## 3 Most Used Dimensional Methods in Additive Manufacturing
[PERSON], in [65], identified four dimensionless variables (the melting and the vaporization efficiency, the welding parameter, and the track size parameter) based on dimensional analysis of the _SLM_ process, which characterize the thermo-dynamical problems of this process. Starting from the 3D printing difficulties and complexity, [PERSON] performed a useful dimensional analysis in [42]. It was proposed for the metal 3D printing, and universal as well as simply scaling laws for keyhole stability and porosity. The proposed scaling laws assure process optimization and defect elimination during printing, as well as a quantitative predictive framework. For the Laser Powder Bed Fusion process, a topological depression, named _keyhole_, appears frequently, which is difficult to predict and to understand. Its geometry influences the energy coupling mechanisms of the high-power laser with the material; thus, it produces unlikely melt pool dynamics, as well as solidification defects. It also can contribute to significant process instability, as well as structural defects, namely: porosity, sputtering, balling effect, and unusual micro-structural phases. Their high-accuracy investigations with high-energy X-ray imaging in laser melting of bare plate, powder bed, and powder flow gave significant results. In the case of the laser melting of austenitic stainless steel, based on in situ X-ray analysis, [PERSON] deeply analyzed the effect of the process conditions on the keyhole behavior in [27]. Based on meticulous analysis, it was stated that the involved laser's parameters significantly influence the keyhole formation and its parameters, such as keyhole depth and width, as well as the decrease of the keyhole depth together with the increasing of the laser power. In addition, the influence of the existence of shielding gas on the keyhole depth was also established. The diminishing of the laser power and the quality of the laser beam have significant influence on this effect due to the interaction between the laser beam and metal vapor. In the case of increasing of the laser transverse speed with respect to the keyhole forming speed, it was observed that a decrease of the keyhole inclination was related to an increase of its width as well as its opening. By increasing the defocus distance, a decreasing of the keyhole inclination was observed, specifically an increase of keyhole depth. Taking into consideration the above-mentioned process parameters, some useful dimensionless variables were proposed in order to improve the laser melting process results. In [23; 30], [PERSON] described a useful implementation of hybrid technologies on the aluminum casting topological optimization. With optical roughness measurement, they compared the surface qualities of the classical wax model versus the _AM_'s offered polymer part of polymethyl methacrylate (PMMA) using the binder jetting method, with PolyPor B used as a binder; the latter was determined to be much better. In addition, this polymer part significantly diminishes the thermal expansion, as was also analyzed with dimensional analysis. In the case of special alloys, in order to eliminate several manufacturing defects, the authors intended to propose some additional heat treatment methods, validated by rigorous experiments. For the study, in order to obtain an acceptable final surface, the model was treated using wax infiltration. Their further studies will be targeted on the evaluation of dimensional accuracy, surface quality, and internal defects in the manufactured metal casting, as well as some efficient heat treatments. Similar useful research, including dimensional analysis, was performed by [PERSON] [25], providing evidence for the thermal treatment's significance. The author offers useful information on the significance of post-AM double aging heat treatment (HT) of alloy IN718 (Inconel 718) obtained through a laser-based powder bed fusion process (L-PBF). The first, as-built samples were subjected for 1 hour to solution annealing at 980 \({}^{\circ}\)C, and later cooled in air.