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Research Papers

Physics-Based Multivariable Modeling and Feedback Linearization Control of Melt-Pool Geometry and Temperature in Directed Energy Deposition

[+] Author and Article Information
Qian Wang

Mechanical and Nuclear Engineering,
The Pennsylvania State University,
State College, PA 16802
e-mail: quw6@psu.edu

Jianyi Li

Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: jxl1080@psu.edu

Michael Gouge

Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: mfg161@psu.edu

Abdalla R. Nassar

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802
e-mail: arn5000@arl.psu.edu

Panagiotis (Pan) Michaleris

Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802;
Pan Computing LLC,
200 Innovation Boulevard,
State College, PA 16803
e-mails: pxm32@psu.edu; pan.michaleris@pancomputing.com

Edward W. Reutzel

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802
e-mail: ewr101@arl.psu.edu

1Corresponding author.

Manuscript received December 18, 2015; final manuscript received July 12, 2016; published online September 21, 2016. Assoc. Editor: Z. J. Pei.

J. Manuf. Sci. Eng 139(2), 021013 (Sep 21, 2016) (12 pages) Paper No: MANU-15-1671; doi: 10.1115/1.4034304 History: Received December 18, 2015; Revised July 12, 2016

There has been continuing effort in developing analytical, numerical, and empirical models of laser-based additive manufacturing (AM) processes in the literature. However, advanced physics-based models that can be directly used for feedback control design, i.e., control-oriented models, are severely lacking. In this paper, we develop a physics-based multivariable model for directed energy deposition. One important difference between our model from the existing work lies in a novel parameterization of the material transfer rate in the deposition as a function of the process operating parameters. Such parameterization allows an improved characterization of the steady-state melt-pool geometry compared to the existing lumped-parameter models. Predictions of melt-pool geometry and temperature from our model are validated using experimental data obtained from deposition of Ti-6AL-4V and deposition of Inconel® 718 on a laser engineering net shaping (LENS) AM process and finite-element analysis. Then based on this multivariable model, we design a nonlinear multi-input multi-output (MIMO) control, specifically a feedback linearization (FL) control, to track both melt-pool height and temperature reference trajectories using laser power and laser scan speed.

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Figures

Grahic Jump Location
Fig. 1

Sample refined mesh: (a) isometric view and (b) top view

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Fig. 2

Schematic plot of the LENS process used to generate experimental data for model validation

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Fig. 5

Inconel® 718: Our model prediction versus experiment measurements of melt-pool geometry and FE prediction of melt-pool temperature, subjected to a multistep trajectory of laser power Q and a fixed scan speed v=10.58mm/s

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Fig. 6

Inconel® 718: Least-squares fit and validation for steady-state cross-sectional area of melt pool. (a) Least-squares fit using measured cross-sectional area data under varying laser power (Scenario I), where Rlin2=0.713 and Rsqr2=0.717. (b) Validation using measured cross-sectional area data under varying laser speed (Scenario II), where Rlin2=0.827 and Rsqr2=0.943.

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Fig. 7

Inconel® 718: Our model prediction versus experiment measurements of melt-pool geometry and FE prediction of melt-pool temperature, validating against a new set of process inputs: a multistep trajectory of laser scan speed v and a fixed laser power Q=450W

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Fig. 8

Our model prediction for deposition of Inconel® 718 on a preheated substrate, under varying laser power Q and a fixed scan speed v=10.58mm/s

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Fig. 9

Our model prediction for deposition of Inconel® 718 deposition on a preheated substrate, under varying laser scan speed v and a fixed laser power Q=450W

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Fig. 10

Simulation of nonlinear MIMO control of melt-pool height and temperature using feedback linearization (FL)

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