## 4 Conclusions  
Trochoidal milling is an appealing machining strategy for increasing the process efficiency. As indicated by the performed studies, it may be effectively employed for the machining of the AZ91D magnesium alloy. The milling process can be considered as relatively stable, since the vibration generated during its performance is low. Furthermore, the following conclusions could be derived from the achieved results:  
* The changes in cutting speed and feed per tooth have substantial impact on the displacement and acceleration of machining vibration generated during the milling process. This applies to both the intensity of the vibration and the sensitivity of the process on their appearance. The selection of appropriate machining parameters can therefore significantly increase the stability and safety of milling. * Considering vibration displacement, the ER or hydraulic toolholder is the most favourable type (depending on the change in technological parameters), while when analysing the vibration acceleration, the most beneficial type is the shrinkfit toolholder. The advantages of using the shrinkfit toolholder were also observed when analysing the signals in the frequency domain, as it generated the lowest vibration magnitude and was the least sensitive type to changes in cutting parameters. * Based on the analysis of the signals using Composite Multiscale Entropy, it can be concluded that trochoidal milling exhibits less abrupt changes in dynamics, which has good influence on the stability of the cutting process. * It was observed that increasing the cutting speed causes a reduction in the Composite Multiscale Entropy level, which implies an increase in signal ordering. Milling performed at a higher cutting speed \(v_{c}\) therefore has a positive impact on the machining process' stability. That phenomenon was observed for all three toolholders used. The ER and hydraulic toolholders can be applied over a wider range of feed per tooth while maintaining stability in milling processes. * The increase in cutting speed caused an increase in amplitude, as well as a decrease in the number of the harmonic frequencies at which peaks occurred. At the highest cutting speed, vibration occurred only at frequencies resulting from the tooth passing frequency and its harmonics. A similar behaviour occurred when changing the feed per tooth. * The results of the FFT analysis corresponded reasonably well with the information available from the generated Stability Lobe Diagram. This confirms that with their use, it is possible to pre-determine the machining condition under which an unfavourable vibration should not occur. * The results of displacement and vibration acceleration measurements varied considerably, and therefore the selection of a suitable measurement sensor is of particular importance. * Entropy did not exceed the values of 1.5 for cutting speed and 2.5 for feed per tooth, respectively. Vibration acceleration did not exceed (in most cases) the value of 20 m/s\({}^{2}\) for the peak-to-peak parameter and the shrinkfit toolholder. For vibration displacement (peak-to-peak parameter), there were oscillations around the value of 0.9 mm for all kinds of toolholders. The trochoidal strategy yielded satisfactory results. Nevertheless, further research is required to fully assess its benefits. In subsequent studies, it is planned to apply trochoidal machining to other magnesium alloys. Not only vibration but also other machinability indices will need to be investigated and evaluated. Conceptualization, J.K. and I.Z. ; methodology, J.K., I.Z. and A.W. ; software, J.K.; validation, J.K., I.Z., A.W. and W.H. ; formal analysis, J.K., I.Z., A.W. and W.H. ; investigation, J.K., I.Z. and A.W. ; resources, I.Z. and A.W. ; data curation, J.K.; writing--original draft preparation, J.K., I.Z., A.W. and W.H. ; writing--review and editing, J.K., I.Z., A.W. and W.H. ; visualization, J.K.; supervision, J.K. and I.Z. ; project administration, J.K. and I.Z. ; funding acquisition, I.Z.