*3.2. Sandblasting and Post-Sandblasting Measurement*

In accordance with the main objective of this work, the surface sandblasting treatment of the test samples was carried out using WFA F100 alumina oxide as the abrasive. The Sablex S-2 blasting machine was programmed to work at a constant pressure of 4 bar.

The roughness of the post-sandblasting spheres was measured with a contact roughness tester (TESA Rugosurf10®), and average values of *Ra* = 0.5~0.6 μm were obtained (with the original roughness values being *Ra* < 0.1 μm). As an example, Figure 6 shows a roughness profile and its main parameters measured by the profilometer. Several roughness measurements were performed showing that the variability of *Ra* between each of the ten spheres was low, and independent of the position of the spheres on the plate. This confirms that the finishing achieved with the sandblasting process was adequate and repeatable.

**Figure 6.** An example of the effect of sandblasting process in the roughness profile and parameters: (**a**) pre-sandblasted Ø 25 mm sphere, original G100; (**b**) post-sandblasted Ø 25 mm sphere.

From the geometrical and dimensional point of view analysis, and in the case of postsandblasting, the measurements made by contact with the CMM machine show higher values for both the diameter of the spheres and the form deviation (Table 2). Please note that the sandblasting process generates a dimensional deviation with an average value of only 2.7 μm and an increase in the form deviation of about 1.7 μm. At this point, it should be taken into account that this value is even lower than the maximum permissible error of the CMM, which is around 2.2 μm. It can therefore be concluded that, apart from a minimal variation in diameter, sandblasting also left the form deviation of the spheres practically unchanged.


**Table 2.** Comparison of contact measurement results regarding diameter and form deviation preand post-sandblasting.

The values obtained in the non-contact laser triangulation measurement were generated, as in the pre-sanding stage, using the capture mode with low sensitivity (high gain). The same type of spurious point filter was then applied, although now these defects appeared to a much lesser extent. In this case, the number of points captured with the laser sensor increased for all of the three ranges of spheres, being 13,975 points for each of the Ø 10 mm, 43,052 points for each of the Ø 18 mm, and 80,126 points for each of the Ø 25 mm spheres (Table 3). The increase with respect to the pre-sanded spheres reached 33.98%, 11.87% and 9.64%, respectively.

**Table 3.** Comparison of laser measurement results regarding diameter and form deviation pre- and post-sandblasting.


Regarding the measured data for the diameter of spheres, Table 3 shows that, while for the larger spheres (Ø 18 and Ø 25 mm) the pre-sandblasting results were lower than the nominal value, for the Ø 10 mm sphere the average value was higher than the nominal value.

However, the comparison before and after sandblasting provides values much closer to the reference (contact) values. This can be considered a success of the sandblasting process, which, by eliminating brightness, allows the laser to measure diameters much closer to the reference ones, even compensating differences as large as 0.116 and 0.164 in spheres of Ø 18 and Ø 25 mm, respectively. A comparison of the form deviation data before and after sandblasting is also shown in Table 3. Initially, the laser measurement averaged large form deviations, on the order of 0.15 to 0.19 mm. However, once the spheres are sandblasted, the laser measurements also offer very sharp improvements, ranging from 0.092 to 0.123 mm, leaving the form deviations at values in the range of 0.052 to 0.068 mm, also closer to the reference values.

With the laser equipment available, two types of improvements could be contrasted. On the one hand, the improvement in the density and coverage of the point cloud. This improvement was evident, since the coverage with pre-sanded spheres was very poor. In fact, in some cases (Ø 10 mm spheres), not all spheres could be correctly reconstructed. Consequently, the pre- and post-sandblasted comparison was only possible on all spheres when using high gain.

The second improvement achieved is related to the dimensional approach of the laser measurements to the CMM measurements (reference). Meaning by improvement the relation (%) between the parameter measured by laser with respect to the parameter measured by contact. In other words, a 100% improvement in any of the measurements would mean that the laser obtains the same measurement as the CMM by contact. Thus, Figure 7 shows the improvements obtained in the values of the diameters, both in high gain and normal gain. The improvements are substantial, although not homogeneous, in

all the range of diameters. An even greater improvement is noted in the large spheres, Ø 18 and Ø 25 mm, where the improvements are very high (>85%). The diameters obtained are very close to the reference values of the spheres, and even more so at high gain.

**Figure 7.** Diameter value improvements in non-contact measurement with medium and high gain in all three diameters.

Regarding the form deviation, the average improvement was 63.80% in high-gain mode and 69.67% in normal-gain mode. On the other hand, in the data relating to the standard deviation of the point cloud, an average percentage improvement of 59.21% was observed with the sensor filter at high gain and 66.29% at normal gain. Both parameters refer to measurements obtained on the spheres in a post-sandblasted state. In any case, homogeneous improvement values are observed regardless of the size of the sphere considered (Figure 8).

**Figure 8.** Improvements with medium- and high-gain laser measurements: (**a**) in form deviation; (**b**) in standard deviation.

The standard deviation value is one of the parameters that best characterizes the quality of a point cloud [5], especially when considering its approximation to a mathematically well-defined geometry, as is the case of the sphere. This value is even a good substitute for metrological form deviation (ISO 1101:2017), measuring how good the point cloud is when fitting to a perfect sphere.

As a summary, and using the standard deviation value as a measure of the quality of the cloud fit, the graph in Figure 9 was produced. Dashed lines show the standard deviation measurements on original spheres, while solid lines show the standard deviation measurements of the laser clouds on sandblasted spheres.

**Figure 9.** Standard deviation values pre- and post-sandblasting (laser measurements).

Here the qualitative leap that the sandblasting process generates on the laser measurements (at high gain) can be clearly observed. While the values of the standard deviation measured before the sandblasting process, oscillate between 0.029 and 0.034 mm, after the sandblasting process, the standard deviations have decreased substantially (between 0.010 mm and 0.015 mm).

Moreover, the graph also shows that, for any range of diameters considered, the "vertical" oscillation range in the standard deviation is very small. This gives an idea of the goodness of the sandblasting process. Despite being a manual process, it achieved a fairly uniform distribution on all the spheres of each plate, regardless of the position of each sphere within the plate.

## **4. Conclusions**

The pre- and post-sandblasting comparison of the spheres by contact and non-contact (laser triangulation sensor) measurement provides interesting data on the modification suffered by the sphere surfaces. In the analysis, the use of a wide number of spheres (three sets of 10 spheres) ensured the repeatability of the process.

The sandblasting process has affected the surface roughness from *Ra* < 0.1 μm to *Ra* = 0.5~0.6 μm for all the spheres, indicating that this parameter has little influence from a dimensional and geometrical point of view. Apart from roughness, three parameters were considered for the study: the sphere diameter, the form deviation (sphericity) and the standard deviation of the point cloud with respect to the best fit sphere. The first two measurands are perfectly defined from a metrological point of view, while the third (standard deviation) is preferable as an indicator of the form deviation of the surface for high density point clouds.

As a first conclusion, the effect of sandblasting on the spheres is acceptably small, with minimal changes in diameter (2.7 μm) and, more importantly, in form deviation (1.7 μm). These characteristics validate the use of these spheres as reference artifacts for calibrating optical equipment, whose estimated accuracies are in the order of 25 μm to 40 μm (or even more).

As a second conclusion, and now derived from the laser measurements, it can be observed that the increase in the density of the point cloud after sandblasting the spheres is very remarkable. So much so that, before sandblasting and at normal gain, the laser sensor was not able to capture clouds with good coverage. This defect was much more pronounced in small spheres. Even in the case of high gain, the improvements in the quality of the point cloud are considerable, with values of improvement in the order of 60 to 70%, both in terms of diameter and form deviation obtained with the best-fit cloud. Therefore, this type of surface finish can be considered as a good solution for the application of these spheres as reference artefacts in GD&T measurements with laser triangulation equipment.

As for the analysis performed with the standard deviation parameter, it can be seen that the value of the standard deviation between the point cloud of the pre-sandblasted and post-sandblasted sphere drops by almost half. That is, the fit of the point cloud to a sphere (value similar to the form deviation) is twice as good (almost 100% improvement) when sandblasted spheres are used. It can be stated that the brightness elimination of the spheres did not involve an important loss of sphericity that, on the contrary, remained within acceptable limits of accuracy.

This study demonstrates that sandblasted spheres, with average sphericity lower than 0.005 mm can be used as reference elements for non-contact measurement equipment with accuracies in the order of 0.040~0.050 mm. The validity of this statement is further supported by the low cost of the finishing process (manual sandblasting) and by the low cost of the stainless-steel spheres commonly used in industrial bearings.

**Author Contributions:** Conceptualization, E.C.; methodology, E.C. and B.J.Á.; formal analysis, V.M. and B.J.Á.; validation, V.M. and B.J.Á.; investigation, E.C. and V.M.; writing—original draft preparation, E.C. and B.J.Á.; writing—review and editing, B.J.Á.; supervision, E.C.; project administration, E.C. and V.M.; funding acquisition, E.C. and V.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the University Institute of Industrial Technology of Asturias, IUTA through the research project ref. SV-21-GIJON-1-06.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are grateful for the grant awarded by the University Institute of Industrial Technology of Asturias, IUTA (ref. SV-21-GIJON-1-06), and, in particular, to the research fellow, Pablo Pastur, for his high dedication and efficiency.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
