**2. Materials and Methods**

Since the process chosen to perform the modification of the surface condition is manual sandblasting, it requires statistical validation to be considered valid, minimizing the operator's influence on a given sphere. Therefore, the experimentation includes a range of different sets of spheres, each set corresponding to a different nominal diameter.

Specifically, 3 sets of spheres of different size were analyzed (3 plates including 10 spheres each, of Ø 10, Ø 18 and Ø 25 mm, respectively, as shown in Figure 2). From these analyses, the average values and standard deviations are determined for each one of the sets of 10 spheres, which are distributed over the corresponding plate with a similar layout. The diameter and form error values of the spheres of each set have been measured by contact (CMM with SP25M scanning probe) and by laser triangulation (Hexagon HP-L-10.6 sensor mounted on the CMM), first at their original polished state, before the surface attack, and secondly after being surface treated by sandblasting.

**Figure 2.** Research methodology.

Contact measurements of the spheres were carried out with a coordinate measuring machine (CMM), the DEA Global Image 091508 model, equipped with a PH10MQ indexing head. A Renishaw SP25 contact scanning probe can be mounted on this head. PC-DMIS 2018 R2 software was used to configure the CMM, setting parameters, paths, and number and distribution of points. The tip used was a Ø 1.5 mm ruby sphere for both polished and post-sanded spheres. The accuracy of this CMM is given by the manufacturer (Hexagon Metrology) according to ISO 10360-2 [21] and according to the latest calibration: *E*0.MPE = 2.2 + 0.003 × *L* (*μ*m), *R*0.MPL = 2.2 *μ*m.

Although this MPE parameter is not a substitute for uncertainty of dimensional or form measurement, the use of a sufficiently representative number of spheres, as well as several repetitions (at least 3 for each sphere), provides enough traceability of the measurements. This is especially true when working with calibrated equipment and obtaining average values.

For the non-contact measurement, a laser triangulation sensor from Hexagon Metrology, HP-L-10.6, was used, also attached to the CMM. This sensor comes with a calibration certificate (ISO 10360-8) [2] with a maximum error specification of 0.020 mm. On the other hand, the surface treatment of the spheres was carried out with the Sablex S-2 machine using WFA F100 alumina oxide (average grain size 106~150 μm, and true density 3.9 g/cm3) as an abrasive element, projected onto the sphere surface at a pressure of 4 bar. Despite

being a manual process, the distance of the nozzle was kept in the range of 200–300 mm, with 5 orientations per plate (one orientation normal to the plate, and the other 4 at 45◦ with respect to the normal vector to the plate, distributed in 4 quadrants). The sandblasting operation time, for all orientations, was inferior to 1 min per plate.

Figure 2 shows a diagram illustrating the methodology followed and the equipment used for the development of the research.

The steps followed in the procedure were:


#### *Test Specimens Manufacturing and Justification of Material Selection*

The material selected for the test plates is AISI 316L stainless steel. AISI 316L was an austenitic stainless steel with <0.03%C, 2%Mn, 17%Cr, 13%Ni, 3%Mo (EN symbol: X2CrNiMoN-17-14-3), with hardness HB < 215 and CTE = 14 × <sup>10</sup>−<sup>6</sup> <sup>K</sup>−1. The plates were also sandblasted prior to any measurement to avoid reflections on the spheres. The precision spheres were drilled using two hemispherical jaws, so that the drill bit did not produce any permanent marks or deformations. Each hole in the sphere was then threaded in order to screw the sphere onto the base plate. All spheres are made of AISI 316L of commercial grade G100 quality, with a sphericity lower than 2.5 μm and an arithmetic mean roughness *Ra* < 0.1 μm.

Figure 3a shows the 3-4-3 matrix design of each set of 10 spheres. This arrangement allows easy sandblasting of each sphere without influence from the adjacent sphere. In addition, it also facilitates the access of the laser triangulation sensor beam (especially above the equator) as well as the contact probe. The designations of the 10 spheres of each set and the coordinate axes of the reference system used for the measurement procedure are also presented in Figure 3a.

The coordinate system of each plate is defined from 3 spheres in such a way that it is independent of the supporting plate. According to its nomenclature (Figure 3a), the coordinate system is formed by spheres 1, 3 and 8 (*XY* plane), with sphere 1 being the origin and sphere 3 defining the *Y* axis. The same alignment definition has been applied for each of the 3 plates with spheres of Ø 10, Ø 18 and Ø 25 mm. Figure 3b shows a detail of the CMM contact measurement (pre-sandblasting) on Ø 25 mm spheres set.

**Figure 3.** Plate with 10 spheres of the same diameter: (**a**) designation of the spheres and reference system; (**b**) CMM contact measurement of a set of ten spheres (25 mm diameter) on the original base plate; (**c**) CMM contact measurement of a sandblasted base plate.
