# Design and Analysis of Guidance Function of Permanent Magnet Electrodynamic Suspension

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## Abstract

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## 1. Introduction

## 2. Operation and Principles

#### 2.1. Presentation of a New Structure

#### 2.2. Basic Principles of the New Structure

_{a}. In normal conditions, the PM and the guidance track are in alignment, and the force analysis of the PM is shown in Figure 2a. The direction of the attraction force is vertically downward, which will cancel part of the levitation force, F

_{l}. When the vehicle exists transverse displacement, the PM will deviate from the guidance track at a certain speed v, and the force analysis of the PM is shown in Figure 2b. The direction of the attraction force F

_{a}’ is oblique downward, and its component in the vertical direction F

_{n}as a normal attraction force will consume part of the levitation force F

_{l}’. Additionally, the component in the horizontal direction F

_{g}will be taken as a guidance force to restore the vehicle’s return to the centered running state. The relationship between F

_{n}, F

_{g}and F

_{a}’ can be expressed as follows:

_{n}= F

_{a}’cosθ

_{g}= F

_{a}’sinθ

## 3. FEM Experimental Verification

#### 3.1. Establishment of Finite Element Model

#### 3.2. Experimental Verification

#### 3.3. Results Comparison

## 4. Analysis on Guidance Performance and Parameter Optimization

#### 4.1. Guidance Performance Analysis

#### 4.2. Parameters Optimization Analysis

_{ratio}), which denotes the guidance capability of the system can be obtained as follows:

_{ratio}= F

_{g}/Weight

_{ratio}) reflects the guidance comprehensive performance of the guidance track; it is defined as:

_{ratio}= F

_{g}/F

_{nmax}

_{ratio}and G-A

_{ratio}. The following optimization work is carried out at a transverse speed of 2 m/s and a suspension gap of 15 mm.

#### 4.3. Geometric Parameters Analysis

_{ratio}increases with the width and thickness of the guidance track. Obviously, the width has a greater gain effect on the attraction force than that under influence of the thickness. As seen in Figure 12, the G-A

_{ratio}is decreasing with the width and thickness, which means that the geometric parameters increase, and the normal attraction force increases more than the guidance force. Additionally, the G-A

_{ratio}decreases much more obviously under the width increase than under the thickness increase. In conclusion, the width of the guidance track has more obvious influence on guidance performance than thickness. The reason for this rule is that the area of interaction between the guidance track and PM increases with the increasing width. Therefore, smaller thickness can be selected based on cost considerations and larger width can be selected to ensure the guidance performance.

#### 4.4. Shape Section Analysis

_{ratio}and the lowest G-A

_{ratio}. So, it is beneficial to improve the guidance capability, but it also increases the normal attraction force. The circle shape has the largest G-A

_{ratio}and the lowest G-W

_{ratio}; thus, it cannot provide sufficient guidance capability. Taking into account the synthesis of the indexes and the installation and maintenance cost, the appropriate section shape can be chosen according to the above rules.

#### 4.5. Installation Position Analysis

_{ratio}decreases synchronously with the increment of the working gap. On the contrary, the G-A

_{ratio}is on an increasing trend. To guarantee the sufficient guidance capability and as small a normal attraction force as possible, the appropriate working gap can be selected for different conditions.

#### 4.6. Material Selection Analysis

_{ratio}and the lowest G-A

_{ratio}, while ferrite has the greatest G-A

_{ratio}and lowest G-W

_{ratio}. Additionally, pure iron shows better comprehensive performance, but it also has a softer texture, which is not appropriate for applications. Hence, considering the practical application and the installation and maintenance cost, the adequate ferromagnetic material can be chosen for the PM EDS system.

## 5. Equivalent Experimental Verification

#### 5.1. Experimental Prototype

#### 5.2. Analysis of Experimental Results

## 6. Conclusions

_{ratio}and G-A

_{ratio}. According to the simulation results, the guidance track can provide a partial guidance force to assist in the guidance performance. The guidance force is close to zero at high speeds. The guidance performance may be further improved by increasing the number of PM bulks, etc. The effectiveness of the proposed structure is verified by building a small-scale annular PM EDS experimental prototype. It can be found from the results that the ferromagnetic guidance track is an effective way to improve the guidance performance of the PM EDS system. The guidance force can be provided and the guidance ability can be improved through the ferromagnetic guidance track. In future work, a full-scale linear PM EDS experimental prototype will be constructed to verify the optimization work, which will facilitate a deeper exploration of the proposed structure.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagrams of the new EDS structure: (

**a**) Overall structure diagram of the new EDS structure; (

**b**) Side view of the new EDS structure.

**Figure 2.**Guidance force analysis under different conditions: (

**a**) PM and track are in alignment; (

**b**) The vehicle exists in transverse displacement.

**Figure 3.**(

**a**) Finite element model of the PM EDS system; (

**b**) The static magnetic field distribution of the FEM model.

**Figure 4.**Photos of the PM EDS high-speed rotating experimental platform: (

**a**) Overall schematic diagram of the device; (

**b**) Schematic diagram of crucial parts.

**Figure 8.**The guidance force and maximum normal force as functions of transverse speed at a working gap of 27 mm (the working gap refers to the distance between the bottom of the PM and the top surface of the guidance track).

**Figure 9.**The guidance force and maximum normal force as functions of the working gap at a transverse speed of 2 m/s.

**Figure 15.**The optimization indexes as functions of working gap at the width is 6 mm and the thickness is 4 mm.

**Figure 17.**Magnetic field intensity at 10 mm vertical projection of PM: (

**a**) Horizontal magnetic field intensity distributions; (

**b**) Vertical magnetic field intensity distributions.

**Figure 20.**The experimental results of normal attraction force and guidance force at different working gaps.

**Figure 21.**The experimental results of levitation force and guidance force at speeds of 500–3000 rpm.

**Figure 22.**The experimental results of guidance forces with and without the installed guidance track.

Parameter | Value |
---|---|

Length of a single magnet (x axis) | 30 mm |

Width of a single magnet (y axis) | 100 mm |

Thickness of a single magnet (z axis) | 30 mm |

Number of PM | 9 |

Magnetization angle | 90° |

Remanence of PM | 1.45 T |

Width of aluminum track (y axis) | 165 mm |

Thickness of aluminum track (z axis) | 30 mm |

Parameter | Value |
---|---|

Length of a single magnet (x axis) | 30 mm |

Width of a single magnet (y axis) | 100 mm |

Thickness of a single magnet (z axis) | 30 mm |

Number of PM | 9 |

Magnetization angle | 90° |

Remanence of PM | 1.45 T |

Width of aluminum track (y axis) | 165 mm |

Thickness of aluminum track (z axis) | 12 mm |

Width of guidance track (y axis) | 10 mm |

Thickness of guidance track (z axis) | 4 mm |

Suspension gap | 15 mm |

Parameter | Value |
---|---|

Length of a single linear magnet | 16 mm |

Width of a single linear magnet | 35 mm |

Thickness of a single linear magnet | 17.5 mm |

Number of linear PM | 5 |

Outer diameter of PM wheel | 50 mm |

Inner diameter of PM wheel | 32.5 mm |

Width of PM wheel | 35 mm |

Pole pairs of PM wheel | 4 |

Remanence of PM | 1.19 T |

Material of PM | NdFeB-N35 |

Parameter | Value |
---|---|

Material of PM | NdFeB-N35 |

External diameter of PM | 50 mm |

Inner diameter of PM | 32.5 mm |

Width of PM | 35 mm |

Remanence of PM | 1.19 T |

Pole pairs of PM | 4 |

Density of PM | 7500 kg/m^{3} |

Material of aluminum track | 1060 |

Conductivity of aluminum track | 3.4 × 10^{7} s/m |

Width of aluminum track | 60 mm |

Thickness of aluminum track | 6.8 mm |

Maximum idling speed of motor | 8000 rpm |

Torque of motor | 2 N·m |

Width of guidance track | 8 mm |

Thickness of guidance track | 4 mm |

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## Share and Cite

**MDPI and ACS Style**

Xiang, Y.; Deng, Z.; Shi, H.; Li, K.; Cao, T.; Deng, B.; Liang, L.; Zheng, J.
Design and Analysis of Guidance Function of Permanent Magnet Electrodynamic Suspension. *Technologies* **2023**, *11*, 3.
https://doi.org/10.3390/technologies11010003

**AMA Style**

Xiang Y, Deng Z, Shi H, Li K, Cao T, Deng B, Liang L, Zheng J.
Design and Analysis of Guidance Function of Permanent Magnet Electrodynamic Suspension. *Technologies*. 2023; 11(1):3.
https://doi.org/10.3390/technologies11010003

**Chicago/Turabian Style**

Xiang, Yuqing, Zigang Deng, Hongfu Shi, Kaiwen Li, Ting Cao, Bin Deng, Le Liang, and Jun Zheng.
2023. "Design and Analysis of Guidance Function of Permanent Magnet Electrodynamic Suspension" *Technologies* 11, no. 1: 3.
https://doi.org/10.3390/technologies11010003