# Finite Element Method-Based Optimisation of Magnetic Coupler Design for Safe Operation of Hybrid UAVs

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- Performing transient analysis on the dynamically modelled state of the MC;
- Dynamic investigation of the effect of misalignments on the transmitted torque;
- Examination of the MC efficiency depending on the operating speed at a critical angle;
- Exploring the negative torque between the rotors in case of a loss of synchronisation;
- Proposing the correction coefficients to identify the error margin of simulations.

## 2. Design Considerations

#### 2.1. Determination of the Minimum Outer Diameter of the Inner Rotor

#### 2.2. Selection of Rotor Topology

#### 2.3. Materials Overview

## 3. Design Studies

#### 3.1. Analytical Preliminary Sizing

_{oi}and r

_{io}are the outer radius of the inner rotor and inner diameter of the outer rotor, respectively.

^{3}, and the number of poles, respectively. ${T}_{total}$ is the total torque exerted on the middle of the air gap used to estimate the torque on the rotors with regard to the total number of poles. The active couplers work without any slip until the pullout torque is exceeded. The pullout torque is expressed as the maximum torque that the MC can handle.

^{3}. The bore diameter of the inner rotor is 29 mm due to the mounting hole diameters on the flange, as shown in Figure 4b. Similarly, the outer diameter of the inner rotor is to be a minimum of 43 mm for the model. Considering the thickness of the rotor yokes and PMs, r

_{mean}is initially chosen to be 27.5 mm. With the initial assumption of an air gap length of 1.5 mm, the outer diameter of the inner rotor and the inner diameter of the outer rotor are found to be 26.75 mm and 28.25 mm, respectively. Thus, the corresponding model length is found to be 5 mm.

#### 3.2. Maxwell 2D Static Analyses

#### 3.2.1. Correlation of Effective Air Gap Diameter and Model Length

#### 3.2.2. Investigation of Optimum Pole Number

#### 3.2.3. Effect of Air Gap Clearance on Pullout Torque

#### 3.2.4. Determination of PM Thickness

#### 3.2.5. Determination of the Thickness of Rotor Yokes

#### 3.2.6. Investigation of the PM Embrace and Offset Effect

#### 3.3. Maxwell 2D Transient Analyses

^{2}and 1.95 kg-cm

^{2}, respectively. Mechanical losses, i.e., wind and friction losses, ventilator losses, and bearing losses, are practically accepted at 3.5% of the output power [56]. The load type is considered such that the load varies nonlinearly with the square of the speed, such as fan load [54].

#### 3.3.1. Comparison of Pole Types

#### 3.3.2. Effect of PM Type, Grade, and Temperature on Pullout Torque

#### 3.3.3. Rotor Flux Density and Mesh Distribution

_{yo2}and t

_{yo1}) can be a minimum of 2 mm to prevent fabrication deformation. The inner rotor inner yoke thickness (t

_{yi1}) is set to a minimum of 2.5 mm to avoid reducing the mechanical strength and flywheel effect, and the inner rotor outer yoke thickness (t

_{yi2}) is set to 5.24 mm to ensure the selected effective air gap diameter.

#### 3.3.4. Investigation of Negative Torque at Loss of Synchronisation

#### 3.4. Maxwell 3D Static and Transient Optimetric Analyses

#### 3.4.1. Static Locked-Rotor Torque and Transient Torque Ripple Analyses

#### 3.4.2. Investigation of Different Rotor Materials and Air Gap Flux Density

#### 3.4.3. Study of Pullout Torque Depending on Misalignment Length

#### 3.4.4. Magnetic Coupler Efficiency and Induced Eddy-Current Losses on PMs

^{2}. On the other hand, vibration due to the natural operation of the PE, load disturbances due to different UAV operating zones, and torque fluctuations during load changes cause the torque angle to change continuously. As a result, high eddy-current losses are induced on the PMs, which increase the temperature of the PMs and reduce the transmitted torque by reducing their residual flux density, and their impact on the system should be investigated. The proposed MC design is realised in light of all these effects and the design requirements are provided.

#### 3.5. Summary List of Various MC Designs

## 4. Results and Discussion

#### 4.1. Locked-Rotor Test Results in Summary

#### 4.2. Investigation of Pullout Torque in Transient and Static Torque versus Torque Angle

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Type of MCs: (

**a**) Active/Reactive coupler; (

**b**) Hysteresis coupler; (

**c**) Eddy-current coupler.

**Figure 5.**Rotor topologies: (

**a**) Arc surface-mounted; (

**b**) Rectangular surface-mounted; (

**c**) Ring-type; (

**d**) Buried arc type; (

**e**) Buried type; (

**f**) Inset type; (

**g**) Halbach arrays; (

**h**) Enhanced hybrid.

**Figure 9.**Pullout torque investigation versus: (

**a**) Pole number in air gap length; (

**b**) Air gap length.

**Figure 18.**Investigation of: (

**a**) Effect of different rotor materials on torque; (

**b**) Air gap flux density.

**Figure 21.**Various MC productions of: (

**a**) 8-pole/0.8-embrace/3 mm-PM thickness/10 mm length; (

**b**) 8-pole/0.98-embrace/4 mm-PM thickness/10 mm length; (

**c**) 10-pole/0.8-embrace/4 mm-PM thickness/10 mm length; (

**d**) 10-pole/0.98-embrace/4 mm-PM thickness/10 mm length; (

**e**) 10-pole/0.98-embrace/4 mm-PM thickness/20 mm length.

**Figure 25.**Test results of the optimum MC in the 10-pole, 0.98-embrace, and 10 mm length configuration: (

**a**) Pullout torque in transients; (

**b**) Static torque versus torque angle in magnetostatics.

Parameters | Value |
---|---|

Pullout torque, with safety factor and correction coefficient | 6.9 N·m |

Minimum torque density, required | 18.4 N·m/kg |

Rated speed | 4500 rpm |

Operation speed range | 2500–6500 rpm |

Design Outputs | 10-Pole |

Air gap volume, minimum required | 1289.5 mm^{3} |

Length of the model, based on r_{mean} | 5 mm |

(θ-dθ), dθ at critical torque angle | 0.314 rad. |

Critical torque angle | 18 (°M) |

Design Assumptions | |

Middle of the air gap radius, r_{mean} | 27.5 mm |

Average air gap flux density | 0.65 T |

Air gap length | 1.5 mm |

Pullout torque, required | 6.9 N·m |

Pole Number | 8-Pole | 10-Pole * | ||||
---|---|---|---|---|---|---|

Embrace | 0.6 | 0.8 | 0.98 | 0.8 | 0.98 * | |

PM Thickness | 3 mm | 4 mm | 4 mm | 4 mm * | ||

Grade of PM | N48H | N45H | N48H | N48H | N48H * | |

Outer diameter of outer rotor | 79 mm | 83 mm | 83 mm * | |||

Inner diameter of outer rotor | 57 mm | 59 mm | 59 mm * | |||

Outer diameter of inner rotor | 54 mm | 56 mm | 56 mm * | |||

Inner diameter of inner rotor | 20 mm | 20 mm | 20 mm * | |||

Air gap length | 1.5 mm | 1.5 mm | 1.5 mm * | |||

Effective air gap diameter | 55.5 mm | 57.5 mm | 57.5 mm * | |||

Model length | 10 mm | 10 mm | 10 mm * | |||

Total weight (gr) | 320 | 350 | 351 | 370 | 352 | 371 |

Pullout torque (N·m), dynamic | 3.9 | 6.9 | 7.2 | 7.5 | 8.1 | 8.7 |

Torque density (N·m/kg) | 12.2 | 19.7 | 20.5 | 20.3 | 23 | 23.45 |

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## Share and Cite

**MDPI and ACS Style**

Arslan, S.; Iskender, I.; Navruz, T.S. Finite Element Method-Based Optimisation of Magnetic Coupler Design for Safe Operation of Hybrid UAVs. *Aerospace* **2023**, *10*, 140.
https://doi.org/10.3390/aerospace10020140

**AMA Style**

Arslan S, Iskender I, Navruz TS. Finite Element Method-Based Optimisation of Magnetic Coupler Design for Safe Operation of Hybrid UAVs. *Aerospace*. 2023; 10(2):140.
https://doi.org/10.3390/aerospace10020140

**Chicago/Turabian Style**

Arslan, Sami, Ires Iskender, and Tuğba Selcen Navruz. 2023. "Finite Element Method-Based Optimisation of Magnetic Coupler Design for Safe Operation of Hybrid UAVs" *Aerospace* 10, no. 2: 140.
https://doi.org/10.3390/aerospace10020140