## 1 Introduction  
Selective laser melting (SLM), which belongs to the category of powder bed fusion [1], is one of the fastest growing additive manufacturing (AM) technologies globally. It allows producing metal components with complex geometry, resulting in severely reduced design and production times of the entire productive process [2]. During the fabrication, metallic powders are uniformly spread on a building platform by a re-coater creating the powder bed; a focused laser beam scans it, according to the designed path, selectively melting the powders [3]. After the consolidation of this layer, the building platform lowers, and the process is repeated until the part is completed. The Wohlers report [4] indicated that 1768 metal AM systems were sold in 2017, a surge of nearly 80% compared to the previous year (983 systems in 2016). This rapid growth is due to the development of new functional applications in different fields such as aerospace, biomedical, defense, automotive, and many other industries thanks to the benefits offered by metal AM with respect to conventional manufacturing technologies. [5]. In particular, SLM permits producing fully dense parts in a direct way, thereby saving on raw material with respect to subtractive technologies [6]. It promotes the possibility of producing customized metal components in a cost-effective manner, allowing great flexibility in production; the design freedom allows improving the efficiency [7] and the functionality [8, 9] of existing designs, as well as the possibility to incorporate more complex features without drastically increasing the costs. This aspect includes the possibility to create features not fabricable conventionally, such as internal structures, e.g., lattice structures [10] or channels [11]. SLM permits shortening the supply chain and the lead time by replacing some production processes with a single step or combining different sub-elements in a single component [12; 13], thereby reducing or in some cases eliminating the assembly operations. Despite these advantages, the limitations for the complete implementation of this technology in the industrial framework are its low productivity and the presence of defects such as porosity, high residual stresses, cracks, inclusions, and surface irregularities that affect the structural integrity and surface quality of an SLM part [14]. In particular, the poor surface finishing and the surface anisotropy [15] are crucial aspects to consider. Typically, in order to improve the surface quality, the SLM surfaces are treated by different post-processing operations such as sand blasting, shoot peening, electropolishing, chemical polishing, and grinding [16]. These operations are skilled operator-dependent, labor-intensive, and typically hard to apply uniformly on complex-shaped parts. In Reference [17], the effect of the post-processing by machining, vibratory finishing, and drag finishing on the surface quality of SLM parts was investigated. The results showed that machining was the best choice because it permitted obtaining very high surface quality in a deterministic way, but it was limited by complex shapes. In the comparison between drag finishing and vibratory finishing, lower roughness values were observed for the former; however, the operation was limited by the need for fixturing the parts. In Reference [18], a magnetic abrasive finishing process was developed to polish SLM planar parts. The results showed that the method removes partially bonded particles and balling defects, obtaining a maximum decrease of about 76% in surface roughness. The system is suitable for planar surfaces but hardly applicable to complex shapes. In Reference [19], cavitation combined with abrasion was used as an SLM finishing process, leading to a reduction in Ra below 4 \(\upmu\)m for external surfaces and internal channels 3 mm in diameter.