Research Papers

Assessment of Dimensional Integrity and Spatial Defect Localization in Additive Manufacturing Using Spectral Graph Theory

[+] Author and Article Information
Prahalad K. Rao

Department of Systems Science
and Industrial Engineering,
Binghamton University,
Binghamton, NY 13902-6000

Zhenyu Kong

Grado Department of Industrial
and Systems Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: zkong@vt.edu

Chad E. Duty

Oak Ridge National Laboratory,
P.O. Box 2008,
Oak Ridge, TN 37831-6083;
Department of Mechanical, Aerospace and
Biomedical Engineering,
The University of Tennessee,
Knoxville, TN 37996-2210

Rachel J. Smith

Department of Biomedical Engineering,
University of California, Irvine,
Irvine, CA 92617

Vlastimil Kunc, Lonnie J. Love

Oak Ridge National Laboratory,
P.O. Box 2008,
Oak Ridge, TN 37831-6083

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received February 27, 2015; final manuscript received September 1, 2015; published online November 19, 2015. Assoc. Editor: Z. J. Pei.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Manuf. Sci. Eng 138(5), 051007 (Nov 19, 2015) (12 pages) Paper No: MANU-15-1093; doi: 10.1115/1.4031574 History: Received February 27, 2015; Revised September 01, 2015

The ability of additive manufacturing (AM) processes to produce components with virtually any geometry presents a unique challenge in terms of quantifying the dimensional quality of the part. In this paper, a novel spectral graph theory (SGT) approach is proposed for resolving the following critical quality assurance concern in the AM: how to quantify the relative deviation in dimensional integrity of complex AM components. Here, the SGT approach is demonstrated for classifying the dimensional integrity of standardized test components. The SGT-based topological invariant Fiedler number (λ2) was calculated from 3D point cloud coordinate measurements and used to quantify the dimensional integrity of test components. The Fiedler number was found to differ significantly for parts originating from different AM processes (statistical significance p-value <1%). By comparison, prevalent dimensional integrity assessment techniques, such as traditional statistical quantifiers (e.g., mean and standard deviation) and examination of specific facets/landmarks failed to capture part-to-part variations, proved incapable of ranking the quality of test AM components in a consistent manner. In contrast, the SGT approach was able to consistently rank the quality of the AM components with a high degree of statistical confidence independent of sampling technique used. Consequently, from a practical standpoint, the SGT approach can be a powerful tool for assessing the dimensional integrity of the AM components, and thus encourage wider adoption of the AM capabilities.

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Grahic Jump Location
Fig. 1

Plots showing surface geometry deviations (inches) obtained from 3D point cloud data for three different AM samples (see Sec. 3.1 for further details). The AM samples shown here measure 100 mm × 100 mm × 8 mm (4 in. × 4 in. × 0.3 in.). (a) and (b) Components produced using ABS thermoplastic but different processing conditions (see Sec. 3.1, Table 1). (c) Component produced using CF impregnated thermoplastic composite (CF-ABS).

Grahic Jump Location
Fig. 2

Summary of the research methodology

Grahic Jump Location
Fig. 3

(a) 3D Point cloud of NIST part (100 mm × 100 mm × 8 mm; 4 in. × 4 in. × 0.3 in.) obtained using the FaroArm laser scanning probe. (b) Zoomed in section showing fine features (4 × zoom).

Grahic Jump Location
Fig. 4

(a) Average deviation of point cloud data in x, y, and z directions (overall deviation). (b) Average deviation in the vertical (z) direction. The ambiguity of statistical feature mining approaches for quantifying dimensional integrity is observed in comparison of (a) and (b).

Grahic Jump Location
Fig. 5

(a) Line scan locations for analysis of specific facets. (b) Feature deviations for facet-specific line scans.

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Fig. 7

Results from applying the SGT approach to experimental test components. (a1) and (b1) The Fiedler number for the three different components using two different sampling methods described in Sec. 3.2.3. The difference in Fiedler number across test components is statistically significant (p-value < 0.01) The trends in Fiedler number are similar irrespective of the sampling method. The error bars represent the two-sided 95% CI on the mean. (a2): The Fiedler number vs. sample size (m) for Method 1. The Fiedler number converges for m>50,000. (b2): The Fiedler number vs. spatial location on component using Method 2 notice the generally smaller magnitude of the CF component.

Grahic Jump Location
Fig. 8

Fiedler number obtained from the simulated point cloud data using SGT methods 1 and 2 at different levels of deviation (Σ). (a) Mean Fiedler number from five-fold cross validation (five replications). The difference between replications is statistically indistinguishable; the mean Fiedler numbers are estimated across replications after averaging over sample windows for a particular replication. (b) The Fiedler number shown along with the 95% CI interval for one particular replication. The mean Fiedler numbers are estimated across sample windows.

Grahic Jump Location
Fig. 9

Localizing component anomalies to specific areas using the Fiedler number. (a) The sorted point cloud data in x-direction. Each differently colored strip represents a sampling area or spatial location. There are 500 such location on the part, each containing approximately of 1000 data points, and measuring ∼10 mils (250 μm) in width and ∼0.3 in. (8 mm) in height. The portion marked in the middle is the location of interest in this case study, and is purposely perturbed. (b) The Fiedler number vs. the sampling location. The blue line is from the experimental ABS chamber part (Σ = 0, normal condition), a clear departure from the norm is observed as Σ increases. (c) Magnified view of the portion highlighted in (b).




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