## 4 Results and Discussion: Unbalanced Magnetic Forces
### Comparison of Slot/Pole Combinations for PMSMs and MPMSMs  
In Table 4, the average forces generated by different DE magnitudes are presented for both the modular and monolithic machines considering different slot/pole combinations. In the first place, it may be noted that not all selected slot/pole combinations exhibit unbalanced magnetic forces in the absence of eccentricity. Secondly, and according to the tendencies of Figure 4a,b, it can be seen that the generated radial forces are directly proportional to the eccentricity magnitude. This means that the radial force created by eccentricity can be quickly predicted from a single ECC value. From Table 4, it can be also noted that the unbalanced magnetic force increases as the slot number and pole number increase. The effect of the slot number can be noted from the comparison of the 18-slot, 20-pole machine to the 24-slot, 20-pole machine, which develops a consistent 20% force increase for all the evaluated ECC values. In consequence, it can be stated that the slot count has a medium impact on the radial forces generated by eccentricity and should not be neglected. In turn, the pole count effect can be deduced from the comparison of the 24-slot, 20-pole and the 24-slot, 28-pole machine, the latter having 12% more radial force. On the other hand, it is observed that in some slot/pole combinations, the radial force generated in the monolithic machine is significantly different from the modular machine. This can be explained by the flux density penalization of modular machines with a high value of \(q\) (See Equation (1)). To this end, Figure 5 shows the flux density lines for two slot/pole combinations that have different \(q\) values. Figure 5a,b show the flux lines when \(q\) is high, in which case the pole number is much smaller than the slot number. In this case, the flux lines require to travel through several teeth, crossing the stator yoke which is absent between the modules of MPMSMs. Therefore, in the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Q/2 pECC** & **0 mm (Faultless)** & **0.25 mm** & & **0.50 mm** & & **0.75 mm** & & **1.00 mm** \\ \hline \multirow{2}{*}{18S 12P} & Mod [N] & Mon [N] & Mod [N] & Mon [N] & Mod [N] & Mod [N] & Mon [N] & Mod [N] & Mon [N] \\  & 0 & 0 & 92 & 116 & 184 & 231 & 277 & 348 & 370 & 466 \\  & 0 & 0 & 148 & 151 & 296 & 304 & 446 & 458 & 599 & 614 \\  & 0 & 0 & 181 & 194 & 362 & 390 & 546 & 588 & 733 & 790 \\  & 0 & 0 & 192 & 200 & 385 & 401 & 580 & 604 & 780 & 813 \\  & 0 & 0 & 203 & 209 & 408 & 419 & 617 & 634 & 833 & 856 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average UMF of different PMSM and MPMSM slot/pole combinations in the presence of DE. modular machine, the flux lines will cross the gap between modules, circulating across a high-reluctance path that penalizes the airgap flux density and, subsequently, the radial forces. Instead, Figure 5c,d show the flux lines when \(q\) is lower, in which case the pole number is closer to the slot number. In this situation, flux lines need to use fewer teeth to close the path, which is the reason why in modular machines the lines can circulate using a single module and not penalize the airgap flux density to a high extend. In Table 5, the maximum radial force (ECC = 1 mm) for each slot/pole combination is presented and compared between modular and monolithic machines. It can be noted that, effectively, the difference between the radial forces generated on the modular machine vs. on the monolithic machine is higher as the value of \(q\) is greater. In Table 6, the radial force ripple generated by different magnitudes of DE is presented for each slot/pole combination. It is worth noting that slot/pole combinations with a lower difference between the slot count and the pole count exhibit the highest force ripple. This is particularly relevant since it translates into higher-frequency vibration and force pulses that can reach the bearings.