# Modeling and Validation of the Radial Force Capability of Bearingless Hysteresis Drives

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Numerical Modeling

**A**over a discretized domain

**H**being the magnetic field vector,

**J**the current density,

**B**the magnetic flux density vector, σ the electrical conductivity,

**v**the velocity of the conductor (which is null in the present analyses),

**J**an externally generated current density and

_{e}**E**the electric field. This simulation can be executed either in stationary mode or, as in this study, in time-stepping mode. Further details about the implemented formulation can be found in [25].

## 4. Test Procedure

- The system is preloaded by unscrewing the fastener interfacing the load cell and the upper plate. This operation causes a relative displacement between the upper and the lower plates. Therefore, the preload is produced by the compliant beams.
- The journal is moved by means of the sliding micrometer to approach the actuator edge. This position is identified as soon as the preload changes.
- The journal is moved through the sliding micrometer to set the desired nominal air gap. The output of the eddy current sensor is recorded as reference.

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Galluzzi, R.; Tonoli, A.; Amati, N. Magnetic hysteresis machines for next-generation electric turbochargers. In Proceedings of the 2017 International Conference of Electrical and Electronic Technologies for Automotive, Torino, Italy, 15–16 June 2017; pp. 1–5. [Google Scholar] [CrossRef]
- Nasiri-Zarandi, R.; Mirsalim, M.; Tenconi, A. A Novel Hybrid Hysteresis Motor With Combined Radial and Axial Flux Rotors. IEEE Trans. Ind. Electr.
**2016**, 63, 1684–1693. [Google Scholar] [CrossRef] - Chiba, A. (Ed.) Magnetic Bearings and Bearingless Drives; OCLC: 179729376; Elsevier/Newnes: Amsterdam, The Netherlands; London, UK, 2005. [Google Scholar]
- Bleuler, H.; Cole, M.; Keogh, P.; Larsonneur, R.; Maslen, E.; Okada, Y.; Schweitzer, G.; Traxler, A. Magnetic Bearings: Theory, Design, and Application to Rotating Machinery; Springer Science & Business Media: Berlin, Germany, 2009. [Google Scholar]
- Lin, F.C.; Yang, S.M. Self-Bearing Control of a Switched Reluctance Motor Using Sinusoidal Currents. IEEE Trans. Power Electr.
**2007**, 22, 2518–2526. [Google Scholar] [CrossRef] - Okada, Y.; Yamashiro, N.; Ohmori, K.; Masuzawa, T.; Yamane, T.; Konishi, Y.; Ueno, S. Mixed Flow Artificial Heart Pump with Axial Self-Bearing Motor. IEEE/ASME Trans. Mech.
**2005**, 10, 658–665. [Google Scholar] [CrossRef] - Lei, S.; Palazzolo, A. Control of flexible rotor systems with active magnetic bearings. J. Sound Vib.
**2008**, 314, 19–38. [Google Scholar] [CrossRef] - Baumgartner, T.; Burkart, R.M.; Kolar, J.W. Analysis and Design of a 300-W 500,000-r/min Slotless Self-Bearing Permanent-Magnet Motor. IEEE Trans. Ind. Electr.
**2014**, 61, 4326–4336. [Google Scholar] [CrossRef] - Filatov, A.; Hawkins, L.; McMullen, P. Homopolar Permanent-Magnet-Biased Actuators and Their Application in Rotational Active Magnetic Bearing Systems. Actuators
**2016**, 5, 26. [Google Scholar] [CrossRef] - Lusty, C.; Bailey, N.Y.; Keogh, P.S. Control of Flexible Rotor Vibration with Flexibly Mounted Active Magnetic Bearings. In Proceedings of the 10th International Conference on Rotor Dynamics—IFToMM; Cavalca, K.L., Weber, H.I., Eds.; Springer International Publishing: Cham, Switzerland, 2019; pp. 65–73. [Google Scholar]
- Bonfitto, A.; Botto, G.; Chiaberge, M.; Suarez Cabrera, L.; Tonoli, A. A multi-purpose control and power electronic architecture for active magnetic. In Proceedings of the 2012 15th International Power Electronics and Motion Control Conference (EPE/PEMC), Novi Sad, Serbia, 4–6 September 2012; p. DS2b.9-1. [Google Scholar]
- Ferreira, J.; Maslen, E.; Fittro, R. Transpermeance Amplifier Applied to Magnetic Bearings. Actuators
**2017**, 6, 9. [Google Scholar] [CrossRef] - Bonfitto, A.; Castellanos Molina, L.M.; Tonoli, A.; Amati, N. Offset-Free Model Predictive Control for Active Magnetic Bearing Systems. Actuators
**2018**, 7, 46. [Google Scholar] [CrossRef] - Bonfitto, A.; Tonoli, A.; Silvagni, M. Sensorless active magnetic dampers for the control of rotors. Mechatronics
**2017**, 47, 195–207. [Google Scholar] [CrossRef] - Castellanos, L.M.; Bonfitto, A.; Tonoli, A.; Amati, N. Identification of Force-Displacement and Force-Current Factors in an Active Magnetic Bearing System. In Proceedings of the 18th Annual IEEE International Conference on Electro Information Technology, Rochester, MI, USA, 3–5 May 2018. [Google Scholar]
- Noshadi, A.; Shi, J.; Lee, W.S.; Shi, P.; Kalam, A. System Identification and Robust Control of Multi-Input Multi-Output Active Magnetic Bearing Systems. IEEE Trans. Control Syst. Technol.
**2016**, 24, 1227–1239. [Google Scholar] [CrossRef] - Noh, M.; Gruber, W.; Trumper, D.L. Hysteresis Bearingless Slice Motors with Homopolar Flux-Biasing. IEEE/ASME Trans. Mech.
**2017**, 22, 2308–2318. [Google Scholar] [CrossRef] [PubMed] - Gerada, D.; Mebarki, A.; Brown, N.L.; Gerada, C.; Cavagnino, A.; Boglietti, A. High-Speed Electrical Machines: Technologies, Trends, and Developments. IEEE Trans. Ind. Electr.
**2014**, 61, 2946–2959. [Google Scholar] [CrossRef][Green Version] - Jagiela, M.; Bumby, J.; Spooner, E. Time-domain and frequency-domain finite element models of a solid-rotor induction/hysteresis motor. IET Electr. Power Appl.
**2010**, 4, 185–197. [Google Scholar] [CrossRef] - Nejad, M.I. Self-Bearing Motor Design & Control. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2013. [Google Scholar]
- Zhou, L.; Imani Nejad, M.; Trumper, D.L. One-axis hysteresis motor driven magnetically suspended reaction sphere. Mechatronics
**2017**, 42, 69–80. [Google Scholar] [CrossRef] - Liu, Y.P.; Liu, K.Z.; Yang, X. Nonlinear Current Control for Reluctance Actuator with Hysteresis Compensation. J. Control Sci. Eng.
**2014**, 2014, 1–7. [Google Scholar] [CrossRef][Green Version] - Katalenic, A.; de Boeij, J.; Butler, H.; van den Bosch, P. Linearization of a current-driven reluctance actuator with hysteresis compensation. Mechatronics
**2013**, 23, 163–171. [Google Scholar] [CrossRef] - Vrijsen, N.H.; Jansen, J.W.; Lomonova, E.A. Prediction of Magnetic Hysteresis in the Force of a Prebiased E-Core Reluctance Actuator. IEEE Trans. Ind. Appl.
**2014**, 50, 2476–2484. [Google Scholar] [CrossRef] - COMSOL Multyphysics Reference Manual, version 5.3; COMSOL, Inc. Available online: www.comsol.com (accessed on 1 October 2018).
- Bergqvist, A. A simple vector generalization of the Jiles–Atherton model of hysteresis. IEEE Trans. Magn.
**1996**, 32, 4213–4215. [Google Scholar] [CrossRef] - Kis, P.; Iványi, A. Parameter identification of Jiles-Atherton model with nonlinear least-square method. Phys. B Condens. Matter
**2004**, 343, 59–64. [Google Scholar] [CrossRef] - Szewczyk, R.; Frydrych, P. Extension of the Jiles-Atherton Model for Modelling the Frequency Dependence of Magnetic Characteristics of Amorphous Alloy Cores for Inductive Components of Electronic Devices. Acta Phys. Pol. A
**2010**, 118, 782–784. [Google Scholar] [CrossRef] - Antila, M.; Lantto, E.; Arkkio, A. Determination of forces and linearized parameters of radial active magnetic bearings by finite element technique. IEEE Trans. Magn.
**1998**, 34, 684–694. [Google Scholar] [CrossRef] - Jiles, D.C.; Atherton, D.L. Theory of ferromagnetic hysteresis (invited). J. Appl. Phys.
**1984**, 55, 2115–2120. [Google Scholar] [CrossRef] - Chwastek, K.; Szczyglowski, J. Identification of a hysteresis model parameters with genetic algorithms. Math. Comput. Simul.
**2006**, 71, 206–211. [Google Scholar] [CrossRef]

**Figure 1.**Experimental test rig (

**a**); section view of the experimental setup (

**b**): 1. Seismic mass; 2. Micrometric planar positioning stage; 3. Support of the journal; 4. Upper plate; 5. Housing of the electromagnetic actuators; 6. Journal; 7. Cores of the electromagnets; 8. Proximitor sensor; 9. Flexible beams; 10. Lower plate; 11. Load cell-upper plate interface; 12. Load cell; 13. Seismic mass.

**Figure 2.**Magnetic characteristic of both the soft magnetic material and the laminated high permeability steel.

**Figure 3.**Radial (

**a**) and tangential (

**b**) magnetic characteristics of the FeCrCo 48/5 alloy: experimental (solid); numerical (dash-dotted).

**Figure 4.**2D finite element model: + and - refer to the domains where a positive and a negative current density ${J}_{e}$ is applied (

**a**); meshed geometry of the system based on the semi-hard magnetic material (

**b**).

**Figure 5.**3D finite element model showing the planes used to reduce the size of the numerical model (

**a**); meshed geometry of the system based on the semi-hard magnetic material (

**b**).

**Figure 6.**Numerical and experimental forces generated by the system based on the soft magnetic journal at 0.55 mm air gap: experimental data (cross); 2D model with magnetic air gap (dashed); 2D model with geometric air gap (dash-dotted); 3D model with geometric air gap (dotted). The dotted and dash-dotted lines are superimposed.

**Figure 7.**Magnetic flux density norm (surface plot) and magnetic vector potential (contour plot) over the cross-section of the 3D model based on the FeCrCo 48/5 at 0.55 mm air gap and 6 A supplied current.

**Figure 8.**Numerical and experimental forces generated by the system based on the FeCrCo 48/5 journal at 0.55 mm (

**a**), 0.50 mm (

**b**) and 0.45 mm (

**c**) air gap: experimental data (cross); 3D model with magnetic air gap (dashed); 2D model with magnetic air gap (dash-dotted). Loading and unloading curves are related to the current increase from 0 to 6 A and the current decrease from 6 to 0 A, respectively. The grey solid line in (

**a**) is the force achieved from the 2D model with magnetic air gap (same as Figure 6).

**Figure 9.**One quarter of the stator of the radial 8-poles radial actuator: ${\mathsf{\Phi}}_{T}$ is the magnetic flux straying through the top face of one polar expansion; ${\mathsf{\Phi}}_{P}$ is the magnetic flux flowing through the polar area.

**Figure 10.**Ratio between the magnetic flux through the top face of one polar expansion of the electromagnet and the flux flowing through the polar area at 0.55 mm (solid), 0.50 mm (dashed) and 0.45 mm (dash-dotted) air gap for the system based on the FeCrCo 48/5 journal. Loading and unloading curves are related to the current increase from 0 to 6 A and the current decrease from 6 to 0 A, respectively.

Symbol | Quantity | Value |
---|---|---|

${A}_{pole}$ | Polar area | 225 mm^{2} |

${d}_{r}$ | Journal inner diameter | $20.0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathrm{m}$ |

${D}_{r}$ | Journal outer diameter | $30.3\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathrm{m}$ |

${d}_{s}$ | Stator inner diameter | $31.4\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathrm{m}$ |

h | Journal height | $22.5\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathrm{m}$ |

N | Turns per electromagnet | 106 |

Symbol | Quantity | Value |
---|---|---|

${\alpha}_{xx},\phantom{\rule{0.166667em}{0ex}}{\alpha}_{zz}$ | Local field factor (radial) | $0.16$ |

${c}_{xx},\phantom{\rule{0.166667em}{0ex}}{c}_{zz}$ | Domain rotation loss (radial) | $0.69$ |

${a}_{xx},\phantom{\rule{0.166667em}{0ex}}{a}_{zz}$ | Langevin parameter (radial) | $9.93\times {10}^{4}\phantom{\rule{0.166667em}{0ex}}\mathrm{A}/\mathrm{m}$ |

${k}_{xx},\phantom{\rule{0.166667em}{0ex}}{k}_{zz}$ | Pinning (radial) | $1.41\times {10}^{5}\phantom{\rule{0.166667em}{0ex}}\mathrm{A}/\mathrm{m}$ |

${M}_{Sxx},\phantom{\rule{0.166667em}{0ex}}{M}_{Szz}$ | Saturation magnetization (radial) | $1.84\times {10}^{6}\phantom{\rule{0.166667em}{0ex}}\mathrm{A}/\mathrm{m}$ |

${\alpha}_{yy}$ | Local field factor (tangential) | $0.15$ |

${c}_{yy}$ | Domain rotation loss (tangential) | $0.20$ |

${a}_{yy}$ | Langevin parameter (tangential) | $9.94\times {10}^{4}\phantom{\rule{0.166667em}{0ex}}\mathrm{A}/\mathrm{m}$ |

${k}_{yy}$ | Pinning (tangential) | $5.16\times {10}^{4}\phantom{\rule{0.166667em}{0ex}}\mathrm{A}/\mathrm{m}$ |

${M}_{Syy}$ | Saturation magnetization (tangential) | $2.02\times {10}^{6}\phantom{\rule{0.166667em}{0ex}}\mathrm{A}/\mathrm{m}$ |

Air Gap [mm] | Current | Error % |
---|---|---|

$0.55$ | 1 $\mathrm{A}$-Unloading | 18 |

$0.50$ | 2 $\mathrm{A}$-Unloading | 19 |

$0.45$ | 3 $\mathrm{A}$-Unloading | 16 |

**Table 4.**Ratio between the forces generated at 0.55 $\mathrm{m}\mathrm{m}$ air gap by the electromagnet based on the soft and the semi-hard magnetic material, respectively.

Current [$\mathbf{A}$] | ${\mathbf{F}}_{\mathbf{soft}}/{\mathbf{F}}_{\mathbf{SHMM}}$ (Loading) | ${\mathbf{F}}_{\mathbf{soft}}/{\mathbf{F}}_{\mathbf{SHMM}}$ (Unloading) |
---|---|---|

1 | $6.9$ | $0.6$ |

2 | $5.7$ | $1.4$ |

3 | $4.8$ | $2.0$ |

4 | $4.3$ | $2.5$ |

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**MDPI and ACS Style**

Circosta, S.; Galluzzi, R.; Bonfitto, A.; Castellanos, L.M.; Amati, N.; Tonoli, A. Modeling and Validation of the Radial Force Capability of Bearingless Hysteresis Drives. *Actuators* **2018**, *7*, 69.
https://doi.org/10.3390/act7040069

**AMA Style**

Circosta S, Galluzzi R, Bonfitto A, Castellanos LM, Amati N, Tonoli A. Modeling and Validation of the Radial Force Capability of Bearingless Hysteresis Drives. *Actuators*. 2018; 7(4):69.
https://doi.org/10.3390/act7040069

**Chicago/Turabian Style**

Circosta, Salvatore, Renato Galluzzi, Angelo Bonfitto, Luis M. Castellanos, Nicola Amati, and Andrea Tonoli. 2018. "Modeling and Validation of the Radial Force Capability of Bearingless Hysteresis Drives" *Actuators* 7, no. 4: 69.
https://doi.org/10.3390/act7040069