**5. Conclusions**

The cost of bonded magnets is lower compared with sintered magnets. Furthermore, in contrast with sintered magnets, bonded magnets are dielectric. Therefore, there is no need for segmentation of bonded magnets when using them in a motor, which leads to a lower motor price and a simpler manufacturing technology for a high-speed motor. However, bonded magnets have lower remanence and coercivity. In this study, the problem of developing a flux reversal motor (FRM) with bonded magnets was considered, in which the proposed FRM with bonded magnets has approximately the same efficiency as an FRM

with sintered magnets [11]. In addition to this requirement, the peak-to-peak value of torque ripple (*PPTR*) is minimized and the minimum instantaneous torque value in two operating modes is maximized.

Due to the lower coercivity of bonded magnets, it is necessary to avoid their demagnetization in the optimized design. For this purpose, a procedure has been developed for the optimal design of a high-speed single-phase FRM with bonded magnets.

The main challenge in this work was the development of a single-phase flux reversal motor with an asymmetrical rotor which was introduced in [11], which has low torque ripple and no negative torque periods when applying bonded magnets, considering a new constraint on the volume of demagnetized magnets. The constraint must be taken into account to enable the use of bonded magnets for this motor. For this, in particular, the optimization criterion (2) with soft constraints was composed.

The optimization criterion was constructed in such a way so as to maximize the efficiency, reduce torque ripple, and reduce the volume of the demagnetized bonded magnets. The one-criterion Nelder–Mead method was applied in this work to optimize the FRM design. After the optimization, the total losses of the FRM decreased by 1.2 times. The demagnetization constraint was met with a margin. The torque oscillations *A* were reduced by 4%.

In future works, we plan to compare various optimization methods in the design of a single-phase flux reversal motor with an asymmetrical rotor and to manufacture and test an experimental prototype of the FRM.

**Author Contributions:** Conceptual approach, V.P. and V.D.; data curation, V.D. and V.K.; software, V.D. and V.P.; calculations and modeling, V.P., V.D. and V.K.; writing—original draft, V.P., V.D. and V.K.; visualization, V.D. and V.K.; review and editing, V.P., V.D. and V.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** All data are contained within the article.

**Acknowledgments:** The authors thank the editors and reviewers for their careful reading and constructive comments.

**Conflicts of Interest:** The authors declare no conflict of interest.
