**6.2 Case study**

verifications of machine performances. If not, reset the initial values such as combination of stator slot and rotor slot number, electric loading, equivalent

magnetic loading, etc.

*Direct Torque Control Strategies of Electrical Machines*

**Figure 27.**

**92**

*Design flow of FRPMM.*

In order show the effectiveness of the introduced analytical method, a FRPMM is designed based on the method. **Table 4** shows the specifications of the FRPMM, which mainly includes the rated torque, machine volume, cooling method, rated power, and speed. According to the rated torque, a design margin of 5% is suggested so as to make sure the torque output. Therefore, the requirement of the torque is 8.4 Nm for this design. Then, the combination of stator slots and rotor slots is determined in the first place. This combination is selected due to its high torque density and low pulsating torque, as shown in **Figure 13**. Then, since the cooling method is natural cooling, the electric loading and the equivalent magnetic loading are chosen as 300A/cm and 0.2 T, respectively. After that, based on the output torque value 8.4 Nm and Eq. (29), the airgap radius is determined as 38.5 mm. Furthermore, assuming the yoke flux density of stator core and rotor core as 1.0 T, and the teeth flux density of stator core and rotor core as 1.2 T, the detailed


#### **Table 4.**

*Design specifications of a three-phase FRPMM.*


#### **Table 5.**

*Design parameters of the FRPMM using the design method.*

## *Direct Torque Control Strategies of Electrical Machines*


geometric parameters can all be determined. At last, the stator outer diameter is worked out as 124 mm, which is less than the requirement 130 mm. So far, this design is effective. **Table 5** summarizes the design parameters of the FRPMM. Finally, in order to verify the accuracy of the proposed analytical design method, the FEA model is built, and the simulated performances are compared to the analytical designed values. It can be seen in **Table 6** that the FEA simulated results match well with the analytical method. More importantly, the simulated performance output satisfies the design specifications. Therefore, this analytical design is

To verify the calculated results by the analytical method and FEA, the FRPMM prototype has been built. Its major parameters are listed in **Table 4**. The structure and test bed of the prototype are shown in **Figures 28** and **29**, respectively.

**Parameter FEA Experiment** Average torque at rated current 7.97 Nm 7.24 Nm Torque per weight 0.66 Nm/kg 0.60 Nm/kg Phase back-EMF magnitude at 300 rpm 42.4 V 41.2 V THD of the phase back-EMF at 300 rpm 1.26% 2.63% Total losses 99.5 W 116.7 W Efficiency 60.3% 57.3% Power factor 0.756 0.746

*Result comparison of FEA and experiment of the FRPMM prototype.*

successful.

**Figure 31.**

**Table 7.**

**95**

*Output torque vs. phase current.*

**6.3 Experimental study**

*Flux Reversal Machine Design*

*DOI: http://dx.doi.org/10.5772/intechopen.92428*

**Table 6.**

*Results comparison of the design method and 2D FEA.*

**Figure 28.** *12-slot/17-pole FRPMM prototype: (a) stator; (b) rotor.*

**Figure 29.** *Test bed of the FRPMM prototype.*

**Figure 30.** *Back-EMF waveforms at rated speed 300 rpm: (a) waveform; (b) FFT analysis.*

#### *Flux Reversal Machine Design DOI: http://dx.doi.org/10.5772/intechopen.92428*

geometric parameters can all be determined. At last, the stator outer diameter is worked out as 124 mm, which is less than the requirement 130 mm. So far, this design is effective. **Table 5** summarizes the design parameters of the FRPMM. Finally, in order to verify the accuracy of the proposed analytical design method, the FEA model is built, and the simulated performances are compared to the analytical designed values. It can be seen in **Table 6** that the FEA simulated results match well with the analytical method. More importantly, the simulated performance output satisfies the design specifications. Therefore, this analytical design is successful.
