# Parameter Optimisation in Selective Laser Melting on C300 Steel
## 3 Experimental Methodology  
The SLM technology printer used was the ALBA 300 model developed jointly by the companies Samylabs and ONA. The machine has a CW fibre laser of 300 W, a wavelength of 1080 nm and a cylindrical working volume with a diameter of 160 mm and a height of 200 mm. It operates in a protected argon atmosphere to minimise oxygen uptake during printing. In addition, it is equipped with an oxygen sensor that monitors the chamber conditions in real time and ensures that the printing process cannot start until the oxygen-free conditions are met. The main printing parameters--laser speed, laser hatching distance, layer height, wavelength and laser power--have a decisive influence on mechanical properties of the manufactured part, particularly on the values of yield strength (\(\sigma_{0.2}\)), ultimate stress (\(\sigma_{uts}\)), elongation (\(\varepsilon_{r}\)) and area under the stress-strain curve (\(A\)). This last parameter represents the total mechanical energy per unit volume absorbed by the material. These parameters, as mentioned above, must be optimised for each material, since the thermal properties and the laser radiation absorption of a certain wavelength result on different energy densities required for fusion. In order to find these optimal parameters for C300 steel, a design of experiments using a response surface methodology has been established. Because of the difficulty of covering all these parameters in the response surface, it was decided to fix some of them. Thus, the wavelength, corresponding to the laser of the ALBA 300 printer, and the layer height have been fixed at 1080 nm and 40 \(\upmu\)m, respectively. Therefore, the response surface of the four studied outcome variables (\(\sigma_{0.2}\), \(\sigma_{uts}\), \(\varepsilon_{r}\) and \(A\)) are determined by the parameters \(P\), \(S\) and \(H\). The range of variation of these parameters is shown in Table 2, where the values shown correspond to the interval [1; 2; 3; 4] in the design of experiments. The relationship that exists among these three parameters and the values of the response surfaces can be expressed as \(S=f(P^{*},S^{*},H^{*})\), where \(f\) is postulated as a quadratic model, as expressed in Equation (1), in which \(P^{*}\), \(S^{*}\) and \(H^{*}\) are the coded variables for \(P\), \(S\) and \(H\), respectively. The real parameter values are coded so all vary within the same interval, normalising the inputs and facilitating a precise estimation of the coefficients that define the function \(f(P^{*},S^{*},H^{*})\). For any real value \(X_{i}\) of the input parameters, coding can be performed through the Expression (2), resulting in the corresponding coded value \(x_{i}\), where \(X_{iNInf}\) is the real value of the lowest level for the parameter \(i\), \(X_{iNSup}\) is the real value of the highest level of the parameter \(i\) and \(\widetilde{X}_{i}\) is the mean of the real values of the highest and lowest levels of the parameter \(i\). \[ \begin{array}{l}f(P^{*},S^{*},H^{*})=b_{0}+b_{1}\cdot P^{*}+b_{2}\cdot S^{*} +b_{3}\cdot H^{*}+b_{11}\cdot P^{*2}+b_{22}\cdot S^{*2}+b_{33}\cdot H^{*2}+\\ +b_{12}\cdot P^{*}\cdot S^{*}+b_{13}\cdot P^{*}\cdot H^{*}+b_{23}\cdot S^{*} \cdot H^{*}\end{array}  \tag{1}\]  
\[x_{i}=\frac{2\cdot\left(X_{i}-\widetilde{X}_{i}\right)}{X_{iNSup}-X_{iNInf}} \quad i=P^{*},S^{*},H^{*} \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Variable Parameters**} \\ \hline Laser Power (\(P\)) & [200, 250] W \\ \hline Scanning Speed (\(S\)) & [500–800] mm/s \\ \hline Hitching Distance (\(H\)) & [0.08–0.14] mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used in the design of experiments. Coefficients of the function \(f(P^{*},S^{*},H^{*})\) for each material property outcome (\(\sigma_{0,2}\), \(\sigma_{uts}\), \(\varepsilon_{r}\) and \(A\)) are determined by performing a central cubic design experiment [18; 19; 20] using Design Expert software to estimate these coefficients.