# Design and Analysis of a Plate Type Electrodynamic Suspension Structure for Ground High Speed Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Ground High Speed System

## 3. Analysis of the Plate Type EDS Structure

#### 3.1. Levitation Working Point

#### 3.2. Guidance Stiffness

#### 3.3. Effects of Speed

#### 3.4. Magnet Design

#### 3.4.1. Distribution of Magnetic Field

#### 3.4.2. Magnet Thickness

#### 3.4.3. Magnet Length

#### 3.4.4. Magnet Arrangement

#### 3.5. Plate Design

#### 3.5.1. Plate Materials

#### 3.5.2. Plate Height

#### 3.5.3. Plate Thickness

#### 3.6. Distribution of Levitation Forces on NS Magnets

## 4. Conclusions

- The levitation working point is better to be set around 1/3 height of PM to get enough levitation force, and it can be moved to a larger h when SC magnet is applied in the design.
- The lateral stiffness at low speeds is relatively insufficient compared with that at high speeds, and guidance wheels can be adopted.
- The effects of different speeds on magnetic forces are studied and the levitation-drag ratio improves with the increasing of magnets speed.
- PM and SC magnet have the same distribution of magnetic field, and the proper thickness and length of magnet are set. NS arranged magnets show better performance than NN arranged magnets.
- Copper plate could provide larger levitation force and higher levitation-drag ratio than aluminum plate. Proper height and thickness of plate are decided based on the performance and the construction cost.
- The non-uniform distribution of levitation forces on NS magnets will disappear at high speeds.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Palacin, R. Hyperloop, the electrification of mobility, and the future of rail travel. IEEE Electr. Mag.
**2016**, 4, 4–51. [Google Scholar] [CrossRef] - Hyperloop Alpha. Available online: http://www.spacex.com/hyperloopalpha (accessed on 12 August 2013).
- Lee, H.W.; Kim, K.C.; Lee, J. Review of maglev train technologies. IEEE Trans. Magn.
**2006**, 42, 1917–1925. [Google Scholar] [CrossRef] - Yan, L. Development and application of the maglev transportation system. IEEE Trans. Appl. Supercond.
**2008**, 18, 92–99. [Google Scholar] [CrossRef] - Davey, K. Analysis of an electrodynamic Maglev system. IEEE Trans. Magn.
**1999**, 35, 4259–4267. [Google Scholar] [CrossRef] - Long, Z.; He, G.; Xue, S. Study of EDS & EMS hybrid suspension system with permanent-magnet halbach array. IEEE Trans. Magn.
**2011**, 47, 4717–4724. [Google Scholar] [CrossRef] - Hsu, Y.H.; Langhom, A.; Ketchen, D.; Holland, L.; Minto, D.; Doll, D. Magnetic levitation upgrade to the Holloman High Speed Test Track. IEEE Trans. Appl. Supercond.
**2009**, 19, 2074–2077. [Google Scholar] [CrossRef] - Okubo, T.; Ueda, N.; Ohashi, S. Effective control method of the active damper system against the multidirectional vibration in the superconducting magnetically levitated bogie. IEEE Trans. Appl. Supercond.
**2016**, 26. [Google Scholar] [CrossRef] - Lee, C.Y.; Jo, J.M.; Han, Y.J. Design, fabrication, and operating test of the Prototype HTS electromagnet for EMS-based maglev. IEEE Trans. Appl. Supercond.
**2012**, 22. [Google Scholar] [CrossRef] - Xu, J.; Geng, Q.; Li, Y.; Li, J. Design, fabrication and test of an HTS magnetic suspension experimental system. IEEE Trans. Appl. Supercond.
**2016**, 26. [Google Scholar] [CrossRef] - Yan, L. Suggestion for selection of Maglev option for Beijing-Shanghai high-speed line. IEEE Trans. Appl. Supercond.
**2004**, 14, 936–939. [Google Scholar] [CrossRef] - Du, J.; Ohsaki, H. Numerical analysis of eddy current in the EMS-Maglev system. In Proceedings of the 6th IEEE International Conference on Electrical Machines and Systems, 2003, ICEMS 2003, Beijing, China, 9–11 November 2003; pp. 761–764. [Google Scholar]
- Ding, J.; Yang, X.; Long, Z.; Dang, N. Three dimensional numerical analysis and optimization of electromagnetic suspension system for 200 km/h maglev train considering eddy current effect. IEEE Access.
**2018**, 6, 1547–1555. [Google Scholar] [CrossRef] - Abdelrahman, A.S.; Sayeed, J.; Youssef, M.Z. Hyperloop transportation system: Analysis, design, control and implementation. IEEE Trans. Ind. Electron.
**2018**, 65, 7427–7436. [Google Scholar] [CrossRef] - Ji, W.Y.; Jeong, G.; Park, C.B.; Jo, I.H.; Lee, H.W. A study of non-symmetric double-sided linear induction motor for Hyperloop all-in-one system (Propulsion, Levitation, and Guidance). IEEE Trans. Magn.
**2018**, 54. [Google Scholar] [CrossRef] - Hao, L.; Huang, Z.; Dong, F.; Qiu, D.; Shen, B.; Jin, Z. Study on electrodynamic suspension system with high-temperature superconducting magnets for a high-speed maglev train. IEEE Trans. Appl. Supercond.
**2019**, 29, 1–5. [Google Scholar] [CrossRef] - Mulcahy, T.M.; He, J.; Rote, D.M.; Rossing, T.D. Forces on a magnet moving past figure-eight coils. IEEE Trans. Magn.
**1993**, 29, 2947–2949. [Google Scholar] [CrossRef] [Green Version] - Knowles, R. Dynamic circuit and Fourier series methods for moment calculation in electrodynamic repulsive magnetic levitation system. IEEE Trans. Magn.
**1982**, 18, 953–960. [Google Scholar] [CrossRef] - Lee, J.; Bae, D.K.; Kang, H.; Ahn, M.C.; Lee, Y.; Ko, T.K. Analysis on ground conductor shape and size effect to levitation force in static type EDS simulator. IEEE Trans. Appl. Supercond.
**2010**, 20, 896–899. [Google Scholar] [CrossRef] - Ko, W.; Ham, C. A novel approach to analyze the transient dynamics of an electrodynamic suspension maglev. IEEE Trans. Magn.
**2007**, 43, 2603–2605. [Google Scholar] [CrossRef]

**Figure 9.**Distribution of eddy currents on plate surface at different speeds with single magnet, (

**a**) 2 m/s, (

**b**) 10 m/s, (

**c**) 70 m/s, and (

**d**) 100 m/s.

**Figure 10.**Simplified illustration of interaction between the magnet and the plate at different speeds with single magnet in cross-section view: (

**a**) low speed and (

**b**) high speed.

**Figure 12.**Distributions of magnetic flux density: (

**a**) Y direction of PM, (

**b**) Z direction of PM, (

**c**) Y direction of SC magnet, and (

**d**) Z direction of SC magnet.

**Figure 15.**Distribution of eddy currents on plate surface at different speeds with NN and NS arranged magnets: (

**a**) NN magnets at 10 m/s, (

**b**) NS magnets at 10 m/s, (

**c**) NN magnets at 100 m/s, and (

**d**) NS magnets at 100 m/s.

**Figure 17.**Simulation results of different thicknesses of plate at speed of 100 m/s. (

**a**) Levitation, drag, and guidance forces, (

**b**) levitation drag ratio.

Variable | Symbol | Value | Unit |
---|---|---|---|

Length of magnet (Y axis) | lm | 230 | mm |

Height of magnet (Z axis) | Hm | 200 | mm |

Thickness of magnet (X axis) | Tm | 20 | mm |

Pole pitch of magnets (Y axis) | $\tau $ | 270 | mm |

Remanence of PM | ${B}_{r}$ | 1.3 | T |

Coercivity of PM | ${H}_{c}$ | 940 | kA/m |

Relative permeability of PM | ${\mu}_{r}$ | 1.09 | |

Height of plate (Z axis) | Hp | 200 | mm |

Thickness of plate (X axis) | Tp | 8 | mm |

Gap between magnet and plate (X axis) | G | 10 | mm |

Height difference between mid-lines of magnet and plate (Z axis) | h | 70 | mm |

Variable | Value | Unit |
---|---|---|

Length | 230 | mm |

Height | 200 | mm |

Thickness | 20 | mm |

Remanence of PM | 1.3 | T |

Coercivity of PM | 940 | kA/m |

Relative permeability of PM | 1.09 | |

Current in SC magnet | 18.8 | kA |

Magnet Length (mm) | Levitation Force (N) |
---|---|

190 | 230 |

200 | 236 |

210 | 240 |

220 | 256 |

230 | 268 |

240 | 280 |

250 | 288 |

260 | 295 |

270 | 297 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, Z.; Zhou, D.; Chen, Q.; Yu, P.; Li, J.
Design and Analysis of a Plate Type Electrodynamic Suspension Structure for Ground High Speed Systems. *Symmetry* **2019**, *11*, 1117.
https://doi.org/10.3390/sym11091117

**AMA Style**

Guo Z, Zhou D, Chen Q, Yu P, Li J.
Design and Analysis of a Plate Type Electrodynamic Suspension Structure for Ground High Speed Systems. *Symmetry*. 2019; 11(9):1117.
https://doi.org/10.3390/sym11091117

**Chicago/Turabian Style**

Guo, Zhaoyu, Danfeng Zhou, Qiang Chen, Peichang Yu, and Jie Li.
2019. "Design and Analysis of a Plate Type Electrodynamic Suspension Structure for Ground High Speed Systems" *Symmetry* 11, no. 9: 1117.
https://doi.org/10.3390/sym11091117