# Torque Analysis of a Flat Reconfigurable Magnetic Coupling Thruster for Marine Renewable Energy Systems Maintenance AUVs

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## Abstract

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## 1. Introduction

- Classical rear propeller with control surface architectures, as in large conventional submarine equipped with rudders;
- Biomimetic propulsion, i.e., inspired by natural propulsion mechanisms present in marine life, e.g., dolphin and whale fins;
- Vectorial thrust (VT), which can be achieved with one or a set of propellers, whose thrust vectors drive and steer the vehicle without the need for control surfaces.

- They do not need to reorient their motor axis to reconfigure the thrust vector. Only their propeller, duct or nozzle must be reoriented. Thus, reduced power and torque values are required in the maneuvers.
- They need three actuators to ensure 2-DOF of VT reconfiguration.
- They need mechanical seals, since the movement is transmitted through shafts or rods, which implies frictions and likely watertightness issues.

- Movement transmission between insulated environments
- Complex and unsure mechanical seals are no longer needed
- Robot watertightness is not jeopardized by a hull breach
- It eliminates the friction inherent to mechanical seals and joints
- The magnetic coupling also works as a mechanical fuse (torque limiter) to protect the motor in case of severe load peaks (where a gearbox would break)
- Eventual vibrations are mitigated (spring effect)
- Low maintenance when it is compared to a mechanical coupling or a universal joint

^{TM}Wolfram language [22]. It is expected to be able to answer the bellow RMCT questions:

- What is the complete reconfigurable magnetic coupling torque behavior, and how does it depend on all angles?
- What torque must the servomotor apply to control the propeller orientation?

## 2. The Flat Reconfigurable Magnetic Coupling Thruster or Flat-RMCT

## 3. Magnetostatic Numerical Modeling

^{TM}[22] software, which calls the solver, receives the results, and manages the optimization process if necessary.

## 4. Numerical and Experimental Investigation

#### 4.1. Numerical Model Validation from Experimental Results

#### 4.2. Magnetic Coupling Torques: Spring and Auto-Driving Rotors Effects

#### 4.3. Auto-Driving Effect Amplitude Model

#### 4.4. Magnetic Spring Effect ${T}_{z}$ Results and Model

^{TM}software function.

#### 4.5. Restoring Torque ${T}_{Rest}$

## 5. Discussion

## 6. Conclusion and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MRE | Marine Renewable Energy |

AUV | Autonomous Underwater Vehicle |

RMCT | Reconfigurable Magnetic Coupling Thrusters |

VT | Vectorial Thrust |

RT | Reconfigurable Thruster |

FT | Fixed Thruster |

DOF | Degree of Freedom |

MMR | Minimum Magnetic Reluctance |

## References

- Chocron, O.; Prieur, U.; Pino, L. A validated feasibility prototype for AUV reconfigurable magnetic coupling thruster. IEEE/ASME Trans. Mechatron.
**2014**, 19, 642–650. [Google Scholar] [CrossRef] - Vega, E.P.; Chocron, O.; Ferreira, J.V.; Benbouzid, M.E.H.; Meirelles, P.S. Evaluation of AUV Fixed and Vectorial Propulsion Systems with Dynamic Simulation and Non-linear Control. In Proceedings of the 41st Annual Conference of the IEEE Industrial Electronics Society (IECON 2015), Yokohama, Japan, 9–12 November 2015; pp. 944–949. [Google Scholar]
- Yu, J.; Su, Z.; Wu, Z.; Tan, M. Development of a Fast-Swimming Dolphin Robot Capable of Leaping. IEEE/ASME Trans. Mechatron.
**2016**, 21, 2307–2316. [Google Scholar] [CrossRef] - Yu, J.; Zhang, C.; Liu, L. Design and Control of a Single-Motor-Actuated Robotic Fish Capable of Fast Swimming and Maneuverability. IEEE/ASME Trans. Mechatron.
**2016**, 21, 1711–1719. [Google Scholar] [CrossRef] - Pollard, B.; Tallapragada, P. An Aquatic Robot Propelled by an Internal Rotor. IEEE/ASME Trans. Mechatron.
**2017**, 22, 931–939. [Google Scholar] [CrossRef] - Zhang, S.; Qian, Y.; Liao, P.; Qin, F.; Yang, J. Design and Control of an Agile Robotic Fish With Integrative Biomimetic Mechanisms. IEEE/ASME Trans. Mechatron.
**2016**, 21, 1846–1857. [Google Scholar] [CrossRef] - Mazumdar, A.; Triantafyllou, M.S.; Asada, H.H. Dynamic Analysis and Design of Spheroidal Underwater Robots for Precision Multidirectional Maneuvering. IEEE/ASME Trans. Mechatron.
**2015**, 20, 2890–2902. [Google Scholar] [CrossRef] - Vega, E.P.; Chocron, O.; Benbouzid, M.E.H. AUV Propulsion Systems Modeling Analysis. Int. Rev. Model. Simul.
**2014**, 7, 827–837. [Google Scholar] [CrossRef] - Jin, S.; Kim, J.; Kim, J.; Seo, T. Six-Degree-of-Freedom Hovering Control of an Underwater Robotic Platform With Four Tilting Thrusters via Selective Switching Control. IEEE/ASME Trans. Mechatron.
**2015**, 20, 2370–2378. [Google Scholar] [CrossRef] - Chocron, O.; Mangel, H. Reconfigurable magnetic-coupling thrusters for agile AUVs. In Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France, 22–26 September 2008; pp. 3172–3177. [Google Scholar]
- Lin, X.; Guo, S. Development of a spherical underwater robot equipped with multiple vectored water-jet-based thrusters. J. Intell. Robot. Syst. Theory Appl.
**2012**, 67, 307–321. [Google Scholar] [CrossRef] - Li, Y.; Guo, S.; Wang, Y. Design and characteristics evaluation of a novel spherical underwater robot. Robot. Auton. Syst.
**2017**, 94, 61–74. [Google Scholar] [CrossRef] - Kopman, V.; Cavaliere, N.; Porfiri, M. MASUV-1: A miniature underwater vehicle with multidirectional thrust vectoring for safe animal interactions. IEEE/ASME Trans. Mechatron.
**2012**, 17, 563–571. [Google Scholar] [CrossRef] - Cavallo, E.; Michelini, R.C.; Filaretov, V.F. Conceptual design of an AUV equipped with a three degrees of freedom vectored thruster. J. Intell. Robot. Syst. Theory Appl.
**2004**, 39, 365–391. [Google Scholar] [CrossRef] - Gao, F.d.; Han, Y.y.; Wang, H.d.; Xu, N. Analysis and innovation of key technologies for autonomous underwater vehicles. J. Cent. South Univ.
**2015**, 22, 3347–3357. [Google Scholar] [CrossRef] - Highfill, G.; Halverson, L. Lowering total cost of ownership with breakthrough magnetic torque transfer technology. In Proceedings of the IEEE Cement Industry Technical Conference, Phoenix, AZ, USA, 9–14 April 2006; p. 15. [Google Scholar]
- Gasparoto, H.F.; Chocron, O.; Benbouzid, M.; Meirelles, P.S. Magnetic design and analysis of a radial reconfigurable magnetic coupling thruster for vectorial AUV propulsion. In Proceedings of the 43rd Annual Conference of the IEEE Industrial Electronics Society (IECON 2017), Beijing, China, 29 October–1 November 2017; pp. 2876–2881. [Google Scholar]
- Vega, E.P.; Chocron, O.; Benbouzid, M.E.H. A Flat Design and Validated Model for AUV Reconfigurable Magnetic Coupling Thruster. IEEE/ASME Trans. Mechatron.
**2016**, 21, 2892–2901. [Google Scholar] [CrossRef] - Lubin, T.; Fontchastagner, J.; Mezani, S.; Rezzoug, A. Comparison of Transient Performances for Synchronous and Eddy-current Torque Couplers. In Proceedings of the 2016 XXII International Conference on Electrical Machines (ICEM), Lausanne, Switzerland, 4–7 September 2016; pp. 697–703. [Google Scholar]
- Chubar, O.; Elleaume, P.; Chavanne, J. A three-dimensional magnetostatics computer code for insertion devices. J. Synchrotron Radiat.
**1998**, 5, 481–484. [Google Scholar] [CrossRef] [PubMed][Green Version] - Chubar, O.; Elleaume, P.; Chavanne, J. RADIA 4.31. 2016. Available online: http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/Radia (accessed on 24 December 2018).
- Wolfram Research Inc. Mathematica 11.0; Wolfram Research Inc.: Champaign, IL, USA, 2016. [Google Scholar]
- Hornreich, R.; Shtrikman, S. Optimal design of synchronous torque couplers. IEEE Trans. Magn.
**1978**, 14, 800–802. [Google Scholar] [CrossRef] - Yonnet, J.P. Permanent magnet bearings and couplings. IEEE Trans. Magn.
**1981**, 17, 1169–1173. [Google Scholar] [CrossRef] - Yonnet, J.P. A new type of permanent magnet coupling. IEEE Trans. Magn.
**1981**, 17, 2991–2993. [Google Scholar] [CrossRef] - Bastos, J.; Sadowski, N. Maxwell Equations, Electrostatics, Magnetostatics and Magnetodynamic Fields. In Electromagnetic Modeling by Finite Element Methods; Bastos, J.P.A., Sadowski, N., Eds.; Marcel Dekker: New York, NY, USA, 2003. [Google Scholar]
- Tlali, P.M.; Wang, R.J.; Gerber, S. Magnetic gear technologies: A review. In Proceedings of the 21st International Conference on Electrical Machines (ICEM 2014), Berlin, Germany, 2–5 September 2014; pp. 544–550. [Google Scholar]
- Chocron, O.; Mangel, H. Models and simulations for reconfigurable magnetic-coupling thrusters technology. Int. Rev. Model. Simul.
**2011**, 4, 325–334. [Google Scholar] - Yan, L.; Liu, D.; Jiao, Z.; Chen, C.Y.; Chen, I.M. Modeling of magnetic field and design optimization for permanent-magnet spherical actuator in three dimensional space. In Proceedings of the 10th IEEE Conference on Industrial Electronics and Applications (ICIEA 2015), Auckland, New Zealand, 15–17 June 2015; pp. 1904–1909. [Google Scholar]
- Meeker, D.C. FEMM—Finite Element Method Magnetics. 2016. Available online: http://www.femm.info/wiki/HomePage (accessed on 24 December 2018).

**Figure 3.**Flat-RMCT plan views: (

**a**) side view with ${\alpha}_{max}$ and $\theta ={\theta}_{m}={\theta}_{h}=0\xb0$. (

**b**) front view without the propeller soft-iron yoke, with $\alpha =0\xb0,\theta >0\xb0,{\theta}_{m}>0\xb0,{\theta}_{h}>0\xb0$.

**Figure 4.**(

**a**) Flat-RMCT model in the neutral configuration ($\alpha =0\xb0$), represented on RADIA. (

**b**) Magnetization $\mathbf{M}$ in each element after the relaxation process.

**Figure 5.**Experimental setup to measure the propeller side rotor torque ${T}_{{h}_{z}}$ in function of $\alpha $ and $\theta $. (

**a**) $\alpha =30.5\xb0$. (

**b**) $\alpha =0\xb0$.

**Figure 6.**Propeller torque variation simulations in function of ${\theta}_{m}$ for ${\alpha}_{max}$, for $\theta =-0.5\xb0$, 0° and 0.5°.

**Figure 8.**Numerical (black dots) and experimental (red dots) results for the magnetic spring effect ${T}_{z}(\alpha ,\theta )$.

**Figure 9.**$\theta $ axis view of simulation and experimental results for the magnetic spring effect ${T}_{z}(\alpha =\{0\xb0,30.5\xb0\},\theta )$, validating the numerical model.

**Figure 10.**$\alpha $ axis view of simulation and experimental results for ${T}_{z}(\alpha ,\theta )$.

**Figure 11.**Error of the approximated torque function for ${T}_{z}(\alpha ,\theta )$ in comparison to simulations.

**Figure 13.**Torques absolute difference $|T{h}_{z}|-|T{m}_{z}|\phantom{\rule{0.166667em}{0ex}}\left[\mathrm{mNm}\right]$ for ${\alpha}_{max}$ in function of $\theta $ and ${\theta}_{m}$.

${\mathit{T}}_{{\mathit{h}}_{\mathit{z}}}$ [mNm] | Experiments | Numerical Model | ||
---|---|---|---|---|

${\mathit{T}}_{{\mathit{h}}_{\mathit{z}}}$ | ${\mathit{T}}_{{\mathit{h}}_{\mathit{z}}}$ | Rel. Error | ||

$\theta =0\xb0$ | $\alpha =\{0\xb0,30.5\xb0\}$ | 0.0 | 0.0 | 0% |

$\theta =45\xb0$ | $\alpha =0\xb0$ | 373.1 ± 3.3 | 371.6 | 0.4% |

$\alpha =30.5\xb0$ | 607.1 ± 5.3 | 595.6 | 1.9% |

${\mathit{A}}_{\mathbf{0}}$ | ${\mathit{A}}_{\mathbf{1}}$ | ${\mathit{A}}_{\mathbf{2}}$ | ${\mathit{A}}_{\mathbf{3}}$ | ${\mathit{B}}_{\mathbf{0}}$ | ${\mathit{B}}_{\mathbf{1}}$ | ${\mathit{B}}_{\mathbf{2}}$ |
---|---|---|---|---|---|---|

14.057 | 1.1654 | 14.676 | 26.306 | 20.578 | 14.461 | −9.1914 |

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## Share and Cite

**MDPI and ACS Style**

Fagundes Gasparoto, H.; Chocron, O.; Benbouzid, M.; Siqueira Meirelles, P.; Saraiva Ferreira, L.O.
Torque Analysis of a Flat Reconfigurable Magnetic Coupling Thruster for Marine Renewable Energy Systems Maintenance AUVs. *Energies* **2019**, *12*, 56.
https://doi.org/10.3390/en12010056

**AMA Style**

Fagundes Gasparoto H, Chocron O, Benbouzid M, Siqueira Meirelles P, Saraiva Ferreira LO.
Torque Analysis of a Flat Reconfigurable Magnetic Coupling Thruster for Marine Renewable Energy Systems Maintenance AUVs. *Energies*. 2019; 12(1):56.
https://doi.org/10.3390/en12010056

**Chicago/Turabian Style**

Fagundes Gasparoto, Henrique, Olivier Chocron, Mohamed Benbouzid, Pablo Siqueira Meirelles, and Luiz Otávio Saraiva Ferreira.
2019. "Torque Analysis of a Flat Reconfigurable Magnetic Coupling Thruster for Marine Renewable Energy Systems Maintenance AUVs" *Energies* 12, no. 1: 56.
https://doi.org/10.3390/en12010056