# Loss Research and Thermal Analysis of BLDC Hollow-Cup Motor Under Reactor Suppression
## 3 Improvement Design Study
### Rotor Eddy Current Loss Analysis  
The motor rotor eddy current loss is caused by the harmonic magnetic field generated by the current harmonics, while the armature potential harmonics cause an increase in rotor eddy current loss [21]. The previous Equations (1)-(8) are analyzed. It can be noticed that the amplitude of the armature potential harmonic is inversely proportional to the armature inductance and directly proportional to the flux density harmonic amplitude. [PERSON]'s law of electromagnetic induction is considered, and it is known that the induced electromotive force is generated in an alternating magnetic field, causing eddy currents to form on the surface of the permanent magnet. Equations for induced electromotive force and induced electromotive force magnitude are shown below [21].  
\[E_{\text{eddy}}=-\frac{\partial B_{m}}{\partial t}l_{\text{PM}}w_{\text{PM}}, \tag{13}\]  
\[E=l_{\text{PM}}w_{\text{PM}}\times\sum nB_{n}f_{n}, \tag{14}\]  
where \(B_{\text{m}}\) is the harmonic magnetic field, \(l_{\text{PM}}\) is the axial length of PM, \(w_{\text{PM}}\) is the radial length of PM, \(n\) is the number of each harmonic, \(B_{n}\) is the harmonic magnetic density amplitude, and \(f_{n}\) is the relative motion frequency. The PM eddy current loss equation is shown below [21].  
\[P_{\text{PM}}=\left[\frac{h_{\text{PM}}w^{3}{{\text{PM}}^{\prime}}^{3}{{\text{ PM}}^{\prime}}}{2(w^{2}{{\text{PM}}}+l^{2}{{\text{PM}}})}\sum\left(\frac{|i_{s}|}{ \sqrt{3/2}l_{\text{m}}}\right)^{2}{n^{2}}{f_{n}}^{2}{B_{n}}^{2}\right].V_{ \text{PM}}, \tag{15}\]  
where \(h_{\text{PM}}\) is the radial length of PM, \(i_{s}\) is the RMS value of the excitation current, \(I_{\text{m}}\) is the motor input current amplitude, and \(V_{\text{PM}}\) is the volume of PM.  
To analyze the effect of reactor inductance value on the rotor eddy current loss, the rotor eddy current loss is analyzed using the FEM when the series reactor inductance value is 0 uH and 15 uH. The rotor eddy current loss cloud diagrams for inductance values of 0 uH and 15 uH are shown in Figure 11.  
Figure 10: Air-gap flux density time-harmonic amplitude before and after series connection of 15 uH reactor: (**a**) radial air-gap flux density time-harmonic amplitude; (**b**) tangential air-gap flux density time harmonic amplitude.  
Analysis of Figure 11 shows that the maximum rotor eddy current loss density is 1204.62 W/m\({}^{3}\) when the value of reactor inductance is 0 uH, and the maximum rotor eddy current loss density is 942.26 W/m\({}^{3}\) when the value of reactor inductance is 15 uH. The rotor eddy current loss of the BLDC hollow-cup motor is significantly reduced, by about 22% at the maximum loss density, with the series connection of a 15 uH reactor.  
Through the above electromagnetic analysis, it is observed that a reactor with an inductance value of 15 uH in series between the BLDC hollow-cup motor and the controller can effectively suppress the current harmonics and the resulting armature potential harmonics. This leads to a reduction in the core loss and rotor eddy current loss generated during motor operation.