## Materials and Methods
### Design and Analysis of AFPMSM  
Designing AFPMSMs, as well as other typologies of drives, has steps. The first step is usually determined by requirements or constraints such as required torque size, speed, maximum permissible dimensions of the machine, cooling method and maximum induced voltage. Therefore, at the beginning of this process, the required dimensions of the machine, especially the internal diameter of the installation of permanent magnets and windings, the external diameter of the machine (rotor and stator) and the axial length of the machine must be specified as accurately as possible. To determine these parameters, the standard approach is to use the so-called sizing equations [7; 26]. Two types of sizing equations can be found in the scientific literature [44]. The first type is a classical equation (Equation (3)) which considers the outer diameter and the axial length of the machine [27] when calculating the output power of the machine \(P_{\rm i}\) (in addition to the electric and magnetic parameters), where \(i(t)\) is phase electrical current, \(m\) is the number of phases, \(e(t)\) the open circuit-induced voltage (phase value), \(\eta\) the efficiency of the machine, \(K_{\rm P}\) the electric power shape factor, \(T\) is one period of induced voltage, and \(E_{\rm pk}\) and \(I_{\rm pk}\) are peak values of the induced voltage and phase current [27]. \[P_{\rm i}=\eta\frac{m}{T}\int\limits_{0}^{T}e(t)i(t)dt\ = \eta mK_{\rm P}E_{\rm pk}I_{\rm pk} \tag{3}\]  
The emphasis of this article is on the second type of sizing equation, which refers to the connection between the electromagnetic torque and the basic geometric, electrical and magnetic parameters (Equation (4)) [45]. \[T_{\rm em}=2\pi B_{\rm z}A_{\rm i}\lambda\big{(}1-\lambda^{2}\big{)}R_{\rm o}^{3} \tag{4}\]  
In Equation (4), \(T_{\rm em}\) is electromagnetic torque, \(B_{\rm z}\) the axial component of magnetic flux density, \(A_{\rm i}\) the average electric load on the radius that matches the inner radius of PMs, \(R_{\rm o}\) the outer PM radius, \(R_{\rm i}\) the inner PM radius and \(\lambda\) the ratio between the inner and outer PM radius. This equation was first introduced in [45], and since then it has been widely used [9; 21; 46], since it is generally useful. From this equation we can detect the magnetic shear stress when divided by the active surface of the rotor. In the presented form, it achieves greater accuracy in the case of a trapezoidal distribution of the magnetic flux density and at higher values of electrical current through areas where the magnetic flux density is maximal. It is also possible to determine the torque density by dividing the equation with the mass of active machine parts (Nm/kg) or the total machine volume (Nm/m\({}^{3}\)). After completing the evaluation of the main geometric parameters, the design process can be continued according to the standard steps [9; 44], which are presented below. The number of the machine's synchronous revolutions according to Equation (5), can be determined:  
\[n_{\rm s}=\frac{60f}{p} \tag{5}\]  
where \(n_{\rm s}\) is the synchronous speed of the machine, \(f\) the network frequency and \(p\) the number of pole pairs. It can be seen that the higher number of poles of the machine is required for lower synchronous rotations. The winding factor (\(k_{\rm w}\)) is determined by the geometric method, from the ratio between the geometric (\(e_{\rm geometric}\)) and arithmetic (\(e_{\rm arithmetic}\)) value of the induced voltage (Equation (6)) [23]. \[k_{\rm w}=\frac{\sum e_{\rm geometric}}{\sum e_{\rm arithmetic}} \tag{6}\]  
Saturation factor (\(k_{\rm sat}\)) is determined by Equation (7) [11]:  
\[k_{\rm sat}=1+\frac{l_{\rm Fe}}{2\mu_{\rm r}\big{(}d_{\rm ag}+0.5d_{\rm Fe} \big{)}} \tag{7}\]  
where \(l_{\rm Fe}\) is the magnetic flux path in the iron, \(d_{\rm ag}\) the air gap thickness (between rotor and stator), \(d_{\rm Fe}\) the rotor disk thickness and \(\mu_{\rm r}\) the relative permeability of steel.