*2.3. The Methodology and Its Experimental Implementation*

The following lines describe the experimental exercise performed on the dummy part to realise the practical implementation of the previously mentioned technological concepts (see Figure 3). In general terms, the suggested workflow is based on three main steps: (1) measurement of the dummy part, including the data acquisition process (×10 repetitions) and automatic data process strategy (MBD) (box 1); (2) reference measurement of the dummy part on a CMM according to the ISO 15530-4 technical specification (box 2), and (3) the task-specific (GD&T) uncertainty assessment process according to the ISO 15530-3 technical specification (box 3).

**Figure 3.** The point cloud measurement uncertainty assessment workflow.

The three main steps of the methodology are explained next and linked to the uncertainty contributors that comprise the uncertainty budget presented in the third step.


The experimental implementation of the suggested methodology is explained next point by point:

## 2.3.1. Measured GD&T Evaluation

A dense 3D point cloud data acquisition process is performed using a GOM ATOS III Triple Scan™ 3D optical system on a medium-sized geometric-type dummy part. The data acquisition process is fully automatic by combining an automatic rotary table with the manual triggering of the measuring instrument. Thus, any potential error source derived from external sources, such as the alignment process between partial scanning or operator influence, is avoided.

The experimental exercise is performed in a metrology laboratory at a temperature of 20 ± 1 ◦C. In this way, thermal stability during the data acquisition process is guaranteed; and therefore, the geometric variation of the dummy part caused by thermal drift is avoided. Figure 4 shows the dummy part employed during the experimental exercise.

**Figure 4.** The medium-size dummy part from Metrologic™ is shown: (**a**) the CAD model and (**b**) the physical part placed on the rotary table.

The measurement instrument configuration is set at a working volume of 320 × 240 × 240 mm<sup>3</sup> so that the measurement resolution was optimised for the specific dummy part under measurement. The automatic data acquisition process is realised by eight angular rotary table equidistant positions, where partial scans are performed and stitched together automatically to reconstruct the overall 3D point cloud. Thus, the entire measurement process is executed within 45 s, and a point cloud comprised of 1 million points is obtained.

The fiducial targets are attached to the rotary table and unequivocally identified in each partial scan. In this manner, the automatic partial point cloud registration problem is solved, and an automatic data merging process between partial scans is performed. Once the reconstructed 3D point cloud is obtained, it is converted into a mesh using the Delaunay triangulation method. In addition to the XYZ information of every point within the point cloud, this mesh also contains information related to the surface normal value for every point which makes the final MBD-based automatic point cloud segmentation process smarter and more robust.

Figure 5 depicts the measurement scenario, comprising a GOM ATOS III Triple Scan™ 3D optical system in combination with the automatic rotary table and the dummy part on it.

**Figure 5.** Automatic measurement data acquisition process set-up.

The batch of experiments comprises ten 3D point cloud measurement repetitions on the dummy part. Once they are completed, an automatic data-processing approach based on the MBD strategy is applied. Thus, the dense point cloud is automatically processed and converted into meaningful GD&T information.

The software employed at this point is GOM Inspect™ metrology software. It allows MBD-type post-processing of data which means that it can digitally establish a relationship between nominal GD&T information and geometric elements within the captured data. This workflow is aligned with the PMI concept and interpreted using the ISO 1101 standard [68]. A different option to run MBD-type post-processing is to define the MBD data within the CAD model by adding the GD&T information to the available CAD file (for example, a catpart file in SolidWorks). Once this nominal MBD data-based file is prepared, the automatic evaluation of every GD&T can be performed. The workflow is as follows.


Following this process, the standard uncertainty associated with the measurement process variability (*up*) is obtained for each feature. The ten available 3D point cloud measurement repetitions are statistically processed, and the uncertainty (*up*) is given by the standard deviation parameter according to the ISO 15530-3 technical specification. In addition, the average value is reported at this step for the evaluation of the systematic error (*ub*) value within the next step.

Figure 6 shows the experimental results for the dummy part of the GOM Inspect™ metrology software.

**Figure 6.** GD&T evaluation (real and nominal values) and representation on the CAD model.
