## 4 Validation
### Methods and Objectives
#### 4.1.2 Segmented Machines Test Cases  
The studied segmented structures (both stator and rotor segmentation) corresponds to the same specifications than the two reference structures of Tables 2 and 3. All the parameters of Tables 2 and 3 except the axial length are kept constant.  
In the case of a stator-segmented structure, the expression of the average linear electrical loading became (14) where \(n_{cd}\) is the total number of conductors per slot.  
\[A_{L}^{{}^{\prime}}=\frac{n_{cd}\times I\times Q_{s}}{\pi\times D}=\frac{n_{cd }\times I\times Q_{s0}(1-p_{gap})}{\pi\times D}=A_{L}\times(1-p_{gap}) \tag{14}\]  
In fact a global linear electric loading \(A_{L}^{{}^{\prime}}\), which will varie to be proportional with \((1-p_{gap})\), is introduced in the torque equation without considering the 3D correction factor (15). The local linear loading, \(A_{L}\), is maintained as constant (\(A_{L}\) is in this case the linear loading in the stator sector parts). In fact, to maintain, at first order, the same thermal behavior of the statoric parts for all the studied structures, \(A_{L}\) and \(J\) (current density in the conductors) are kept identical for all the studied cases (heat sources are supposed only located in the stator windings and heat is supposed to be evacuated radially).  
\[T_{em}=\sqrt{2}\times k_{w}\times A_{L}^{{}^{\prime}}\times B_{1}\times cos( \psi)\times L_{z0}\times\frac{\pi D^{2}}{4} \tag{15}\]  
To keep a constant torque, a new preliminary iron axial length, \(L_{z}^{{}^{\prime}}\) needs to be recalculated as a function of the segmentation rate \(p_{gap}\) (16).  
\[L_{z}^{{}^{\prime}}=\frac{T_{em}}{\sqrt{2}\times k_{w}\times A_{L}\times(1-p_{ gap})\times B_{1}\times cos(\psi)\times\frac{\pi\times D^{2}}{4}} \tag{16}\]  
It can be noticed that the 1 st harmonic of the no-load air gap flux density \(B_{1}\) does not vary with \(p_{gap}\). However the corrective factor \(\zeta_{\text{3D}}\) depends on the axial length (10), and thus depends on the gap ratio \(p_{gap}\).  
For each preliminary axial length, \(L_{z}^{{}^{\prime}}\), found for the different \(p_{gap}\) value, a corrective factor is calculated with the Equation (10). Thus this preliminary axial length is divided by the corresponding correction value \(\zeta_{\text{3D}}\) to have a final axial length, \(L_{z}\), that take into account the end effects in the segmented machine (Equation (17)).  
\[L_{z}=\frac{L_{z}^{{}^{\prime}}}{\zeta_{\text{3D}}(L_{z}^{{}^{\prime}})} \tag{17}\]  
Figure 14 shows the evolution of the axial length depending on the proportion of segmentation, with and without considering the 3D correction, for the machines designed for stator segmentation (Figure 14a) and for the ones designed for rotor segmentation (Figure 14b).  
It can be noticed that the suppression of the active part is compensated by the increase of the axial length. In other words, with the increase of \(p_{gap}\), the removed part due to the segmentation is added at the end of the machine in order to obtain the same torque performances. The relative parts of 3D effects decrease with the segmentation because higher the axial length value is, lower the relative part of 3D effects is.  
For the validation part, the considered gap topologies are presented in the Table 4.  
For the \(p_{gap}\) variation, angular gaps are located on the circumference of the machine with a regular distribution, as said in Section 2.  
In the case of a rotor-segmented structure, the equations that describe the analytical models presented earlier (Section 3.3), does not depend of \(n_{gap}\). So the number of gaps does not affect electromagnetic performance estimation like the cogging torque and the electromotive forces for this case. This hypothesis is verified by numerical simulations. The effects of \(n_{gap}\) are negligible for structure with segmented rotor (\(n_{gap}>0\)). So the influence of the variation of \(n_{gap}\) is only studied for stator-segmented structures.