# Design and Optimization of Synchronous Motor Using PM Halbach Arrays for Rim-Driven Counter-Rotating Pump

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Electromagnetic Design

#### 2.1. Design of Halbach Array Permanent Magnets

#### 2.2. Magnetic Circuit Design

#### 2.2.1. Tooth Sizing

#### 2.2.2. Yokes Thickness

#### 2.2.3. Slot Sizing

#### 2.3. Machine Efficiency

## 3. Thermal Sizing

#### 3.1. Iron Losses

#### 3.2. Copper Losses

#### 3.3. Iron Part Thermal Circuit Modeling

#### 3.4. Slot and Winding Modeling

#### 3.5. Heat Transfer Modeling

- The lateral surfaces are in contact with a gas (natural air or hydrogen).
- The internal surfaces are in contact with the liquid pushed by the blades of the rotor.

- For the external surface, the Nusselt number is given by:$${N}_{{u}_{ex}}=1.13\xb7{R}_{e}^{1.5}\xb7{P}_{r}^{1/3}$$
- For the internal side (gap), the determination of ${N}_{uex}$ is more complex. In the literature, there are several formulas that are used in the case of a thin space. In this paper, the expression used is the one described in [19]. ${h}_{c}$ is decomposed into an axial component ${h}_{ax}$ and tangential component ${h}_{tan}$. The Nusselt number for the axial convection, ${N}_{uax}$, is given by Equation (23), and for the tangential convection, the Nusselt number ${N}_{{u}_{tan}}$ is expressed in Equation (24)$${N}_{{u}_{ax}}=0.023\xb7{R}_{e}^{0.8}\xb7{P}_{r}^{1/3}$$$${N}_{{u}_{tan}}=0.409\xb7{T}_{a}^{0.241}.$$

## 4. Optimization Strategy, Objective, and Constraints

#### 4.1. Strategy

#### 4.2. Design Variables

#### 4.3. Objective

#### 4.4. Constraints

#### 4.5. Optimization Results

## 5. Finite Elements Method

#### 5.1. Flux Density and Back Electromotive Force

#### 5.2. Electromagnetic Torque and Cogging Torque

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

- Thermal model formulas

## References

- Dehnavi, E.; Kebdani, M.; Danlos, A.; Moises, S.; Bakir, F. Numerical analysis of Counter-Rotating Pump (CRP) including inducer and centrifugal impeller. In Proceedings of the 25ème Congrès Français de Mécanique Nantes, Nantes, France, 29 August–2 September 2022. [Google Scholar]
- Tuohy, P.M.; Smith, A.C.; Husband, M.; Hopewell, P. Rim-drive marine thruster using a multiple-can induction motor. IET Electr. Power Appl.
**2013**, 7, 557–565. [Google Scholar] [CrossRef] - Zhao, H.; Eldeeb, H.H.; Zhan, Y.; Ren, Z.; Xu, G.; Mohammed, O.A. Robust Electromagnetic Design of Double-Canned IM for Submergible Rim Driven Thrusters to Reduce Losses and Vibration. IEEE Trans. Energy Convers.
**2020**, 35, 2045–2055. [Google Scholar] [CrossRef] - Bolam, R.C.; Vagapov, Y. Implementation of electrical rim driven fan technology to small unmanned aircraft. In Proceedings of the 2017 Internet Technologies and Applications (ITA), Wrexham, UK, 12–15 September 2017; pp. 35–40. [Google Scholar] [CrossRef]
- Touimi, K.; Benbouzid, M.; Chen, Z. Optimal Design of a Multibrid Permanent Magnet Generator for a Tidal Stream Turbine. Energies
**2020**, 13, 487. [Google Scholar] [CrossRef][Green Version] - Zhou, Z.; Benbouzid, M.; Charpentier, J.F.; Scuiller, F.; Tang, T. Developments in large marine current turbine technologies—A review. Renew. Sustain. Energy Rev.
**2017**, 71, 852–858. [Google Scholar] [CrossRef] - Kaiser, B.E.; Poroseva, S.V.; Snider, M.A.; Hovsapian, R.O.; Johnson, E. Flow Simulation Around a Rim-Driven Wind Turbine and in Its Wake; Amer Soc Mechanical Engineers: New York, NY, USA, 2013. [Google Scholar]
- Djebarri, S.; Charpentier, J.F.; Scuiller, F.; Benbouzid, M.; Guemard, S. Rough Design of a Double-Stator Axial Flux Permanent Magnet Generator for a Rim-Driven Marine Current Turbine. In Proceedings of the 2012 IEEE International Symposium on Industrial Electronics, Hangzhou, China, 28–31 May 2012. [Google Scholar] [CrossRef][Green Version]
- Li, Y.; Song, B.; Mao, Z.; Tian, W. Analysis and Optimization of the Electromagnetic Performance of a Novel Stator Modular Ring Drive Thruster Motor. Energies
**2018**, 11, 1598. [Google Scholar] [CrossRef][Green Version] - Bolam, R.C.; Vagapov, Y.; Laughton, J.; Anuchin, A. Optimum Performance Determination of Single-Stage and Dual-Stage (Contra-Rotating) Rim Driven Fans for Electric Aircraft. In Proceedings of the 2020 XI International Conference on Electrical Power Drive Systems (ICEPDS), IEEE, Saint Petersburg, Russia, 4–7 October 2020; pp. 1–6. [Google Scholar]
- Ojaghlu, P.; Vahedi, A. Specification and Design of Ring Winding Axial Flux Motor for Rim-Driven Thruster of Ship Electric Propulsion. IEEE Trans. Veh. Technol.
**2019**, 68, 1318–1326. [Google Scholar] [CrossRef] - Cheng, B.; Pan, G.; Cao, Y. Analytical design of the integrated motor used in a hubless rim-driven propulsor. IET Electr. Power Appl.
**2019**, 13, 1255–1262. [Google Scholar] [CrossRef] - Amri, L.; Kebdani, M.; Zouggar, S.; Charpentier, J.F. Design and optimization of a rim driven motor for pump application. Mater. Today Proc.
**2022**, 72, 3775–3779. [Google Scholar] [CrossRef] - Atallah, K.; Howe, D. The application of Halbach cylinders to brushless ac servo motors. IEEE Trans. Magn.
**1998**, 34, 2060–2062. [Google Scholar] [CrossRef] - Dwari, S.; Parsa, L. Design of Halbach-Array-Based Permanent-Magnet Motors With High Acceleration. IEEE Trans. Ind. Electron.
**2011**, 58, 3768–3775. [Google Scholar] [CrossRef] - Sakamoto, H.; Harada, K.; Abe, H.; Tokuomi, S. A magnetic coupled charger with no-load protection. IEEE Trans. Magn.
**1998**, 34, 2057–2059. [Google Scholar] [CrossRef] - Drouen, L.; Hauville, F.; Charpentier, J.F.; Semail, E.; Clénet, S. A coupled electromagnetic/hydrodynamic model for the design of an integrated rim- driven naval propulsion system. In Proceedings of the ElectrIMACS, Quebec City, QC, Canada, 8–11 June 2008. [Google Scholar]
- Agrebi, H.Z.; Benhadj, N.; Chaieb, M.; Sher, F.; Amami, R.; Neji, R.; Mansfield, N. Integrated Optimal Design of Permanent Magnet Synchronous Generator for Smart Wind Turbine Using Genetic Algorithm. Energies
**2021**, 14, 4642. [Google Scholar] [CrossRef] - Drouen, L.; Charpentier, J.; Hauville, F.; Astolfi, J.; Semail, E.; Clenet, S. A multi physical approach for the design of RIM-DRIVEN Tidal Turbines. La Houille Blanche
**2015**, 101, 14–21. [Google Scholar] [CrossRef][Green Version] - Martínez, D. Design of a Permanent-Magnet Synchronous Machine with Non- Overlapping Concentrated Windings for the Shell Eco Marathon Urban Prototype. Master’s Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2012. [Google Scholar]
- Krøvel, Ø.; Nilssen, R.; Skaar, S.E.; Løvli, E.; Sandoy, N. “Design of an integrated 100kW Permanent Magnet Synchronous Machine in a Prototype Thruster for Ship Propulsion” in CD Rom. In Proceedings of the ICEM’2004, Cracow, Poland, 5–8 September 2004; pp. 117–118. [Google Scholar]
- Hanselman, D. Brushless Permanent Magnet Motor Design; The Writers’ Collective: Cranston, RI, USA, 2003. [Google Scholar]
- Mellor, P.H.; Roberts, D.; Turner, D.R. Lumped parameter thermal model for electrical machines of TEFC design. IEE Proc. B (Electr. Power Appl.)
**1991**, 138, 205–218. [Google Scholar] [CrossRef] - Proca, A.; Keyhani, A.; El-Antably, A.; Lu, W.; Dai, M. Analytical model for permanent magnet motors with surface mounted magnets. IEEE Trans. Energy Convers.
**2003**, 18, 386–391. [Google Scholar] [CrossRef] - Chebak, A.; Viarouge, P.; Cros, J. Analytical Model for Design of High-Speed Slotless Brushless Machines with SMC Stators. In Proceedings of the 2007 IEEE International Electric Machines and Drives Conference, Antalya, Turkey, 3–5 May 2007; Volume 1, pp. 159–164. [Google Scholar] [CrossRef]
- Perez, I.J.; Kassakian, J.G. A Stationary Thermal Model for Smooth Air-Gap Rotating Electric Machines. Electr. Mach. Power Syst.
**1979**, 3, 285–303. [Google Scholar] [CrossRef] - Irasari, P.; Alam, H.; Kasim, M. Magnetic Simulation and Analysis of Radial Flux Permanent Magnet Generator using Finite Element Method. J. Mechatron. Electr. Power Veh. Technol.
**2012**, 3, 23–30. [Google Scholar] [CrossRef][Green Version] - Abbasnezhad, N.; Kebdani, M.; Shirinbayan, M.; Champmartin, S.; Tcharkhtchi, A.; Kouidri, S.; Bakir, F. Development of a Model Based on Physical Mechanisms for the Explanation of Drug Release: Application to Diclofenac Release from Polyurethane Films. Polymers
**2021**, 13, 1230. [Google Scholar] [CrossRef] [PubMed] - Vijayan, A.K.; Xiao, D.; Batkhishig, B.; Callegaro, A.D.; Baranwal, R.; Emadi, A. Comparative Study on Pulse Pattern Optimization for High-Speed Permanent Magnet Synchronous Motors. In Proceedings of the 2022 IEEE Transportation Electrification Conference and Expo (ITEC), Haining, China, 28–31 October 2022; pp. 708–713. [Google Scholar] [CrossRef]
- Karnavas, Y.L.; Korkas, C.D. Optimization methods evaluation for the design of radial flux surface PMSM. In Proceedings of the 2014 International Conference on Electrical Machines (ICEM), IEEE, Berlin, Germany, 2–5 September 2014; pp. 1348–1355. [Google Scholar]
- Dridi, S.; Salem, I.B.; Amraoui, L.E. A Multi-Energetic Modeling Approach based on Bond Graph Applied to In-Wheel-Motor Drive System. Int. J. Adv. Comput. Sci. Appl.
**2018**, 9, 422–429. [Google Scholar] [CrossRef][Green Version] - Marquis-Favre, W.; Jardin, A. Bond Graphs and Inverse Modeling for Mechatronic System Design. In Bond Graph Modelling of Engineering Systems: Theory, Applications and Software Support; Borutzky, W., Ed.; Springer: New York, NY, USA, 2011; pp. 195–226. [Google Scholar] [CrossRef]
- Kebdani, M.; Dauphin-Tanguy, G.; Dazin, A.; Albach, R.; Dupont, P. Two-phase reservoir: Development of a transient thermo-hydraulic model based on bond graph approach with experimental validation. Math. Comput. Model. Dyn. Syst.
**2017**, 23, 476–503. [Google Scholar] [CrossRef] - Kebdani, M.; Dauphin-Tanguy, G.; Dazin, A.; Dupont, P. Experimental development and bond graph dynamic modelling of a brazed plate heat exchanger. Int. J. Simul. Process Model.
**2017**, 12, 249–263. [Google Scholar] [CrossRef][Green Version] - Felez, J.; Romero, G.; Maroto, J.; Martinez, M.L. Simulation of Multi-body Systems Using Multi-bond Graphs. In Bond Graph Modelling of Engineering Systems: Theory, Applications and Software Support; Borutzky, W., Ed.; Springer: New York, NY, USA, 2011; pp. 323–354. [Google Scholar] [CrossRef]
- Mohammed, A.; Sirahbizu, B.; Lemu, H.G. Optimal Rotary Wind Turbine Blade Modeling with Bond Graph Approach for Specific Local Sites. Energies
**2022**, 15, 6858. [Google Scholar] [CrossRef]

**Figure 1.**Structure of counter-rotating pump [1].

**Figure 4.**Peak magnetic flux density in the airgap as a function of ${l}_{g}$ and ${h}_{m}$. at a characterstic points A, B and C. Magnetic flux density at points A, B and C is given in Table 2.

**Figure 6.**Variation of the equivalent conductivity of the homogenate medium as a function of the filling factor ${k}_{r}$.

**Figure 8.**Structure with Halbach array magnet with progressive magnetization (

**a**) and its 2D mesh (

**b**).

**Figure 11.**Torque, electromagnetic toque and cogging torque for HAPMS (

**a**) and MMS (

**b**) as a function of electrical angle.

Parameter | Symbol | Unit | Value |
---|---|---|---|

Turbine external diameter | ${D}_{hel}$ | mm | 80 |

Remanence of the magnet | ${B}_{r}$ | T | 1.2 |

Rotor yoke thickness | ${h}_{ry}$ | mm | 7.67 |

Pole pair number | p | $--$ | 3 |

Point | ${\mathit{l}}_{\mathit{g}}$ (mm) | ${\mathit{h}}_{\mathit{m}}$ (mm) | ${{\mathit{B}}_{\mathit{e}}}_{\mathbf{max}}$ |
---|---|---|---|

A | 1 | 4 | 0.372 |

B | 5 | 4 | 0.2881 |

C | 1 | 20 | 1.071 |

Parameter | Unit | Symbol | Value |
---|---|---|---|

Rated speed | rpm | ${N}_{n}$ | 5000 |

Rated torque | N·m | ${T}_{m}$ | 10 |

Propeller diameter | m | ${D}_{h}el$ | 0.08 |

Airgap to propeller ratio | - | ${K}_{D}$ | $2\%$ |

Parameter | Symbol | Unit | Range of Variation |
---|---|---|---|

Current density | J | ${\mathrm{A}/\mathrm{mm}}^{2}$ | $[2..5]$ |

Electrical load | ${A}_{l}$ | A/mm | $[20..40]$ |

Pole pair number | p | − | $[1..3]$ |

Magnet height | ${h}_{m}$ | mm | $[1..10]$ |

Active length | L | mm | $[50..130]$ |

Parameter | Symbol | Unit | MMS | HAPM |
---|---|---|---|---|

Current density | J | ${\mathrm{A}/\mathrm{mm}}^{2}$ | 3.5 | 3.5001 |

Electrical load | ${A}_{l}$ | A/mm | 20.196 | 20 |

Pole pair number | p | − | 2 | 2 |

Maximal flux density | ${B}_{{e}_{max}}$ | T | 0.6831 | 0.6950 |

Active length | L | mm | 100 | 124.4 |

Total volume | V | ${\mathrm{mm}}^{3}$ | ${24.10}^{3}$ | ${12.10}^{3}$ |

Parameter | Unit | MMS | HAPM |
---|---|---|---|

L | mm | 100 | 124.36 |

D | mm | 109.13 | 102.06 |

${h}_{sy}$ | mm | 12.84 | 5.73 |

${h}_{ry}$ | mm | 12.84 | 1.4 |

${h}_{m}$ | mm | 1.56 | 8 |

${h}_{ss}$ | mm | 28.29 | 16.3 |

${w}_{tooth}$ | mm | 25 | 11.5 |

${T}_{average}$ | mm | 10.00 | 10.0008 |

Material | Characteristics | |
---|---|---|

Permeability | 14,872 | |

Iron | Electrical conductivity | 10.44 MS/m |

Thermal conductivity | 76.2 W/m·K | |

Magnets | Remanent flux density | 1.2 T |

Coercivity | 836.42 kA/m | |

Electrical conductivity | 0.667 MS/m | |

Work temperature | 80 °C |

Structure | Analytical Value (V) | FEM Value (V) | Error (%) |
---|---|---|---|

HAPMS | 222 | 254.55 | 12 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Amri, L.; Zouggar, S.; Charpentier, J.-F.; Kebdani, M.; Senhaji, A.; Attar, A.; Bakir, F. Design and Optimization of Synchronous Motor Using PM Halbach Arrays for Rim-Driven Counter-Rotating Pump. *Energies* **2023**, *16*, 3070.
https://doi.org/10.3390/en16073070

**AMA Style**

Amri L, Zouggar S, Charpentier J-F, Kebdani M, Senhaji A, Attar A, Bakir F. Design and Optimization of Synchronous Motor Using PM Halbach Arrays for Rim-Driven Counter-Rotating Pump. *Energies*. 2023; 16(7):3070.
https://doi.org/10.3390/en16073070

**Chicago/Turabian Style**

Amri, Lahcen, Smail Zouggar, Jean-Frédéric Charpentier, Mohamed Kebdani, Abdelhamid Senhaji, Abdelilah Attar, and Farid Bakir. 2023. "Design and Optimization of Synchronous Motor Using PM Halbach Arrays for Rim-Driven Counter-Rotating Pump" *Energies* 16, no. 7: 3070.
https://doi.org/10.3390/en16073070