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Research Papers

An Extended Lumped-Parameter Model of Melt–Pool Geometry to Predict Part Height for Directed Energy Deposition

[+] Author and Article Information
Jianyi Li

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

Qian Wang

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

Panagiotis (Pan) Michaleris

Autodesk, Inc.,
200 Innovation Boulevard,
State College, PA 16803
e-mail: pan.michaleris@autodesk.com

Edward W. Reutzel

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

Abdalla R. Nassar

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

1Corresponding author.

Manuscript received March 2, 2017; final manuscript received June 24, 2017; published online July 26, 2017. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 139(9), 091016 (Jul 26, 2017) (14 pages) Paper No: MANU-17-1126; doi: 10.1115/1.4037235 History: Received March 02, 2017; Revised June 24, 2017

There is a need for the development of lumped-parameter models that can be used for real-time control design and optimization for laser-based additive manufacturing (AM) processes. Our prior work developed a physics-based multivariable model for melt–pool geometry and temperature dynamics in a single-bead deposition for a directed energy deposition process and then validated the model using experimental data from deposition of single-bead Ti–6AL–4V (or Inconel®718) tracks on an Optomec® Laser Engineering Net Shaping (LENS) system. In this paper, we extend such model for melt–pool geometry in a single-bead deposition to a multibead multilayer deposition and then use the extended model on melt–pool height dynamics to predict part height of a three-dimensional build. Specifically, the extended model incorporates temperature history during the build process, which is approximated by super-positioning the temperature fields generated from Rosenthal's solution of point heat sources, with one heat source corresponding to one bead built before. The proposed model for part height prediction is then validated using builds with a variety of shapes, including single-bead thin wall structures, a patch build, and L-shaped structures, all built with Ti–6AL–4V using an Optomec® LENSTM MR-7 system. The model predictions on average part height show reasonable agreement with the measured average part height, with error rate less than 15%.

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References

Figures

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Fig. 1

Coordinate systems used in Rosenthal's solution

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Fig. 2

A schematic plot of a single-bead wall

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Fig. 3

A schematic plot for the layer-by-layer approach to compute Tinitial before deposition

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Fig. 4

Pseudo-code for computing Tinitial iteratively for a single-bead thin-wall structure

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Fig. 5

Single-bead thin walls (figure from Ref. [10]): (a) wall 1: no interlayer dwell time and (b) wall 2: 20 s interlayer dwell time

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Fig. 6

Initial temperature Tinitial in terms of wall distance and layer number: (a) wall 1: Tinitial for the first three layers, (b) wall 1: Tinitial for all 62 layers, (c) wall 2: Tinitial for the first three layers, and (d) wall 2: Tinitial for all 62 layers

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Fig. 7

Model predicted height contours of walls 1 and 2 after 62 layers, and model predicted height contours of walls 1 and 2 after every ten layers of deposition. Wall 1 has a length of 39.2 mm, and wall 2 has a length of 37.2 mm. The deposition direction of the first layer is from left to right, and it switches after each layer.

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Fig. 8

Model predicted height contour of wall 2 versus the scanned image of wall 2. The deposition direction of the first layer in the plot is from right to left, and it switches after each layer. Since the height contour of the build is calculated by adding up the melt–pool height trajectory of each layer among all layers, the two ends of the predicted height contour do not start from zero.

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Fig. 9

Sensitivity of Tinitial with respect to laser power: (a) Tinitial of several layers at x = half of the wall length, as a function of the laser power and (b) model predicted wall height profile at different laser power

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Fig. 10

Sensitivity of Tinitial with respect to laser scan speed: (a) Tinitial of several layers at x = half of the wall length, as a function of the laser scan speed and (b) model predicted wall height profile at different laser scan speed

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Fig. 11

A schematic plot of a patch build with a parallel build plan (reproduction of figure from Ref. [32]): (a) front view of the patch build, (b) top view of the patch build, and (c) build plan

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Fig. 12

Photo and scan image of the patch sample: (a) top view of the half patch, where (x = 0, y = 0) denotes the starting point of the deposition of the first layer, and the first bead of first layer is deposited along the x direction.7 (b) Top view (in the “Scan x–y” coordinates) of the scanned image (represented by scatter plot of the image data) of the two quarter patches.

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Fig. 13

Three-dimensional surface plot (in right-handed coordinates) of the simulated three-layer patch build: top surface after layer 1 being deposited, top surface after layer 2 being deposited, and top surface after layer 3 being deposited

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Fig. 14

Model predicted height for each of the four line segments A, B, C, D in Fig. 12(a) versus the scan image (matlab scatter plot of the image data with color as a function of height) of the corresponding thin-band segments A1/A2, B1/B2, C1/C2, D1/D2 in Fig. 12(b). Since the images of A1 and A2 (same for B1 and B2, C1 and C2, D1 and D2) are stitched together, a vertical merging line is shown. The horizontal axis “Y distance” corresponds to the distance in the y direction defined in Fig. 12(a). (a) Segment A, (b) segment B, (c) segment C, and (d) segment D.

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Fig. 15

Images of the L-shaped structures: (a) L-1 with no dwell; (b) L-2 with 4 s dwell; (c) top view of the scan image of L-1, which was rotated from (a) when going through scanning; and (d) top view of the scan image of L-2, which was rotated from (b) when going through scanning

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Fig. 16

Deposition path of the L-shaped structures (figure from Ref. [29]), where hatch 1 went from (x = 0, y = 0) to (x = 0, y = 1) inch, and without pausing, hatch 2 went from (0,1) inch to (1,1) inch, and after a jump, hatch 3 went from (1, 1 + 0.032) inches to (0, 1 + 0.032) inches, and after a jump, hatch 4 went from (0, 1 + (2 × 0.032)) inches to (1, 1 + (2 × 0.032)) inches

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Fig. 17

Simulated L-shaped structures: (a) L-1 (no interlayer dwell time) and (b) L-2 (4 s interlayer dwell time)

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Fig. 18

Predicted height versus scan image (scatter plot of the image data with color as a function of height) for the one-bead leg and three-bead leg of L-1 and L-2: (a) L-1: predicted height for the one-bead leg versus scatter plot of image data for the one-bead leg (wall 1), (b) L-1: predicted height for wall 2, wall 3, and wall 4 of the three-bead leg versus scatter plot of image data for the three-bead leg (walls 2, 3, and 4 cannot be differentiated in the scan image), (c) L-2: predicted height for the one-bead leg versus scatter plot of image data for the one-bead leg, and (d) L-2: predicted height for walls 2, 3, and 4 of the three-bead leg versus scatter plot of image data for the three-bead leg

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