## Materials and Methods
### Materials  
For the fabrication of the SLM specimens and the complex components, the employed machine was an EOSINT(R)M290 characterized by a building volume of 250 \(\times\) 250 \(\times\) 325 mm\({}^{3}\) and a 400-W yterbium fiber continuum laser, with a beam spot diameter of 100 \(\upmu\)m. The process was carried out in an argon inert atmosphere with less than 0.1% oxygen. The building platform was preheated at 200 \({}^{\circ}\)C in order to reduce residual stresses. The first material was Ti6 Al4V, characterized by the chemical composition reported in Table 1. In Figure 1, the SEM image and the granulometry distribution of the employed powders are reported. The shape of the particles was highly spherical, and a large scattering of diameters could be observed (Figure 1a). As shown in Figure 1b, this distribution (blue curve) was asymmetrical,and the corresponding cumulative volume (red curve) was characterized by the following metrics: d\({}_{10}\), d\({}_{50}\), and d\({}_{90}\), which were the intercepts for 10%, 50%, and 90%, paired to 27.1 \(\upmu\)m, 42.5 \(\upmu\)m, and 67.8 \(\upmu\)m, respectively. The used process parameters were as follows: 30 \(\upmu\)m layer thickness, 140 \(\upmu\)m hatch spacing, 1200 mm/s scan speed, and 280 W laser power. The scanning strategy was the stripe type, with a stripe length and an overlap of 5 mm and 0 mm, respectively. The scanning direction was rotated between consecutive layers by 67\({}^{\circ}\) in order to minimize the out-of-plane distortion. The detaching from the building platform was performed by abrasive cutting, and no other finishing operation was performed. The second considered material was Inconel718; this powder is shown in the SEM image of Figure 2a, highlighting an almost spherical shape with some oblong particles and aggregates. Its granulometry distribution was narrower than that of Ti6 Al4V (Figure 2b); in this case, the d\({}_{10}\), d\({}_{50}\), and d\({}_{90}\) corresponded to 17.3 \(\upmu\)m, 23.7 \(\upmu\)m, and 33. The applied process parameters were as follows: laser power 285 W, layer thickness 40 \(\upmu\)m, scan speed 960 mm/s, and hatch spacing 110 \(\upmu\)m. Furthermore, in this case the scan strategy was the stripe type, with a stripe length and an overlap of 10 mm and 0.8 mm, respectively. The BF process was carried out using an industrial equipment Rotar EMI 47 (second and third phases); it is an eccentric-flow rotating barrel with an inclined octagonal section 400 mm in diameter moved by an asynchronous motor with a variable shift speed electric control system. The volume of the barrel was 47 L, and the maximum filling was 64 kg. The employed charges were composed of media with the same shape but different size; the shape was angled cut cylindrical and the dimensions were 15 mm in diameter, 25 mm in height (Figure 3a) and 3.5 mm in diameter, 10 mm in height (Figure 3b). The composition of both media was a matrix of a synthetic resin and powders of alumina, silica, and silicon carbide as abrasive. The different sizes were suitable for the processing of complex shapes because the bigger media allowed speeding up the machining of the external surfaces, whereas the smaller media allowed reaching the internal surfaces or overhang zones, where there was not enough space for the relative motion of the bigger media. In the experimentation, three different charge types were considered: only big media (charge 1), only small media (charge 3), and a 50:50 volume fraction mixture of both (charge 2). In order to determine the flow regimes and achieve important motion features, in the first phase, an experimental apparatus was employed. The barrel geometry and the internal material lining were the same of the industrial barrel. In this way, it was expected that the same motion regime could be observed on both barrels loaded with the same charge, employing the same process parameters. A transparent porthole allowed watching the motions and taking measures through digital image processing.