# Design Optimisation Approach of an Outer Rotor Multiphase PM Actuator for Multirotor Aerial Vehicle Applications

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Design Requirements

^{2}), g (m/s

^{2}) and ${F}_{drag}$ (N) are, respectively, the vehicle acceleration, the gravitational acceleration and the drag force which is a function dependent on the vehicle speed and geometry.

^{3}), ${C}_{T}$, ${C}_{M}$, and N (rpm) are, respectively, air density, thrust coefficient, torque coefficient, and propeller velocity. The air density, $\rho $, is determined by both the local temperature ${T}_{t}$ (°C) and the air pressure p, which is further determined by altitude h (m). The thrust and torque coefficients are dependent on the propeller blade airfoil shape. Their model and their approximative values are presented in [21]. Based on the sizing methodology presented in [21], it is suggested that with a carbon fiber propeller of ${D}_{p}=1.2$ m and ${H}_{p}=0.456$ m, the developed thrust is 74 kg at a velocity of 3300 rpm. The propeller parameters and its thrust and torque in terms of the velocity are, respectively, given by Table 1 and Figure 2. It is noticeable, as shown in Figure 2, that the working motor torque is 36 N · m.

## 3. Design Methodology and Elements for Optimal Design

#### 3.1. Design Methodology

#### 3.2. Selection fo the $s/p$ Combination

#### 3.3. Winding Configuration Design

- Step 1: The initial repeatable sequence is: 11000000000;
- Step 2: The optimal repeatable sequence is: 10000010000;
- Step 3: The usual phase sequence is associated with the hole sequence. In the case of 5-phase, given by: $AC\prime EB\prime DA\prime CE\prime BD\prime $ ($A\prime $ characterizes the return conductor corresponding to coil of phase A);
- Step 4: The conductors associated with the numbers 1 of the sequence are selected to make the first layer of winding. This allows to obtain the first layer winding. The second layer winding is obtained by reproducing and shifting the initial layer by a tooth or a slot width. Figure 4 gives the winding layout for a quarter of the machines (${Q}_{s}=10$). The whole winding configuration is completed by an antiperiodic symmetry, as $y=11$ is an odd number in this case.

#### 3.4. PM Configurations

#### 3.5. Analytical Pre-Sizing

^{3}[34]. Regarding the $SR$ value, in the case of the outer runner motor, it must avoid the motor shearing. In this paper, a $SR$ initial value of $1/5$ is considered. It is remarkable that in the case of the outer rotor configuration, the torque density ($TD=\frac{{T}_{max}}{\frac{\pi}{4}\xb7{D}_{or}^{2}\xb7{L}_{stk}}$ and $TRV$ coincide with each other. Then, the outer rotor diameter ${D}_{or}$ and the stack length ${L}_{stk}$ are, respectively, given by:

## 4. Multiobjective Optimisation Problem

#### 4.1. Problem Formulation

^{3}· Hz· T

^{2})), ${C}_{e}$ (W/(m

^{3}· Hz

^{2}· T

^{2})), f (Hz), ${B}_{m}$ (T), V (m

^{3}), ${V}_{t}$ (m/s) are, respectively, the motor torque, speed, a phase resistance, hysteresis loss coefficient, eddy current loss coefficient, frequency, flux density peak amplitude, core volume, and tangential speed. The phase resistance is directly estimated in terms of winding and stator parameters as:

- SPM configuration: $8\le {h}_{m}\le 12,3\le {t}_{m}\le 5$, and $3\le {h}_{ry}\le 6$.
- V-shape configuration: $0.7\le {l}_{PM}\le 0.9,1\le {t}_{m}\le 2.5$, and $3\le {h}_{ry}\le 6$.
- Spoke configuration: $4\le {t}_{m}\le 6,$ and $8\le {h}_{ry}={h}_{m}\le 12$.

#### 4.2. Optimisation Algorithm

#### 4.3. Optimal Harmonic Current Injection Ratio

- In the case of peak value, this constraint is expressed as:$${I}_{S}={I}_{NS}\xb7max\left(\sum _{h=0}^{\infty}{A}_{2h+1}\xb7sin\left((2h+1)\xb7\left(p\xb7{\theta}_{m}-\frac{2\pi}{{n}_{ph}}j\right)\right)\right)$$Thus, the term $max\left({\sum}_{h=0}^{\infty}{A}_{2h+1}\xb7sin\left((2h+1)\xb7\left(p\xb7{\theta}_{m}-\frac{2\pi}{{n}_{ph}}j\right)\right)\right)$ must be minimised, in order to maximise the motor output torque. This constraint, in this case, consists of finding the ratios ${A}_{2h+1}$ that satisfy the following problem:$$\left\{\begin{array}{c}A=min\left(max\left(\sum _{h=0}^{\infty}{A}_{2h+1}\xb7sin\left((2h+1)\xb7\left(p\xb7{\theta}_{m}-\frac{2\pi}{{n}_{ph}}j\right)\right)\right)\right)\hfill \\ {I}_{NS}=\frac{{I}_{S}}{A}\hfill \\ with\phantom{\rule{3.33333pt}{0ex}}0\le {A}_{2h+1}<1\phantom{\rule{3.33333pt}{0ex}}and\phantom{\rule{3.33333pt}{0ex}}{A}_{1}=1\hfill \end{array}\right.$$Based on this formulation, the optimal harmonic ratio ${A}_{2h+1}$, in the case of 5 and 6-phase, the optimal third harmonic current injection is ${A}_{3}=0.167$. In the case of 7-phase, the optimal third and fifth harmonics current injection are ${A}_{3}=0.24,{A}_{5}=0.07$.
- In the case of RMS value, this constraint is expressed as:$$\frac{{I}_{S}}{\sqrt{2}}=\frac{{I}_{NS}}{\sqrt{2}}\xb7\sqrt{\left(\sum _{h=0}^{\infty}{\left({A}_{2h+1}\right)}^{2}\right)}$$As in the previous case, in order to maximise the motor torque, the term $\sqrt{\left({\sum}_{h=0}^{\infty}{\left({A}_{2h+1}\right)}^{2}\right)}$ must be minimised. This constraint, in this case, consists of finding the ratios ${A}_{2h+1}$ that satisfy the following problem:$$\left\{\begin{array}{c}A=min\left(\sqrt{\left({\sum}_{h=0}^{\infty}{\left({A}_{2h+1}\right)}^{2}\right)}\right)\hfill \\ {I}_{NS}=\frac{{I}_{S}}{A}\hfill \\ with\phantom{\rule{3.33333pt}{0ex}}0\le {A}_{2h+1}<1\phantom{\rule{3.33333pt}{0ex}}and\phantom{\rule{3.33333pt}{0ex}}{A}_{1}=1\hfill \end{array}\right.$$It is remarkable that the minimum of the considered function is attainable for ${A}_{2h+1}=0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}for\phantom{\rule{3.33333pt}{0ex}}h>1$; however, it is possible to inject higher harmonics in a limit of 20% as shown in [41]. Thus, in the optimisation part, they will be the consideration of the current injection in both cases $Sin$ and $Sin+h$ with peak constraint.

## 5. Results Analysis and Performances Comparison

#### 5.1. Design Optimisation Results of the Case ${n}_{ph}=3$

^{2}, and DC bus voltage ${U}_{dc}=400$ V. Figure 11a–i gives, respectively, the optimisation results for the 3 PM configuration. It is remarkable that in this case, the maximum core flux density amplitude stays below 2 T for the 3 PM positions, which allows avoiding the core saturation. Moreover, the EMF harmonic spectrum shows a weak presence of higher harmonics in comparison to the fundamental frequency ${F}_{s}=\frac{p\xb7{\omega}_{m}}{60}$.

#### 5.2. Design Optimisation Results of the Case ${n}_{ph}=5$

^{2}, and DC bus voltage ${U}_{dc}=400$ V. Figure 12a–i gives, respectively, the optimisation results for the 3 PM positions, where every three subfigures of the same column show the field lines and flux density in no-load conditions with the corresponding EMFs and its harmonic composition. The obtained EMFs, as excepted, present a non-sinusoidal waveform, where the fifth harmonic presents higher amplitude for the 3 PM positions. The amplitude of the third harmonic increases by passing from the SPM configuration to the IPM (Spoke and V-shape) configuration, which is explained by the higher harmonic component of the IPM configuration. The core saturation is avoided, as the maximum core flux density amplitude remains below 2 T for the 3 PM positions

#### 5.3. Design Optimisation Results of the Case ${n}_{ph}=6$

^{2}, and DC bus voltage ${U}_{dc}=400$ V. The optimisation results for the 3 PM positions are reported in Figure 13a–i, where every three subfigures of the same column show the field lines and flux density in no-load conditions with the corresponding FEM and its harmonic composition. The obtained EMFs present a weak amplitude for the fifth, explaining the low effect on its waveform, especially in the SPM case. However, the amplitude of the third and fifth harmonics increase by passing from the SPM configuration to the IPM (Spoke and V-shape) configuration, which is explained by the higher harmonic component of the IPM configuration.

#### 5.4. Design Optimisation Results of the Case ${n}_{ph}=7$

^{2}, and DC bus voltage ${U}_{dc}=400$ V. The optimisation results for the 3 PM positions are reported in Figure 14a–i, where the same conditions are considered as the previous cases. For this motor topology, the obtained EMFs present non-sinusoidal waveform, where the third harmonic amplitude is more present than the fifth and seventh for the 3 PM positions.

#### 5.5. Assessment of Number of Phases and PM Configuration Effects on the EM Performances

#### 5.6. Assessment of Current Harmonics Effects on the EM Performances

^{2}and peak amplitude of the injected current of ${I}_{max}=18$ A.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

${\mathit{n}}_{\mathit{ph}}$ | ${\mathit{n}}_{\mathit{ph}}=3$ | ${\mathit{n}}_{\mathit{ph}}=5$ | ${\mathit{n}}_{\mathit{ph}}=6$ | ${\mathit{n}}_{\mathit{ph}}=7$ |
---|---|---|---|---|

$s/p$ combination | $48/40$ | $40/44$ | $48/44$ | $56/44$ |

Stator outer diameter ${D}_{os}$ (mm) | $190.4$ | $190.4$ | $198.4$ | $198.4$ |

Stator inner diameter ${D}_{is}$ (mm) | $120.08$ | $155.0$ | $153.59$ | $164.87$ |

Stator yokeless thickness ${h}_{sy}$ (mm) | 3 | 3 | 3 | 3 |

Stator pole pitch ${\tau}_{s}$ (mm) | $12.46$ | 15 | $12.46$ | $10.68$ |

$PM$ width ${h}_{m}$ in the $SPM$ case | 11.78 | 10.71 | 10.71 | 10.71 |

PM materiel | NdFeB | |||

teeth width ${h}_{t}$ (mm) | 3 | 3 | 3 | 2 |

Tooth hight h (mm) | 27 | 8 | 6.5 | 5 |

Airgap length ${l}_{g}$ (mm) | 0.8 | 0.8 | 0.8 | 0.8 |

Slot opening ${b}_{s}$ (mm) | 3 | 3 | 3 | 3 |

Tooth head width ${W}_{t}$ (mm) | 9.64 | 12.0 | 9.46 | 7.68 |

Number of turns per coil ${N}_{s}$ | 20 | 17 | 14 | 12 |

Maximum currents ${I}_{max}$ (A) | 28 | 17 | 14 | 12 |

Currents density ${J}_{max}$ (A/mm^{2}) | 12 | |||

DC bus voltage ${U}_{dc}$ (V) | 400 | |||

Stator materiel | Pure Iron (M19 Jauge 1.9 mm) | |||

Stator flux density ${B}_{sy}$ | 0.9 T | |||

Teeth width flux density ${B}_{t}$ | 1.8 T |

${\mathit{n}}_{\mathit{ph}}$ | ${\mathit{n}}_{\mathit{ph}}=3$ | ${\mathit{n}}_{\mathit{ph}}=5$ | ${\mathit{n}}_{\mathit{ph}}=6$ | ${\mathit{n}}_{\mathit{ph}}=7$ |
---|---|---|---|---|

$s/p$ combination | $48/40$ | $40/44$ | $48/44$ | $56/44$ |

Outer rotor diameter ${D}_{or}$ (mm) | 206 | 206 | 206 | 206 |

Stack length ${L}_{stk}$ (mm) | $41.2$ | $41.2$ | $41.2$ | $41.2$ |

Inner rotor diameter ${D}_{ir}$ (mm) | 200 | 196 | 200 | 200 |

$s/p$ combination | 3 | 3 | 3 | 3 |

Rotor materiel | Pure Iron (M19 Jauge 1.9 mm) | |||

Rotor flux density ${B}_{ry}$ | 0.9 T |

${\mathit{n}}_{\mathit{ph}}$ | ${\mathit{n}}_{\mathit{ph}}=3$ | ${\mathit{n}}_{\mathit{ph}}=5$ | ${\mathit{n}}_{\mathit{ph}}=6$ | ${\mathit{n}}_{\mathit{p}\mathit{h}}=7$ |
---|---|---|---|---|

$s/p$ combination | $48/40$ | $40/44$ | $48/44$ | $56/44$ |

Stator outer diameter ${D}_{os}$ (mm) | $198.4$ | $198.4$ | $198.4$ | $198.4$ |

Stator inner diameter ${D}_{is}$ (mm) | $142.72$ | $164.11$ | 170 | $173.7$ |

Stator yokeless thickness ${h}_{sy}$ (mm) | 3 | 3 | 3 | 3 |

Stator pole pitch ${\tau}_{s}$ (mm) | 13 | 15 | 13 | $11.13$ |

$PM$ width ${h}_{m}$ in the $IPM$ case | 12.55 | 11.41 | 11.41 | 11.41 |

$PM$ width ${h}_{m}$ in the $spoke$ case | 3 | 3 | 3 | 3 |

PM materiel | NdFeB | |||

Tooth width ${h}_{t}$ (mm) | 3 | 3 | 3 | 2 |

Tooth hight h (mm) | 24.27 | 5.3 | 6 | 4.2 |

Airgap length ${l}_{g}$ (mm) | 0.8 | 0.8 | 0.8 | 0.8 |

Slot opening ${b}_{s}$ (mm) | 3 | 3 | 3 | 3 |

Tooth head width ${W}_{t}$ (mm) | 10 | 12.58 | 10 | 8.13 |

Number of turns per coil ${N}_{s}$ | 20 | 17 | 14 | 12 |

Maximum currents ${I}_{max}$ (A) | 28 | 17 | 14 | 12 |

Currents density ${J}_{max}$ (A/mm^{2}) | 12 | |||

DC bus voltage ${U}_{dc}$ (V) | 400 | |||

Stator materiel | Pure Iron (M19 Jauge 1.9 mm) |

${\mathit{n}}_{\mathit{ph}}$ | SPM Configuration | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{R}}_{\mathit{or}}$ | ${\mathit{h}}_{\mathit{m}}$ | ${\mathit{L}}_{\mathit{stk}}$ | ${\mathit{b}}_{\mathit{s}}$ | ${\mathit{h}}_{\mathit{ry}}$ | ${\mathit{h}}_{\mathit{sy}}$ | ${\mathit{t}}_{\mathit{m}}$ | ${\mathit{l}}_{\mathit{g}}$ | ${\mathit{N}}_{\mathit{S}}$ | ${\mathit{d}}_{\mathbf{2}}$ | ${\mathit{d}}_{\mathbf{3}}$ | |

3 | 102.00 | 11.33 | 40.78 | 1.78 | 3.42 | 3.42 | 3.17 | 0.30 | 6 | 1.50 | 1.50 |

5 | 91.00 | 8.67 | 37.34 | 2.00 | 4.78 | 4.78 | 4.17 | 0.25 | 15 | 1.11 | 2.70 |

6 | 92.89 | 10.00 | 37.11 | 2.70 | 3.42 | 3.42 | 3.17 | 0.38 | 14 | 2.00 | 1.50 |

7 | 93.00 | 11.00 | 40.83 | 2.33 | 3.42 | 3.42 | 4 | 0.30 | 14 | 1.67 | 1.12 |

${\mathit{n}}_{\mathit{ph}}$ | Spoke Configuration | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{R}}_{\mathit{or}}$ | ${\mathit{h}}_{\mathit{m}}$ | ${\mathit{L}}_{\mathit{stk}}$ | ${\mathit{b}}_{\mathit{s}}$ | ${\mathit{h}}_{\mathit{ry}}$ | ${\mathit{h}}_{\mathit{sy}}$ | ${\mathit{l}}_{\mathit{g}}$ | ${\mathit{N}}_{\mathit{S}}$ | ${\mathit{d}}_{\mathbf{2}}$ | ${\mathit{d}}_{\mathbf{3}}$ | |

3 | 86.67 | 7.05 | 42.00 | 1.4 | 12.12 | 5.33 | 0.38 | 4 | 1.40 | 1.33 |

5 | 80.33 | 10.11 | 37.50 | 1.80 | 6.02 | 3.93 | 0.38 | 15 | 2.50 | 1.33 |

6 | 93.00 | 8.33 | 34.50 | 2.7 | 8.00 | 3.93 | 0.35 | 13 | 1.89 | 2.00 |

7 | 80.33 | 8.33 | 39.89 | 1.5 | 8.00 | 3.93 | 0.38 | 12 | 1.50 | 1.33 |

${\mathit{n}}_{\mathit{ph}}$ | V-Shape Configuration | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{R}}_{\mathit{or}}$ | ${\mathit{h}}_{\mathit{m}}$ | ${\mathit{L}}_{\mathit{stk}}$ | ${\mathit{b}}_{\mathit{s}}$ | ${\mathit{h}}_{\mathit{ry}}$ | ${\mathit{h}}_{\mathit{sy}}$ | ${\mathit{t}}_{\mathit{m}}$ | ${\mathit{l}}_{\mathit{g}}$ | ${\mathit{N}}_{\mathit{S}}$ | ${\mathit{d}}_{\mathbf{2}}$ | ${\mathit{d}}_{\mathbf{3}}$ | ${\mathit{\alpha}}_{\mathit{m}}$ | |

3 | 103.78 | 10.00 | 45.89 | 1.20 | 13.00 | 4.00 | 2.00 | 0.37 | 5 | 2.00 | 1.33 | 24.50 |

5 | 80.33 | 10.1 | 37.5 | 1.78 | 6.03 | 3.93 | 2.00 | 0.38 | 15 | 2.00 | 1.33 | 24.50 |

6 | 91.00 | 9.50 | 38.56 | 1.80 | 9.11 | 3.75 | 2.33 | 0.30 | 12 | 1.50 | 1.33 | 26.67 |

7 | 92.00 | 9.50 | 41.33 | 2.00 | 9.00 | 3.75 | 2 | 0.30 | 14 | 1.80 | 1.11 | 26.00 |

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**Figure 4.**Optimal winding layout for a quarter of the 5-phase $s/p\phantom{\rule{3.33333pt}{0ex}}40/44$.

**Figure 11.**FEA analysis for the case ${n}_{ph}=3$. (

**a**) Field lines and flux density of the SPM case, (

**b**) Field lines and flux density of the Spoke case, (

**c**) Field lines and flux density of the V-shape case, (

**d**) No-load EMF of the SPM case, (

**e**) No-load EMF of the Spoke case, (

**f**) No-load EMF of the V-shape case, (

**g**) EMF harmonic composition, (

**h**) EMF harmonic composition, (

**i**) EMF harmonic composition.

**Figure 12.**FEA analysis for the case ${n}_{ph}=5$. (

**a**) Field lines and flux density of the SPM case, (

**b**) Field lines and flux density of the Spoke case, (

**c**) Field lines and flux density of the V-shape case, (

**d**) No-load EMF of the SPM case (

**e**) No-load EMF of the Spoke case, (

**f**) No-load EMF of the V-shape case, (

**g**) EMF harmonic composition, (

**h**) EMF harmonic composition, (

**i**) EMF harmonic composition.

**Figure 13.**FEA analysis for the case ${n}_{ph}=6$. (

**a**) Field lines and flux density of the SPM case, (

**b**) Field lines and flux density of the Spoke case, (

**c**) Field lines and flux density of the V-shape case, (

**d**) No-load EMF of the SPM case, (

**e**) No-load EMF of the Spoke case, (

**f**) No-load EMF of the V-shape case, (

**g**) EMF harmonic composition, (

**h**) EMF harmonic composition, (

**i**) EMF harmonic composition.

**Figure 14.**FEA analysis for the case ${n}_{ph}=7$. (

**a**) Feild lines and flux density of the SPM case, (

**b**) Feild lines and flux density of the Spoke case, (

**c**) Feild lines and flux density of the V-shape case, (

**d**) No-load EMF the SPM case, (

**e**) No-load EMF the Spoke case, (

**f**) No-load EMF the V-shape case, (

**g**) EMF harmonic composition, (

**h**) EMF harmonic composition, (

**i**) EMF harmonic composition.

Specifications | Value |
---|---|

Propulsion chain number ${N}_{p}$ | 6 |

Propeller diameter ${D}_{p}$ (m) | 1.2 |

Propeller pitch ${H}_{p}$ (m) | 0.465 |

Thrust coefficient ${C}_{t}$ | 0.09787 |

Torque coefficient ${C}_{m}$ | 0.00402 |

Gross take-off weight $GTOW$ (kg) | 445 |

Thrust T (kg) | 74 |

Propeller speed ${N}_{p}$ (rpm) | 3300 |

Propeller torque ${M}_{p}$ N · m | 36 |

${\mathit{n}}_{\mathit{ph}}$ | $\mathit{s}/\mathit{p}$ Combination | $\mathit{LCM}$ | $\mathit{GCD}$ | k | ${\mathit{K}}_{\mathit{w}}$ | ||
---|---|---|---|---|---|---|---|

${\mathit{K}}_{\mathit{w}\mathbf{1}}$ | ${\mathit{K}}_{\mathit{w}\mathbf{3}}$ | ${\mathit{K}}_{\mathit{w}\mathbf{5}}$ | |||||

3 | 48/40 | 240 | 8 | 2 | 0.933 | - | - |

5 | 40/44 | 440 | 4 | 2 | 0.976 | 0.794 | - |

6 | 48/44 | 528 | 4 | 2 | 0.950 | 0.604 | - |

7 | 56/44 | 616 | 4 | 2 | 0.891 | 0.717 | 0.988 |

Injected Harmonic Current | Corresponding Odd Harmonics |
---|---|

$h=1$ (Main fictious machine) | $1,5,7,9,17,19,\cdots (2\xb7k=3c\pm 1)$ |

Injected Harmonic Current | Corresponding Odd Harmonics |
---|---|

$h=1$ (1st fictious machine) | $1,9,11,19,21,29,\cdots (2k+1=5c\pm 1)$ |

$h=3$ (2nd fictious machine) | $3,7,13,17,23,27,\cdots (2k+1=5c\pm 2)$ |

Injected Harmonic Current | Corresponding Odd Harmonics |
---|---|

$h=1$ (1st fictious machine) | $1,5,7,11,13,17,\cdots (2k+1=6c\pm 1)$ |

$h=3$ (2nd fictious machine) | $3,9,15,21,27,33,\cdots (2k+1=6c\pm 3)$ |

Injected Harmonic Current | Corresponding Odd Harmonics |
---|---|

$h=1$ (1st fictious machine) | $1,5,7,11,13,17,\cdots (2k+1=7c\pm 1)$ |

$h=5$ (2nd fictious machine) | $5,9,19,23,33,37,\cdots (2k+1=7c\pm 2)$ |

$h=3$ (third fictious machine) | $3,11,17,25,31,\cdots (2k+1=7c\pm 3)$ |

${\mathit{n}}_{\mathit{ph}}$ | SPM Configuration | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{avg}}$ | ${\mathit{T}}_{\mathit{rip}}$ | ${\mathit{T}}_{\mathit{md}}$ | ${\mathit{T}}_{\mathit{vd}}$ | ${\mathit{M}}_{\mathit{mot}}$ | ${\mathit{M}}_{\mathit{PM}}$ | ${\mathit{\eta}}_{\mathit{mot}}$ | ${\mathit{B}}_{\mathit{m}}$ | ${\mathit{P}}_{\mathit{core}}$ | ${\mathit{P}}_{\mathit{copper}}$ | ${\mathit{P}}_{\mathit{mv}}$ | |

3 | 36.26 | 12.77 | 8.79 | 66.38 | 4.13 | 0.51 | 93.78 | 2.028 | 662.05 | 262.35 | 83.18 |

5 | $36.96$ | $1.92$ | $12.03$ | $90.6$ | $3.08$ | $0.46$ | $93.97$ | $1.95$ | 426.01 | 499.51 | 67.49 |

6 | $36.3182$ | 5 | $13.05$ | $98.5$ | $2.78$ | $0.41$ | $93.77$ | $1.96$ | 387.44 | 554.10 | 69.09 |

7 | $37.83$ | $0.64$ | $11.53$ | $87.23$ | $3.29$ | $0.62$ | $91.76$ | $2.05$ | 476.71 | 873.47 | 72.15 |

${\mathit{n}}_{\mathit{ph}}$ | Spoke Configuration | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{avg}}$ | ${\mathit{T}}_{\mathit{rip}}$ | ${\mathit{T}}_{\mathit{md}}$ | ${\mathit{T}}_{\mathit{vd}}$ | ${\mathit{M}}_{\mathit{mot}}$ | ${\mathit{M}}_{\mathit{PM}}$ | ${\mathit{\eta}}_{\mathit{mot}}$ | ${\mathit{B}}_{\mathit{m}}$ | ${\mathit{P}}_{\mathit{core}}$ | ${\mathit{P}}_{\mathit{copper}}$ | ${\mathit{P}}_{\mathit{mv}}$ | |

3 | 35.708 | 16.01 | 9.13 | 68.98 | 3.91 | 0.68 | 91.64 | 2.08 | 1130.5 | 174.32 | 59.09 |

5 | $37.11$ | $6.30$ | $12.82$ | $95.50$ | $2.89$ | $0.42$ | $93.60$ | $2.02$ | 453.66 | 559.04 | 52.81 |

6 | $37.82$ | $4.25$ | $10.41$ | $77.49$ | $3.64$ | $0.47$ | $93.35$ | $2.02$ | 578.88 | 481.89 | 68.04 |

7 | $36.91$ | $4.23$ | $9.36$ | $69.79$ | $3.94$ | $0.49$ | $91.03$ | $2.036$ | 669.94 | 786.28 | 66.40 |

${\mathit{n}}_{\mathit{ph}}$ | V-Shape Configuration | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{avg}}$ | ${\mathit{T}}_{\mathit{rip}}$ | ${\mathit{T}}_{\mathit{md}}$ | ${\mathit{T}}_{\mathit{vd}}$ | ${\mathit{M}}_{\mathit{mot}}$ | ${\mathit{M}}_{\mathit{PM}}$ | ${\mathit{\eta}}_{\mathit{mot}}$ | ${\mathit{B}}_{\mathit{m}}$ | ${\mathit{P}}_{\mathit{core}}$ | ${\mathit{P}}_{\mathit{copper}}$ | ${\mathit{P}}_{\mathit{mv}}$ | |

3 | 36.00 | 15.27 | 6.90 | 52.01 | 5.21 | 0.83 | 91.13 | 2.50 | 1133.4 | 249.28 | 85.49 |

5 | $36.82$ | $5.19$ | $9.91$ | $73.98$ | $3.72$ | $0.49$ | $92.25$ | $2.06$ | 707.05 | 522.93 | 65.76 |

6 | $36.78$ | $9.81$ | $8.18$ | $60.78$ | $4.50$ | $0.52$ | $90.51$ | $2.59$ | 924.74 | 624.36 | 67.16 |

7 | $37.21$ | $3.86$ | $10.59$ | $79.43$ | $3.51$ | $0.56$ | $88.69$ | $2.50$ | 949.54 | 968.31 | 69.44 |

Performanaces of the 5-Phase Spoke EM | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{avg}}$ | ${\mathit{T}}_{\mathit{rip}}$ | ${\mathit{T}}_{\mathit{md}}$ | ${\mathit{T}}_{\mathit{vd}}$ | ${\mathit{M}}_{\mathit{mot}}$ | ${\mathit{M}}_{\mathit{PM}}$ | ${\mathit{\eta}}_{\mathit{mot}}$ | ${\mathit{B}}_{\mathit{m}}$ | ${\mathit{P}}_{\mathit{core}}$ | ${\mathit{P}}_{\mathit{copper}}$ | ${\mathit{P}}_{\mathit{mv}}$ | |

(a) | 36.58 | 1.42 | 10.25 | 76.41 | 3.57 | 0.60 | 93.01 | 2.03 | 600.41 | 488.88 | 61.53 |

(b) | $37.11$ | $6.30$ | $12.82$ | $95.50$ | $2.89$ | $0.42$ | $93.60$ | $2.02$ | 453.66 | 559.04 | 52.81 |

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© 2024 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chahba, S.; Krebs, G.; Morel, C.; Sehab, R.; Akrad, A.
Design Optimisation Approach of an Outer Rotor Multiphase PM Actuator for Multirotor Aerial Vehicle Applications. *Aerospace* **2024**, *11*, 150.
https://doi.org/10.3390/aerospace11020150

**AMA Style**

Chahba S, Krebs G, Morel C, Sehab R, Akrad A.
Design Optimisation Approach of an Outer Rotor Multiphase PM Actuator for Multirotor Aerial Vehicle Applications. *Aerospace*. 2024; 11(2):150.
https://doi.org/10.3390/aerospace11020150

**Chicago/Turabian Style**

Chahba, Saad, Guillaume Krebs, Cristina Morel, Rabia Sehab, and Ahmad Akrad.
2024. "Design Optimisation Approach of an Outer Rotor Multiphase PM Actuator for Multirotor Aerial Vehicle Applications" *Aerospace* 11, no. 2: 150.
https://doi.org/10.3390/aerospace11020150