## Materials and Experimental Procedure
### Experimental Procedures  
The selection of process parameters is of fundamental importance in order to achieve dimensional accuracy, smooth surface and cut edge quality. Therefore, the range of parameters to be tested was identified on the basis of pre-design tests and literature studies. For each material the best-known practice was adopted. As for the assistant gas, AlMg3 and AISI 304 were cut by using nitrogen, whereas St37-2 was cut with oxygen. The assisting gas was ejected coaxially through the conical nozzle of the cutting head. Adjustments of the nozzle diameter allow pressure stabilization and avoid turbulence in the melt. In general, common values for the nozzle diameter are in the range 0.8 - 3 mm, according to material and thickness. The assisting gas jet provides the mechanical action required to drag the molten metal from the kerf, and it forms a boundary layer over the molten surface in which heat transfer occurs, thus avoiding overheating [21]. Furthermore, in oxygen-assisted cutting, the active gas provides an additional thermal contribution to the energy balance. In general, in oxygen-assisted laser cutting, the active gas is injected into the cutting area with a pressure of approximately 0.2-0.6 bar depending on thickness, whereas the injection pressure of nitrogen is considerably higher (of about 16 bar for 10 mm thick sheets). In inert gas-assisted cutting, the focus position is typically placed on the top or below the surface (negative focus position) to facilitate the inlet of the assisting gas and the ejection of the molten material. Conversely, in oxygen-assisted cutting, the focus position is generally set on the upper surface of the workpiece to rapidly trigger the oxidation reaction, especially for cutting thick sections [22]. Proper setting of the focus position reduces loss of beam intensity and defocusing. Consequently, optimal focal position and nozzle diameter were found for each condition (material-interaction mechanism) at standard standoff distance and kept constant throughout the experimentation. Cutting speed has a significant influence on material removal and cut front temperature because it governs the laser-material interaction for a given output power. Unsuitably low cutting speeds lead to under-utilization of laser beam energy, whereas excessively high cutting speeds (exceeding a critical threshold) result in a loss of the cutting conditions. Then, once the beam focus was established (depending on the gas type), the maximum cutting speed for each material was found by increasing the cutting speed as long as continuous through-thickness cut was obtained. In order to study the influence of process parameters on geometrical accuracy and kerf quality, a \(3^{2}\times 2^{2}\) full factorial design was developed according to the Design of Experiment (DoE). This is a very effective approach for planning experiments that provides valid and objective results using 'factorial designs', in which the factors are changed simultaneously to verify a great number of factors and their interactions without the need for a large number of experimental runs, thus reducing development time and efforts. The control factors adopted were material and thickness as regards workpiece parameters, cutting speed and pressure as regards process parameters. In order to implement the aforementioned method, it is important to normalize the values of numerical parameters. Two levels of cutting speed were adopted corresponding to 100% and 50% of the maximum cutting speed. The same was applied to the limiting assistant gas pressure. However, it was decided to not include in the experimentation the condition 50%-50%, corresponding to the combination of the low levels, because it was considered not a sufficient condition for ensuring adequate cutting. Therefore, the reduced factorial design consisted of 27 tests. For each condition, two replications were