Conformance and nonconformance in segmentation-free X-ray computed tomography geometric inspection
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 is theoretically possible knowing the conditional distributions of and given the actual . Arguably, this knowledge is impossible to gather in practice. Let's propose a different approach.
First, please consider that, in general, 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 in both and (
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 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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