inverse Modeling of Layer-by-Layer Deposition Processes,” J. Mater. Eng. Perform., 18(3), pp. 221–230. [CrossRef]
Khairallah, S. A. , Anderson, A. T. , Rubenchik, A. , and King, W. E. , 2016, “ Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Spatter, and Denudation Zones,” Acta Mater., 108, pp. 36–45. [CrossRef]
Michopoulos, J. G. , Lambrakos, S. , and Iliopoulos, A. , 2014, “ Multiphysics Challenges for Controlling Layered Manufacturing Processes Targeting Thermomechanical Performance,” ASME Paper No. DETC2014-35170.
Birnbaum, A. , Michopoulos, J. G. , and Iliopoulos, A. P. , 2016, “ Simulating Geometric and Thermal Aspects of Powder-Jet Laser Additive Manufacturing,” ASME Paper No. DETC2016-59644.
Schoinochoritis, B. , Chantzis, D. , and Salonitis, K. , 2017, “ Simulation of Metallic Powder Bed Additive Manufacturing Processes With the Finite Element Method: A Critical Review,” Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf., 231(1), pp. 96–117. [CrossRef]
Denlinger, E. R. , Heigel, J. C. , and Michaleris, P. , 2014, “ Residual Stress and Distortion Modeling of Electron Beam Direct Manufacturing Ti–6Al–4V,” Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf., 229(10), pp. 1803–1813.
Denlinger, E. R. , Irwin, J. , and Michaleris, P. , 2014, “ Thermomechanical Modeling of Additive Manufacturing Large Parts,” ASME J. Manuf. Sci. Eng., 136(6), p. 061007. [CrossRef]
Heigel, J. , Michaleris, P. , and Reutzel, E. , 2014, “ Thermo-Mechanical Model Development and Validation of Directed Energy Deposition Additive Manufacturing of Ti–6Al–4V,” Addit. Manuf., 5, pp. 9–9.
Martukanitz, R. , Michaleris, P. , Palmer, T. , DebRoy, T. , Liu, Z.-K. , Otis, R. , Heo, T. W. , and Chen, L.-Q. , 2014, “ Toward an Integrated Computational System for Describing the Additive Manufacturing Process for Metallic Materials,” Addit. Manuf., 1–4, pp. 52–63. [CrossRef]
Michaleris, P. , 2014, “ Modeling Metal Deposition in Heat Transfer Analyses of Additive Manufacturing Processes,” Finite Elem. Anal. Des., 86, pp. 51–60. [CrossRef]
Witherell, P. , Feng, S. , Simpson, T. W. , Saint John, D. B. , Michaleris, P. , Liu, Z.-K. , Chen, L.-Q. , and Martukanitz, R. , 2014, “ Toward Metamodels for Composable and Reusable Additive Manufacturing Process Models,” ASME J. Manuf. Sci. Eng., 136(6), p. 061025. [CrossRef]
Denlinger, E. R. , Heigel, J. C. , Michaleris, P. , and Palmer, T. , 2015, “ Effect of Inter-Layer Dwell Time on Distortion and Residual Stress in Additive Manufacturing of Titanium and Nickel Alloys,” J. Mater. Process. Technol., 215, pp. 123–131. [CrossRef]
Pal, D. , Patil, N. , Nikoukar, M. , Zeng, K. , Kutty, K. H. , and Stucker, E. B. , 2013, “ An Integrated to Cyber-Enabled Additive Manufacturing Using Physics Based Coupled Multi-Scale Process Modeling,” In Solid Freeform Fabrication Proceedings, Austin, TX, Aug. 12, pp. 12–14.
Pal, D. , Patil, N. , Zeng, K. , Teng, C. , Xu, S. , Sublette, T. , and Stucker, B. , 2014, “ Enhancing Simulations of Additive Manufacturing Processes Using Spatiotemporal Multiscaling,” Solid Freeform Fabrication Symposium, Austin, TX, Aug. 4, pp. 1213–1228.
Francois, M. M. , Sun, A. , King, W. E. , Henson, N. J. , Tourret, D. , Bronkhorst, C. A. , Carlson, N. N. , Newman, C. K. , Haut, T. S. , Bakosi, J. , Gibbs, J. W. , Livescu, V. , Vander Wiel, S. A. , Clarke, A. J. , Schraad, M. W. , Blacker, T. , Lim, H. , Rogers, T. , Owen, S. , Abdeljawad, F. , Madison, J. , Anderson, A. T. , Fattebert, J-L. , Ferencz, R. M. , Hodge, N. E. , Khairallah, S. A. , Walton, O. , 2017, “ Modeling of Additive Manufacturing Processes for Metals: Challenges and Opportunities,” Curr. Opin. Solid State Mater. Sci., 21(1), pp. 198–206
Parteli, E. J. , and Pöschel, T. , 2016, “ Particle-Based Simulation of Powder Application in Additive Manufacturing,” Powder Technol., 288, pp. 96–102. [CrossRef]
Haeri, S., Wang, Y., Ghita, O., and Sun, J., 2017, “Discrete Element Simulation and Experimental Study of Powder Spreading Process in Additive Manufacturing,” Power Technol., 306, pp. 45–54.
Zohdi, T. I. , 2014, “ Additive Particle Deposition and Selective Laser Processing a Computational Manufacturing Framework,” Comput. Mech., 54(1), pp. 171–191. [CrossRef]
Zohdi, T. , 2014, “ A Direct Particle-Based Computational Framework for Electrically Enhanced Thermo-Mechanical Sintering of Powdered Materials,” Math. Mech. Solids, 19(1), pp. 93–113. [CrossRef]
Zohdi, T. I. , 2015, “ Modeling and Simulation of Cooling-Induced Residual Stresses in Heated Particulate Mixture Depositions in Additive Manufacturing,” Comput. Mech., 56(4), pp. 613–630. [CrossRef]
Zohdi, T. I. , 2015, “ Modeling and Simulation of Laser Processing of Particulate-Functionalized Materials,” Arch. Comput. Methods Eng., 24(1), pp. 89–113 https://doi.org/10.1007/s11831-015-9160-1
Steuben, J. C. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2016, “ Discrete Element Modeling of Particle-Based Additive Manufacturing Processes,” Comput. Methods Appl. Mech. Eng., 305, pp. 537–561. [CrossRef]
Steuben, J. , Iliopoulos, A. , and J, M. , 2016, “ On Multiphysics Discrete Element Modeling of Powder-Based Additive Manufacturing,” ASME Paper No. DETC2016-59634.
Steuben, J. C. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2017, “ Recent Developments of the Multiphysics Discrete Element Method for Additive Manufacturing Modeling and Simulation,” ASME Paper No. DETC2017-67597.
Hu, D. , and Kovacevic, R. , 2003, “ Sensing, Modeling and Control for Laser-Based Additive Manufacturing,” Int. J. Mach. Tools Manuf., 43(1), pp. 51–60. [CrossRef]
Craeghs, T. , Bechmann, F. , Berumen, S. , and Kruth, J.-P. , 2010, “ Feedback Control of Layerwise Laser Melting Using Optical Sensors,” Phys. Procedia, 5, pp. 505–514. [CrossRef]
Kruth, J.-P. , Mercelis, P. , Van Vaerenbergh, J. , and Craeghs, T. , 2007, “ Feedback Control of Selective Laser Melting,” Third International Conference on Advanced Research in Virtual and Rapid Prototyping, Leiria, Portugal, Sept. 24, pp. 521–527. https://limo.libis.be/primo-explore/fulldisplay?docid=LIRIAS66104&context=L&vid=Lirias&search_scope=Lirias&tab=default_tab&lang=en_US&fromSitemap=1
Everton, S. K. , Hirsch, M. , Stravroulakis, P. , Leach, R. K. , and Clare, A. T. , 2016, “ Review of In-Situ Process Monitoring and In-Situ Metrology for Metal Additive Manufacturing,” Mater. Des., 95, pp. 431–445. [CrossRef]
Steuben, J. C. , Birnbaum, A. J. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2018, “ Enriched Analytical Solutions for Additive Manufacturing Modeling and Simulation,” ASME Paper No. DETC2018-86011.
Carslaw, H. , and Jaeger, J. , 1986, Conduction of Heat in Solids, Oxford Science Publications, Oxford, UK.
Rosenthal, D. , 1946, “ The Theory of Moving Sources of Heat and Its Application of Metal Treatments,” Trans. ASME, 68, pp. 849–866.
Pinkerton, A. J. , and Li, L. , 2004, “ The Development of Temperature Fields and Powder Flow During Laser Direct Metal Deposition Wall Growth,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 218(5), pp. 531–541. [CrossRef]
Pinkerton, A. J. , and Li, L. , 2004, “ The Significance of Deposition Point Standoff Variations in Multiple-Layer Coaxial Laser Cladding (Coaxial Cladding Standoff Effects),” Int. J. Mach. Tools Manuf., 44(6), pp. 573–584. [CrossRef]
Soylemez, E. , Beuth, J. L. , and Tamingerf, K. , 2010, “ Controlling Melt Pool Dimensions Over a Wide Range of Material Deposition Rates in Electron Beam Additive Manufacturing,” 21st Solid Freeform Fabrication Symposium, Austin, TX, Aug. 9, pp. 9–11.
Cline, H. , and Anthony, T. , 1977, “ Heat Treating and Melting Material With a Scanning Laser or Electron Beam,” J. Appl. Phys., 48(9), pp. 3895–3900. [CrossRef]
Eagar, T. , and Tsai, N. , 1983, “ Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355.
Woodard, P. R. , and Dryden, J. , 1999, “ Thermal Analysis of a Laser Pulse for Discrete Spot Surface Transformation Hardening,” J. Appl. Phys., 85(5), pp. 2488–2496. [CrossRef]
Kaplan, A. F. , 1997, “ Surface Processing With Non-Gaussian Beams,” Appl. Phys. Lett., 70(2), pp. 264–266. [CrossRef]
Mackwood, A. , and Crafer, R. , 2005, “ Thermal Modelling of Laser Welding and Related Processes: A Literature Review,” Opt. Laser Technol., 37(2), pp. 99–115. [CrossRef]
Sundqvist, J. , Kaplan, A. , Shachaf, L. , and Kong, C. , 2017, “ Analytical Heat Conduction Modelling for Shaped Laser Beams,” J. Mater. Process. Technol., 247, pp. 48–54. [CrossRef]
Quintino, L., Costa, A., Miranda, R., Yapp, D., Kumar, V., Kong, C. J., 2007, “ Welding With High Power Fiber Lasers—A Preliminary Study,” Mater. Des., 28(4), pp. 1231–1237. [CrossRef]
Lambrakos, S. , 2013, “ Inverse Thermal Analysis of 304l Stainless Steel Laser Welds,” J. Mater. Eng. Perform., 22(8), pp. 2141–2147. [CrossRef]
Davis, J. , 1998, Metals Handbook Desk Edition (75th Anniversary ASM Handbooks), 2nd ed., Taylor & Francis, Milton Park, UK.
Li, J. J. , Johnson, W. L. , and Rhim, W.-K. , 2006, “ Thermal Expansion of Liquid Ti–6Al–4V Measured by Electrostatic Levitation,” Appl. Phys. Lett., 89(11), p. 111913. [CrossRef]
Veldman, D. , Fey, R. , Zwart, H. , van de Wal, M. , van den Boom, J. , and Nijmeijer, H. , 2018, “ Semi-Analytic Approximation of the Temperature Field Resulting From Moving Heat Loads,” Int. J. Heat Mass Transfer, 122, pp. 128–137. [CrossRef]
Toyserkani, E. , Khajepour, A. , and Corbin, S. , 2003, “ Three-Dimensional Finite Element Modeling of Laser Cladding by Powder Injection: Effects of Powder Feed rate and Travel Speed on the Process,” J. Laser Appl., 15(3), pp. 153–160. [CrossRef]
Michopoulos, J. G. , Iliopoulos, A. P. , Steuben, J. C. , Birnbaum, A. J. , and Lambrakos, S. G. , 2018, “ On the Multiphysics Modeling Challenges for Metal Additive Manufacturing Processes,” Addit. Manuf., 22, pp. 784–799. [CrossRef]

Figures

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

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In