**7. Conclusions**

The design of FRPMMs is usually based on time-stepping FEA, which are accurate but time-consuming. To save the design time meanwhile maintain the accuracy, this chapter proposes an analytical design method of FRPMMs. First, the sizing equation is derived, and then the dimensional parameters of stator and rotor are calculated. Finally, based on the above equations, an analytical design procedure is established. Moreover, in order to help to choose the initial design parameters in the sizing equation, including number of stator slots and rotor slots, airgap radius, electrical loading, and equivalent magnetic loading, their effects on the average torque, cogging torque, torque ripple, and power factor are investigated, providing reliable guidance for designers. At last, in order to make the introduced design methodology easier to understand, a FRPMM is designed and tested.

### **Acknowledgements**

This work was supported by National Natural Science Foundation of China (NSFC) under Project Number 51807076, and Alexander von Humboldt Foundation.

#### **Nomenclature**


**Author details**

*Flux Reversal Machine Design*

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

\* and Yang Liu2

provided the original work is properly cited.

1 Karlsruhe Institute of Technology, Karlsruhe, Germany

\*Address all correspondence to: gyt626890@gmail.com

2 Wuhan Institute of Marine Electric Propulsion, Wuhan, China

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Yuting Gao<sup>1</sup>

**97**

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

**Figure 30** compares the phase back-EMF waveform and spectrum at 300 rpm. It can be seen that the back-EMF waveforms are very sinusoidal. This is because the total harmonic distortion (THD) of FEA and experiments are only 1.26% and 2.63%, respectively. The sinusoidal back-EMF is inherent without any special design techniques such as skewing or pole shaping. Then, **Figure 31** shows the FEA simulated and experimental results of average torque at different winding current values. In addition, the analytical design value is also plotted as the blue triangle. It indicates that the simulated, analytical and experimental results have reached good agreements. Finally, **Table 7** compares the electromagnetic performances by FEA and experiments. Thus, the feasibility of the analytical design method can be seen.

*Direct Torque Control Strategies of Electrical Machines*

The design of FRPMMs is usually based on time-stepping FEA, which are accurate but time-consuming. To save the design time meanwhile maintain the accuracy, this chapter proposes an analytical design method of FRPMMs. First, the sizing equation is derived, and then the dimensional parameters of stator and rotor are calculated. Finally, based on the above equations, an analytical design procedure is established. Moreover, in order to help to choose the initial design parameters in the sizing equation, including number of stator slots and rotor slots, airgap radius, electrical loading, and equivalent magnetic loading, their effects on the average torque, cogging torque, torque ripple, and power factor are investigated, providing reliable guidance for designers. At last, in order to make the introduced design

methodology easier to understand, a FRPMM is designed and tested.

This work was supported by National Natural Science Foundation of China (NSFC) under Project Number 51807076, and Alexander von Humboldt Foundation.

**7. Conclusions**

**Acknowledgements**

**Nomenclature**

*g* airgap length *rg* airgap radius

*lstk* active stack length *Zr* number of rotor teeth

phase *a*

**96**

*Zs* number of stator teeth SPP slot per pole per phase

*Br* remanent flux density

*μ<sup>r</sup>* relative permeability of magnets

*Ns* number of series turns per phase *P* number of stator winding pole pairs

*ω<sup>m</sup>* mechanical angular speed of rotor

*g'* effective airgap length considering PM thickness *hm* PM height along the magnetization direction

*SO* stator slot opening ratio (=slot opening width/slot pitch)

*θ* angular position of rotor axis with respect to the axis of phase *a*

PR pole ratio (=rotor pole number/winding pole pair)

*θ<sup>s</sup>* particular position in the stator reference frame measured from the axis of
