## 3 PMSM Design Process
With the help of the specific equations, the following factors, among others, were determined: width \(B_{s2}\), diameter of the rotor \(D_{r}\), diameter of the shaft \(D_{shaft}\), outer diameter of the stator \(D_{o}\), area of the groove of the stator \(A_{s}\), mass of the rotor core M\({}_{Rovale}\), mass of the magnets M\({}_{magnets}\), mass of the shaft M\({}_{shaft}\), friction losses P\({}_{t}\), Reynolds coefficient R\({}_{sg}\), coefficient \(C_{f}\), windage losses P\({}_{wind}\), converted power P\({}_{conv}\), phase current \(I_{ph}\), total area of copper conductors inside the groove \(A_{Cu}\), and slot filling factor of the groove \(s_{f}\). The iteration structure was completed when all constraints had been met and the stator geometric characteristics had been defined. The equations below include various quantities, such as density of the steel \(\rho_{sted}\) that was used to make the stator core and rotor and shaft, density of the magnet material \(\rho_{magnets}\), and density of air \(\rho_{air};k_{v}\) is the kinematic viscosity of air. It is noted that for the case of the stator core and the rotor, electrical steel was used. Instead, non-magnetic steel was used for the shaft. \[\mathrm{N_{s}}=\frac{\mathrm{Q_{s}n_{s}}}{6} \tag{17}\]7  
\[\mathrm{N_{s}}=\frac{\mathrm{Q_{s}n_{s}}}{6} \tag{17}\]8  
\[\mathrm{N_{s}}=\frac{\mathrm{Q_{s}n_{s}}}{6} \tag{17}\]9  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]0  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]1  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]2  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]3  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]4  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]5  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]6  
\[B_{mr}(r,\theta)=\sum_{n=1,3,5}^{\infty}K_{B}(n)f_{Br}(r)\cos(np\theta) \tag{18}\]7  
\[C_{f}=\left\{ \begin{array}{c}1.03\frac{\left(\text{L}_{g}/D_{r}\right)^{0 3}}{R_{sg}^{03}},\text{\qquad for \ }R_{eg}\geq 50\text{ and }R_{eg}\leq 10^{4}\\ 0.065\frac{\left(\text{L}_{g}/D_{r}\right)^{03}}{R_{sg}^{03}},\text{\qquad for \ }R_{eg}>10^{4}\end{array} \right. \tag{52}\]  
\[\text{P}_{\text{wind}}=\left(\frac{D_{r}}{2}\right)^{4}\text{L}\left(\frac{ 120f}{2p}\right)^{3}\pi\rho_{air}C_{f} \tag{53}\]  
\[\text{P}_{\text{conv}}=\text{P}_{\text{out}}+\text{P}_{t}+\text{P}_{\text{ wind}} \tag{54}\]  
\[I_{ph}=\frac{\text{P}_{\text{conv}}}{3\text{E}} \tag{55}\]  
\[A_{Cu}=\frac{I_{ph}}{I_{s}} \tag{56}\]  
\[s_{f}=\frac{A_{Cu}}{A_{s}} \tag{57}\]With the geometric characteristics of the engine now being known, we proceeded to calculate its electrical quantities. These included the resistance of stator winding \(R\) and its total inductance \(L\). Resistance \(R\) was determined through Equation (58), where \(\rho_{\text{Cu}}\) is the density of the copper and \(k_{ew}\) is a coefficient related to the end-windings. The value of the specific resistance had to be corrected using to Equation (59), taking into account the temperature adopted during the design process. \[R=\frac{\rho_{\text{Cu}}n_{s}^{2}q[2 pL+k_{ew}\pi(D_{s}+H_{s0}+H_{s1}+H_{s2})]}{ s_{f}A_{s}} \tag{58}\]  
\[R^{\prime}=R(1+0.004041(T-20)) \tag{59}\]  
As far as the inductance of the winding is concerned, it included two components: (a) the synchronous magnetizing inductance \(L_{m}\); and (b) the leakage inductance \(L_{l}\). The first component was calculated using (60). The leakage inductance was a sum of the leakage inductance due to slots \(L_{sl}\), the leakage inductance due to stator teeth \(L_{tl}\), and leakage inductance due to the ends of the windings \(L_{el}\). The specific values were calculated using Equations (61)-(65).