# Parametric Analysis of the Toothed Electromagnetic Spring Based on the Finite Element Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Finite Element Simulation

#### 2.1. Structure of the TES

#### 2.2. Finite Element Simulation

#### 2.2.1. Finite Element Model

_{i}is the weighted integral, and ω

_{i}is a weighted function.

#### 2.2.2. Grid Demarcation

#### 2.2.3. Application of Constraints

#### 2.2.4. Results

## 3. Model Verification

_{i}is the observed value, ŷ

_{i}is the predicted value, and y

_{i}

_{max}and y

_{i}

_{min}are the maximum and minimum observed value, respectively.

^{2}. The quantitative analysis of model accuracy was performed according to Equations (6)–(8), and the results are illustrated in Table 4. Obviously, R

^{2}was quite close to 1, indicating that the prediction accuracy of the model was substantially high.

_{i}is the mean of the observed value.

## 4. Parametric Analysis

#### 4.1. Influence of the Number of Teeth

#### 4.2. Influence of Tooth Height

#### 4.3. Influence of Tooth Width

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Comparisons of the force–displacement curves of the TES under different currents: (

**a**) 0.5 A, (

**b**) 1.0 A, (

**c**) 1.5 A, (

**d**) 2.0 A, and (

**e**) 2.5 A.

**Figure 10.**Electromagnetic force characteristics for different numbers of teeth: (

**a**) electromagnetic force–displacement curve and (

**b**) maximum electromagnetic force under different currents.

**Figure 11.**Electromagnetic force characteristics for different tooth heights: (

**a**) electromagnetic force–displacement curve and (

**b**) maximum electromagnetic force under different currents.

**Figure 12.**Electromagnetic force characteristics for different tooth widths: (

**a**) electromagnetic force–displacement curve and (

**b**) maximum electromagnetic force under different currents.

Parameters | Coil Height (mm) | Coil Width (mm) | Air Gap (mm) | Tooth Number | Tooth Pitch (mm) |

Value | 32 | 20 | 0.25 | 3 | 10 |

Parameters (mm) | Tooth Height | Tooth Width | Stator Shell Thickness | Armature Diameter | Shaft Diameter |

Value | 5 | 2 | 10 | 100 | 20 |

Region | Shaft | Stator | Armature | Coil | Solution Domain |
---|---|---|---|---|---|

Maximum length (mm) | 10 | 5 | 5 | 2 | 15 |

Equipment | Model | Parameters | Manufacture |
---|---|---|---|

Force sensor | AR-DN23 | Range: 0–5 kN Accuracy: 0.015% F.S | Ailixun, Chian |

Displacement sensor | ML33-12.5-A | Range: 0–12.5 mm Accuracy: 0.1% F.S | Miran, China |

Servo electric | ECMA-C200807SS | Output: 3000 rpm | Delta, China |

Power supply | DC-3010D | Range: 0–10 A, 0–30 V | Yihua, China |

Current (A) | RSS | TSS | R^{2} |
---|---|---|---|

0.5 | 3.9947 × 10^{4} | 1.8890 × 10^{6} | 0.9788 |

1.0 | 4.8120 × 10^{5} | 2.9294 × 10^{7} | 0.9835 |

1.5 | 4.6403 × 10^{5} | 1.0754 × 10^{8} | 0.9956 |

2.0 | 3.5733 × 10^{6} | 3.2686 × 10^{8} | 0.9890 |

2.5 | 1.0330 × 10^{7} | 4.5877 × 10^{8} | 0.9774 |

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## Share and Cite

**MDPI and ACS Style**

Zheng, X.; Zhang, C.; Lou, Y.; Xue, G.; Bai, H.
Parametric Analysis of the Toothed Electromagnetic Spring Based on the Finite Element Model. *Aerospace* **2023**, *10*, 750.
https://doi.org/10.3390/aerospace10090750

**AMA Style**

Zheng X, Zhang C, Lou Y, Xue G, Bai H.
Parametric Analysis of the Toothed Electromagnetic Spring Based on the Finite Element Model. *Aerospace*. 2023; 10(9):750.
https://doi.org/10.3390/aerospace10090750

**Chicago/Turabian Style**

Zheng, Xiaoyuan, Cheng Zhang, Yifang Lou, Guangming Xue, and Hongbai Bai.
2023. "Parametric Analysis of the Toothed Electromagnetic Spring Based on the Finite Element Model" *Aerospace* 10, no. 9: 750.
https://doi.org/10.3390/aerospace10090750