Elsevier

Precision Engineering

Volume 72, November 2021, Pages 25-40
Precision Engineering

Conformance and nonconformance in segmentation-free X-ray computed tomography geometric inspection

https://doi.org/10.1016/j.precisioneng.2021.03.019Get rights and content

Highlights

  • Additive manufacturing (AM) requires design and verification paradigms renewal.

  • Volumetric representation flexibly describes AM parts, including tolerances.

  • X-ray CT is a flexible measuring technique for AM and measures volumetrically.

  • Direct verification of volumetric geometric tolerances is possible by volumetric measurement.

  • This paper analyzes the customer's and consumer's risks in volumetric verification of tolerances.

Abstract

Additive Manufacturing (AM) is changing the manufacturing paradigm as it makes it possible to generate complex geometries that are impossible using conventional technologies. However, conventional GPS/GD&T practices are inadequate both at specifying and verifying geometric tolerances. In both cases, they lack the required flexibility. Applying volumetric instead of surface representations helps to solve the problem of specifying tolerances and coheres with topological optimization. The verification paradigm must be modified, too, as AM allows an increase in part complexity without a corresponding increase of cost. Among measurement techniques, only X-ray computed tomography (XCT), which is volumetric, is capable of easily measure complex parts. Leaving the discussion of volumetric tolerance specifications to the future, the aim of this work is exploring a part geometric accuracy verification by direct comparison between its nominal geometry and geometric tolerance volumetric representation, and an XCT volumetric image of it. Unlike the conventional use of XCT for geometric verification, this is a segmentation-free verification. The method is based on the “mutual information” of the two, i.e. information shared by the measured and nominal representations. The output is a conformance statement that does rely on a measurement but nor on a specific measured value not rely on a measurement result. This makes defining a decision rule considering consumer's and producer's risks difficult: uncertainty does not exist in this case. Statistic and simulation techniques make it possible to estimate these risks, defining a numerical model of the distribution of the gray values in a specific portion of the XCT image. Finally, an additive manufacturing case study validates the methodology.

Section snippets

Specifications and verification for additive manufacturing parts

The shift of Additive Manufacturing (AM) from prototyping to production has changed mechanical production. Now it is possible to provide “complexity for free” products, i.e. the main cost driver in additive manufacturing is part volume rather than part complexity. However, to take advantage of this novelty, design, production, and verification of AM products still need a significant improvement [[1], [2], [3], [4]]. Complex geometries, material-process interaction, and internal features are the

Basics of the segmentation free geometric verification

The authors proposed a criterion for the segmentation-free verification of the geometry of parts by X-ray computed tomography in a previous article [33]. To allow the reader to understand the following discussion on the reliability criterion, we report and demonstrate it here in-depth for the sake of completeness.

Reliability of the segmentation-free verification

After defining a criterion to distinguish conforming parts from nonconforming parts, the next step is calculating the probability of the criterion failing in identifying part conformance. Let's start by introducing the situations where the criterion succeeds in categorizing parts.

First, the histogram in Fig. 4 exemplifies a case where the criterion states that a conforming part conforms: the two histograms of the values in the inner/outer shells show no shared value.

This is what one expects

Estimate of conformance probability: simulation

Calculating pc is theoretically possible knowing the conditional distributions of LOUI and LIUO given the actual NSM. Arguably, this knowledge is impossible to gather in practice. Let's propose a different approach.

First, please consider that, in general, NSM contains many values - even for small XCT images thousands or millions of voxels constitute the shells. With this large amount of data, empirically estimating the statistical distribution of GVi,j,k in both NSMI and NSMO (fe,NSM(GVi,j,k)

Validation

To validate the proposed method, two case studies are proposed. The first one is based on an AM part, and aims at demonstrating the application of the method. The second one considers a calibrated sample characterized by a simple geometry. The repeated measurements of this sample allows the verification of the predicted pc reliability.

Conclusions and future aims

In this paper, a new tool for the volumetric verification of AM parts introduced in previous papers has been deepened. The tool is based on mutual information between a volumetric representation of the nominal part together with its tolerance and a measured volumetric representation of the real part. The tool particularly performs well if using volumetric design and representation on the part, and XCT is adopted for the verification. The new tool required introducing the concepts of maximum and

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Financial support to this work was provided as part of the AMaLa – Advanced Manufacturing Laboratory project, funded by Politecnico di Milano (Italy), CUP: D46D13000540005.

The Italian Ministry of Education, University and Research is acknowledged for the support provided through the Project “Department of Excellence LIS4.0 - Lightweight and Smart Structures for Industry 4.0” (CUP: D56C18000400006).

The authors wish to thank Trumpf GMbH for providing the TruPrint 3000 system on which the AM part

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