## 5 Conclusions  
In this work, a sensitivity analysis procedure to optimize the design of PMSMs was developed. A global sensitivity analysis procedure was employed, based on the Monte Carlo method, in order to study the influence of the most critical design parameters of the machine in a wide input parameter range.  
Regarding the definition of the sensitivity analysis, it was concluded that the method is not suitable when there are dependencies between the input parameters. In order to obtain consistent results, all the input parameters must be independent. According to the Monte Carlo probable error and the definition of the sensitivity indices, 5000 samples were selected to reach an agreement between accuracy and computational cost.  
Figure 9: Scattered plot of all the simulated cases.  
Moreover, the nominal value of the inputs affects their influence on the output parameters, but as long as the variation is not very significant, the differences are not remarkable. Thus, the conclusions obtained with the proposed calculation procedure for a particular machine can be extrapolated to similar configurations.  
The method is more sensitive to the upper and lower limits of the input parameters. Generally, if an input is varied within a higher range, its effect on the output parameters will be increased. Therefore, the ranges of the input parameters should be defined according to the design restrictions of every specific study case.  
After analysing the correct definition of the sensitivity analysis procedure, the particular case of a PMSM was studied, and some design guidelines were presented, with the objective of maximizing the torque produced by the machine while minimizing the vibrations.  
Increasing the internal diameter of the rotor or the height of the magnets, the permanent magnet volume is increased, which produces higher magnetic forces. Thus, although a higher torque could be obtained by modifying these two parameters, they penalize the vibration response at the same extent, so modifying them would not be an adequate solution.  
An interesting option would be to increase the length of the stator, as the machine would produce a higher torque, with a negligible effect on the vibration response. This conclusion is valid for short machines, as the influence of this parameter on the vibration response will be more significant in much longer machines.  
The opposite phenomenon occurs with the height of the stator yoke. As this parameter affects the stiffness of the stator, it changes the vibration significantly, but it does not affect the magnetic forces. Therefore, a thicker stator would improve the vibration response without compromising the torque.  
Increasing the length of the air gap could be another interesting solution. Even though a slightly lower torque would be produced, the reduction of vibrations would be more significant. In addition, the length of the air gap has a high sensitivity to the manufacturing tolerances, so a higher value would help reduce its variability.  
Conceptualization, M.M. and A.M.; methodology, A.M. and J.P.; software, M.M.; validation, J.P. and S.Z.; investigation, M.M. and A.M.; resources, L.I.; data curation, S.Z.; writing--original draft preparation, M.M.; writing--review and editing, S.Z. and L.I.; visualization, M.M.; supervision, J.P.; project administration, L.I.; funding acquisition, A.M. and L.I. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Basque Government (MECOVA ZL-2019/00554 and VEGAN KK21-0044, and predoctoral grant), by the Provincial Council of Gipuzkoa (NVHCONTROL), and by Orona EIC.  
The authors declare no conflict of interest.  
The following abbreviations are used in this article:  
GCD Greatest Common Divisor  
PMSM Permanent Magnet Synchronous Motor  
RMS Root-Mean Square