# Design Optimization of a Reluctance Lead Screw for Wave Energy Conversion

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, the transmission efficiency is limited to about 60% [5]. In addition, the hydraulic components require constant maintenance, which is unacceptable for most deep sea applications.

## 2. Fundamentals and Topology of the RLS

_{p}is the pole pitch (m), ω is the rotor angular velocity (rad/s), and υ is the translator linear speed (m/s).

## 3. Design Optimization

#### 3.1. Ferromagnetic Structure Aspects

_{pPM}, and it can be calculated by the following equations:

_{pm}is the total PM volume, which can be calculated with the simulation parameters; n is the total number of helical magnet turns.

_{a}(R

_{a}= R

_{rti}− h

_{m}). The air gap radius increases from 20 to 80 mm. It can be seen from the results that the maximum thrust force grows linearly when the air gap radius increases. The reason for this is that when the air gap radius increases, the magnet surface areas increase; at the same time, the magnetic flux density remains unchanged, so the force increases with the magnet surface areas. In [23], the MLS maximum thrust force is about 2.5 kN, and the PM volume is 211.0 cm

^{3}; the thrust force per PM volume is 11.8 N/cm

^{3}. In RLS, the maximum thrust force is about 585 N, the PM volume is 44 cm

^{3}, and F

_{pPM}is 13.3 N/cm

^{3}. Benefitting from the novel structure, the value of F

_{pPM}is higher in the RLS compared with in the MLS. In other words, the RLS is able to generate more force than the MLS with the same magnet volume, and it can be concluded that RLS gives better utilization of magnets.

_{pPM}can hardly increase any more.

#### 3.2. Magnet Aspects

^{3}and 211.0 cm

^{3}, respectively. Considering the fact that the price of rare earth is about 100 times that of iron, although the iron consumption of the RLS is more than that of the MLS, its total material cost is still lower than that of the MLS.

_{pPM}value reaches the maximum when the magnet thickness is set to 10 mm. For the design aspects, this point is preferred as the best magnet thickness point.

## 4. Prototype Design for WECs

#### 4.1. RLS Prototype Design

#### 4.2. Potential Applications in WECs

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Magnetic field distribution. (

**a**) Stable state (aligned position), (

**b**) unstable state (displaced axially by 3/5 pole pitch).

**Figure 5.**Physical meaning of the parameters shown in Table 1.

**Figure 6.**Variation in the thrust force with different axial displacements between the rotor and translator.

**Figure 8.**Variation in the maximum thrust force and force per permanent magnet (PM) volume with different air gap lengths.

**Figure 10.**The maximum thrust force and force per PM volume when the thread thickness varies from 1 to 10 mm.

**Figure 12.**Variation in the maximum thrust force and force per PM volume with different PM thicknesses.

**Figure 16.**Two potential applications of RLS. (

**a**) RLS-based oscillating wave energy converter (WEC). (

**b**) RLS-based heaving buoy WEC.

Parameter | Quantity | Unit |
---|---|---|

Translator radius R_{tl} | 19 | mm |

Translator length L_{tl} | 200 | mm |

Rotor outer radius R_{rto} | 50 | mm |

Rotor internal radius R_{rti} | 40 | mm |

Rotor length L_{rt} | 80 | mm |

magnet thickness h_{m} | 10 | mm |

Pole pitch τ_{p} | 10 | mm |

Lead λ | 40 | mm |

Air gap g | 1 | mm |

Thread width w_{i} | 10 | mm |

Thread thickness h_{i} | 10 | mm |

PM remanence B_{r} | 1.1 | T |

PM coercivity H_{c} | 838.0 | kA/m |

Parameters and Units | RLS | MLS |
---|---|---|

Translator radius/mm | 19 | 18 |

Translator length/mm | 2000 | 2000 |

Rotor outer radius/mm | 50 | 41 |

Rotor length/mm | 120 | 36 |

Maximum Force/kN | 1.8 | 1.5 |

PM consumption/cm^{3} | 131.9 | 1543.5 |

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**MDPI and ACS Style**

Tian, T.; Wu, W.; Jiang, J.; Zhu, L.; Lu, K.; Blaabjerg, F.
Design Optimization of a Reluctance Lead Screw for Wave Energy Conversion. *Energies* **2020**, *13*, 5388.
https://doi.org/10.3390/en13205388

**AMA Style**

Tian T, Wu W, Jiang J, Zhu L, Lu K, Blaabjerg F.
Design Optimization of a Reluctance Lead Screw for Wave Energy Conversion. *Energies*. 2020; 13(20):5388.
https://doi.org/10.3390/en13205388

**Chicago/Turabian Style**

Tian, Tian, Weimin Wu, Jiacheng Jiang, Lixun Zhu, Kaiyuan Lu, and Frede Blaabjerg.
2020. "Design Optimization of a Reluctance Lead Screw for Wave Energy Conversion" *Energies* 13, no. 20: 5388.
https://doi.org/10.3390/en13205388