## 4 Conclusions  
The experimental and mathematical data obtained in the study reported in this work enabled the following conclusions.  
1. Lower values of roughness parameters after milling were obtained at the end face of the specimen (e.g., for AZ31 and \(\mathrm{s_{tr}}\) = 30%: end face \(\mathrm{Rz}\) = 9.22 \(\mathrm{\SIUnitSymbolMicro m}\), lateral face \(\mathrm{Rz}\) = 14 \(\mathrm{\SIUnitSymbolMicro m}\)).
2. The changes in the analyzed roughness parameters were different in response to \(\mathrm{v_{c}}\) and \(\mathrm{s_{tr}}\).
3. For both alloys, similar values of the analyzed roughness parameters were achieved (e.g., for \(\mathrm{v_{c}}\) = 400 m/min, Rz: AZ31 was 8.66 \(\mathrm{\SIUnitSymbolMicro m}\) and AZ91D was 9.15 \(\mathrm{\SIUnitSymbolMicro m}\)). The discrepancies could only be considered at the statistical level; however, they are technologically irrelevant.
4. Although the change in the tested milling input parameters (\(\mathrm{v_{c}}\)/\(\mathrm{s_{tr}}\)) induced a change in the investigated surface roughness parameters, it is, however, difficult to observe a distinctive trend.
5. In relation to milling, brushing treatment reduces the roughness parameters of the tested Mg alloy specimens by several times. Following brushing, an approximately 5.6-fold decrease in the roughness (Ra parameter) was observed for the AZ31 alloy and about 3.9-fold for the AZ91D alloy, compared to the initial machining, i.e., milling with a variable trochoidal step.
6. The largest increase in the value of the surface free energy (16%) was observed for the AZ91D alloy during the change of the \(\mathrm{s_{tr}}\) parameter. The increase in the SFE directly impacts the increase in the polar component of the SFE, which for the AZ91D alloy was 96%.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & \multicolumn{6}{c}{**Hypothesis of Equal Variances**} & \multicolumn{6}{c}{**Hypothesis of Equal Means**} \\ \cline{2-10}
**Par.** &
\begin{tabular}{c} \(\mathrm{s_{tr}}\) \\ [\%] \\ \end{tabular} & \begin{  
Considering the simulation results of the roughness parameters and their correlation with the actual cutting data, the error was shown not to exceed the acceptable level of 15% (10% for milling and 15% for milling and brushing). ANNs exhibit good potential for the simulation of accurate data for the preliminary determination of milling parameters.
* The ANNs succeeded in representing the non-linear dependence between machining and roughness parameters. This may prove their fitness for the analysis of milling without the need for implementing time-, labor-, and cost-consuming machining.
* ANN simulation may be the cornerstone of modelling tools for the analysis of phenomena in machining. If effectively implemented, it can aid the decision-making process by producing precise cutting data that ensures the required surface roughness. A set of parameters (v\({}_{\text{c}}\) and s\({}_{\text{tr}}\)) fed into the system as input for computation is transformed into surface roughness parameter values (\(R\)z) for the tested machining parameters (milling, brushing) of the tested Mg alloys, AZ31 and AZ91D.
* The statistical analysis of Ra confirms that in the milling and brushing variant, the change in s\({}_{\text{tr}}\) is reflected in the statistically significant change in the values of Ra. The observed variance of means, however, appears to indicate a favorable effect of a higher trochoidal step on the surface finish (for s\({}_{\text{tr}}\) = 5% was 1.91 \(\upmu\)m and s\({}_{\text{tr}}\) = 30% was 1.63 \(\upmu\)m). A reverse effect was shown in the milling and brushing of AZ31 alloy.  
The authors declare no conflicts of interest.