## Materials and Methods
### Least Square Approximation Method  
Values for \(B_{\rm z,min}\) were used to produce a polynomial using a least square approximation (LSA) method. This is a mathematical procedure that can find a curve that fits best to a known set of given points by minimizing the sum of the squares of the offsets (\"the residuals\") of the points from the curve [42]. The sum of the squares of the offsets was used instead of the offset absolute values because this allows the residuals to be treated as a continuous differentiable quantity [43]. Vertical least squares fitting proceeds by finding the sum of the squares of the vertical deviations \(R^{2}\) of a set of \(n\) data points [43], which is presented in Equation (1). \[R^{2}\equiv\sum_{i=1}^{n}[y_{\rm i}-f(x_{\rm i},a_{1},a_{2},\ldots,a_{\rm n})] ^{2} \tag{1}\]  
where \(R\) is the residual, \(y_{\rm i}\) is the data point calculated using simplified FEM, \(f\) is the fitting function, \(x_{\rm i}\) is an independent variable of the fitting function, and \(a_{1}\), \(a_{2}\), and \(a_{\rm n}\) are coefficients of the fitting function. In our case the polynomial was chosen as a fitting function. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Quantity** & **Value/Unit** \\ \hline \(d_{\rm Fe}\) & Rotor disk thickness & 7 mm \\ \(h_{\rm PM}\) & Permanent magnet thickness & 5 mm \\ \(\tau_{\rm m}\) & Magnetic pitch & 25\({}^{\circ}\) \\ \(D_{\rm i}\) & Inner diameter of PM & 80 mm \\ \(D_{\rm o}\) & Outer diameter of PM & 150 mm \\ \(\tau_{\rm p}\) & Pole pitch & 36\({}^{\circ}\) \\ \(I\) & Electrical current & \(2\times 10\) A \\  & Number of windings & 6 \\ \(d_{s}\) & Winding thickness & 15 mm \\ \(d_{c}\) & Coil width & 20 mm \\ \(S_{\rm w}\) & Copper wire cross section & 1.23 mm\({}^{2}\) \\ \(d_{\rm ag}\) & Air gap thickness & 1 mm \\ \(k_{\rm w}\) & Winding factor & 0.966 \\ \(p\) & Number of pole pairs & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: This geometry and parameters of the AFPMSM with 10 poles. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Quantity** & **Value/Unit** \\ \hline \(d_{\rm Fe}\) & Rotor disk thickness & 7 mm \\ \(h_{\rm PM}\) & Permanent magnet thickness & 5 mm \\ \(\tau_{\rm m}\) & Magnetic pitch & 12\({}^{\circ}\) \\ \(D_{\rm i}\) & Inner diameter of PM & 80 mm \\ \(D_{\rm o}\) & Outer diameter of PM & 150 mm \\ \(\tau_{\rm p}\) & Pole pitch & 18\({}^{\circ}\) \\ \(I\) & Electrical current & 2 \(\times\) 10 A \\  & Number of windings & 12 \\ \(d_{s}\) & Winding thickness & 15 mm \\ \(d_{c}\) & Coil width & 15 mm \\ \(S_{\rm w}\) & Copper wire cross section & 1.23 mm\({}^{2}\) \\ \(d_{\rm ag}\) & Air gap thickness & 1 mm \\ \(k_{\rm w}\) & Winding factor & 0.966 \\ \(p\) & Number of pole pairs & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: This geometry and parameters of the AFPMSM with 20 poles. Different order functions were used in order to determine the best fitting polynomial. Since three parameters were considered (stator thickness, rotor thickness and PM thickness) a function with 3 unknowns must be included (Figure 3). Using the procedure described above, a mathematical model in explicit form was obtained for the calculation of the axial component of magnetic flux density in the middle of the stator, where PM thickness (from 5 to 10 mm), stator (up to 4 times PM thickness) and rotor disk thickness (from 4 to 15 mm) was considered (Equation (2)):  
\[