# Magnetic Noise Reduction of In-Wheel Permanent Magnet Synchronous Motors for Light-Duty Electric Vehicles

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## Abstract

**:**

## 1. Introduction

#### 1.1. Research Gap and Original Contributions

#### 1.2. Paper’s Organization and Presentation

## 2. Analytical Vibro-Acoustic Modelling Using Multi-Slice Subdomain Model (MS-SDM) for Wheel Hub-Mounted Permanent Magnet Synchronous Motor (WHM-PMSM)

_{skew}is the skew angle.

_{x}and F

_{y}are defined based on the cylindrical coordinate system [7]:

_{zgj}is the vector potential in the middle of air-gap for the jth subdomain slice, F

_{rj}is the radial magnetic force for the jth subdomain slice, B

_{rj}and B

_{tj}are the radial and tangential components of magnetic flux density in the middle of air-gap jth subdomain slice, θ is the mechanical angular position, n is the spatial harmonic order, k is the time harmonic order, ω is the angular velocity, r is the radius of the rotor, and m is the mass of rotor. F

_{c}is the centrifugal force.

_{0j}denotes the air acoustic impedance, S

_{cj}is the WHM-PMSM frame area at jth slice, and σ

_{mj}is the modal radiation factor at jth slice. The maximum sound power level W

_{ωj}at jth subdomain slice [15] can be computed using:

_{0}can be defined as [16]:

_{f}as the frame width, K

_{fsj}is the stator stacking factor at jth slice, ρ

_{sj}is the stator stack mass density at jth slice, and Δ

_{m}denotes the increasing mass because of the winding and teeth.

- Both stator and rotor are subjected to find the optimal angle of skew at each jth subdomain slice.
- End effects are neglected because FSCW with non-overlapping configuration have very short end-windings at the studied WHM-PMSM.
- Leakage flux in axial direction is ignored.
- Main slotting magnetic forces wavenumbers and frequencies are considered.
- The range of slice number j is 20 which means one slice per each 5 mm, in case of 100 mm stack length.
- Variable speed analysis is targeted for the electromagnetic-acoustic performance of the WHM-PMSM.
- The magnetic flux density along the axial axis is applied using 2D FEA for a higher accuracy.
- The demagnetization characteristics of the permanent magnets are considered non-linear.
- The analysis is done under load condition.
- Natural frequencies are considered at variable speed analysis for the WHM-PMSM.

## 3. Results and Discussion

^{−3}. The elastic characteristics of the lamination is E

_{x}= 215 MPa, E

_{y}= 215 MPa, and E

_{z}= 80 MPa, besides, shear modulus is G

_{xy}= 82.7 MPa, G

_{yz}= 2 MPa, and G

_{zx}= 2 Mpa; the mechanical properties of the material used can be seen in Table 1. All the following sections are based on 3D FEA unless specifically indicated otherwise.

_{r}from the inner stator excited coils, F

_{c}, due to its mechanical essence, has a clockwise vector direction (based on the right’s hand law) because of the body’s inertia with a uniform distribution. Both the radial and centrifugal forces have a distribution with a radial vector direction and have an overlapped influence on each other. A summation of them, leading up to the resultant blue curve in this graph, indicates the total (or actual) radial force on the rotor.

_{x}and A-weighted maximum sound power level W

_{p,max}(shown in Figure 3) was calculated at variable speeds from N

_{min}= 15 rpm to N

_{max}= 1000 rpm. To find the best possible angle for each part (stator and rotor), this computation evaluates the impact of each variable on the objectives with respect to each other. Each graph is also a function of the number of skew slices. Figure 3a presents two main regions (red and blue dashed areas) in which the red area is where the stator skew obtains the highest rate, between 1 to 1.2, whereas the rotor skew rate is lower. This area provides a higher level of W

_{p,max}, between 92.4 to 92.5 dBA. The lowest W

_{p,max}(optimal area) is reached when the highest rate of rotor skew angle (including magnets), and smaller stator angle skew were chosen (92.2 dBA). Comparing to the initial skew angle, which is analytically calculated (black arrow), an enhancement of approximately 1 dBA has been achieved. The analytical MS-SDM method used is based on the average flux density in 2D along the axial direction. Additionally, this graph (Figure 3a) depicted the skew model by j = 20 slices. Figure 3b illustrates the optimal area as the same as Figure 3a with ratings of 1.2 and 0.8 for the rotor and stator. However, a larger F

_{x}with skew slice of 20 in comparison with lower slice numbers, which produces consequently higher outputs, such as torque. Figure 3c demonstrates how the odd number (15) of the skew slots again decreases F

_{x}by nearly 100 N. In this configuration, W

_{p}has been enhanced by 1.5 dBA when compared to the initial model. As presented in Figure 3d, higher F

_{x}has been produced by maximum value of 874 N, when an even number (20) of skew slice has been used. Therefore, the importance of the skew slice number on F

_{x}and its harmonics are considerable with respect to the number of stator slots and rotor magnets (or slots, in case of other machine topologies) which can be an even or odd variable), has significant influence on the sound power level as function of speed. This figure helps in identifying number proportionally, although, it could not directly reduce W

_{p}.

_{p}amplitude is decreased for the optimum skew angles, as shown in Figure 4b.

_{s}is an integer involved in permeance Fourier series, and ±ε varies between −1 to 1. There are two main resonances marked as 1 and 2, which have occurred at 172 Hz and 516 rpm, as well as 185 Hz and 554 rpm. In addition, the WHM-PMSM rotates in the flux weakening condition at 430 rpm which is indicated by the red dashed line. Afterwards, the largest 736 rpm, 488 Hz. Note that the first resonance at structural mode (2,0) happens when the electrical frequency of the traveling force wave of wavenumber r matches with the circumferential mode natural frequency, where 2 is the rank of the circumferential deflection, and 0 denotes the rank of the longitudinal deflection in the structural mode. To evaluate all the natural frequencies of the WHM-PMSM with rated speed of 15–150 rpm (0 to 50 Hz), the radial velocity in unit of dBA should be computed for over 5000 Hz.

## 4. FEA and Experimental Verifications

#### Electromagnetic-Based Investigations

^{−3}) in higher number of slices, such as 10 to 20.

_{max}− T

_{min}/T

_{avg}× 100) is also ideally decreased, in which the initial and optimum PMSMs have 9% and 7.9%, respectively. In Figure 9e, the total loss as a function of slice number is provided, using MS-SDM and FEA simulations. The study reinforces that the slice number can reduce the total loss due to presence of high eddy-current loss at both iron cores and magnets. However, this modification comes with cost in the manufacturing stage; therefore, it is indeed an engineering trade-off among several factors, such as noise and vibration reduction and electromagnetic capability, as well as the manufacturing costs. In addition, the results show that the current phase angle affects the total core and magnet losses at certain armature current amplitude of 150A. The transient eddy-current loss produced at the magnets is simulated under different current angles of 60° and 90°. Additionally, the simulations indicate that PWM converter and sinusoidal supply can highly influence the amplitude of the magnet loss because of the harmonics injected by the PWM converter. The FEA-based simulation and experimental results verify that the semi-analytical MS-SDM approach is reliable for electromagnetic capabilities (including noise and vibration) predictions.

- (a)
- Displacement (frequency range of below 100 Hz).
- (b)
- Speed (frequency range of 10 Hz to 1 kHz).
- (c)
- Acceleration (high frequency measurement > 1 kHz).

_{vib,max}shows the maximum magnitude of vibration in the defined speed range of 15–150 rpm, in which the vibration has reduced in the optimized model by 7.2 dB in comparison to initial model. Furthermore, small improvements can be reported for output power P

_{o}, electromagnetic torque T, efficiency η, and constant power speed range constant-power-speed-range (CPSR). In addition, the fundamental d-axis phase flux linkage λ

_{m}remains almost constant.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Simplified drivetrain scheme for the light-duty fully electric vehicle. BWHM = brushless wheel hub-mounted; PMSM = permanent magnet synchronous motor; UC = ultra-capacitor.

**Figure 2.**Maximum radial force (normal and centrifugal components) of the wheel hub-mounted permanent magnet synchronous motor (WHM-PMSM) under 4.9A root mean square (RMS) excitation current with 30° rotation.

**Figure 3.**Objective-variable-based variation of stator and rotor skew angle versus F

_{x}and L

_{p,max}as function of skew slice number (

**a**) 5 slices, (

**b**) 10 slices, (

**c**) 15 slices, and (

**d**) 20 slices.

**Figure 4.**Modal contribution of the machine’s structure on the magnetic noise (sound power), listed as: (

**a**) Initial and (

**b**) Optimized WHM-PMSMs.

**Figure 5.**One third octave A-weighted acoustic noise spectrum, as listed: (

**a**) Initial, (

**b**) Optimized WHM-PMSM.

**Figure 7.**Convergence of the relative error on the maximum magnetic noise W

_{p}using different multi-slice subdomain models (MS-SDMs).

**Figure 8.**Magnitude fast fourier transform (FFT) of radial flux density using MS-SDM and 3D-FEA, as listed: (

**a**) as function of space and (

**b**) as function of time.

**Figure 9.**Electromagnetic capability validations of the in-wheel PMSM, listed as: (

**a**) three-phase back-EMF, (

**b**) critical back-EMF harmonics, (

**c**) cogging torque (

**d**) torque, (

**e**) effect of iron core slice number on the total loss as function of different current phase angles, and (

**f**) transient magnet loss.

**Figure 11.**Manufactured WHM-PMSM based on optimized skew angles, listed as: (

**a**) Permanent magnets including rotor iron back, (

**b**) stator slots, (

**c**) assembled wheel hub-mounted-PMSM.

Parameters | Values | Units |
---|---|---|

Geometrical | ||

R_{ri}/R_{ro} | 217/230 | mm |

R_{si}/R_{so} | 115/209.5 | mm |

S_{w} | 15 | mm |

δ_{g} | 0.6 | mm |

Q_{s}/2P | 36/40 | - |

α_{p} | 0.55 | - |

SP | 0.9 | - |

Electrical | ||

m | 3 | - |

N_{c} | 80 | turns |

J_{rms} | 1.2206 | - |

I_{rms} | 4.899 | A/mm^{2} |

Number of parallel circuit per phase | 2 | - |

Slot/pole/phase | 0.3 | - |

λ_{d} | 1703.9381 | mVs |

Line-to-line inductance (d-axis) | 937.8789 | mH |

Magnetic | ||

μ_{0} | 4π × 10^{−7} | H/m |

μ_{s} | 2500 | - |

μ_{PM} | 1.05 | - |

μ_{air} | 1 | - |

B_{rm} | 1.2 | T |

H_{k} | 891 × 10^{3} | A/m |

Magnet permeance per half pole | 0.1437 | μWb/At |

Skew Rates/h. Order | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 1.1 | 1.2 |
---|---|---|---|---|---|---|---|

1 | 0.83 | 0.84 | 0.89 | 0.91 | 0.92 | 0.96 | 0.99 |

3 | 0.71 | 0.69 | 0.67 | 0.66 | 0.61 | 0.56 | 0.53 |

5 | 0.47 | 0.46 | 0.44 | 0.41 | 0.41 | 0.38 | 0.37 |

7 | 0.38 | 0.37 | 0.34 | 0.35 | 0.33 | 0.33 | 0.33 |

9 | −0.25 | −0.25 | −0.26 | −0.24 | −0.27 | −0.27 | −0.28 |

11 | −0.3 | −0.29 | −0.33 | −0.34 | −0.3 | −0.29 | −0.29 |

13 | −0.22 | −0.21 | −0.23 | −0.23 | −0.22 | −0.21 | −0.21 |

15 | 0.1 | 0.09 | 0.11 | 0.04 | 0.05 | 0.04 | 0.02 |

17 | 0.23 | 0.19 | 0.18 | 0.21 | 0.2 | 0.2 | 0.19 |

19 | 0.29 | 0.29 | 0.25 | 0.23 | 0.25 | 0.23 | 0.2 |

21 | −0.06 | −0.04 | −0.04 | −0.05 | −0.02 | −0.01 | 0 |

23 | −0.12 | −0.1 | −0.11 | −0.08 | −0.07 | −0.04 | −0.01 |

25 | −0.09 | −0.07 | −0.07 | −0.05 | −0.04 | −0.04 | −0.04 |

27 | 0.07 | 0.01 | 0.01 | 0 | 0.01 | 0 | 0 |

29 | 0.12 | 0.12 | 0.08 | 0.08 | 0.13 | 0.09 | 0.07 |

31 | 0.07 | 0.08 | 0.07 | 0.04 | 0.02 | 0.02 | 0.01 |

Component | Model | Range |
---|---|---|

PULSE Empty C-Size Front End (5In)-Dyn-X | 3560-C-E12 | - |

Microphone of ½ (free field) | 4188 | 8–12.5 kHz, pre-polarized |

preamplifier microphone ½ | 2669B | - |

Microphone Cable LEMO | AO-0419-d-150 | 0 B to 1 B connector 15m |

windscreen of ½ mod. UA0459 | EG-9999 | - |

PULSE Sound Power, Node-locked License | 7799-N | - |

CPB analysis program and overall of 1 channel | 7771-N1 | - |

program analysis of FFT and Overall of 1 channel | 7770-N1 | - |

Sound level calibrator | 4231 | - |

Parameters/Model | No Skew | Initial | Optimized | Test |
---|---|---|---|---|

λ_{m} (mVs) | 1691.5 | 1714 | 1721.3 | 1718 |

P_{o} (W) | 449.2 | 503.2 | 514.7 | 511.7 |

η (%) | 92.1 | 95.8 | 97 | 96.9 |

CPSR | 434.5 | 477.3 | 487.9 | 505.8 |

Net Torque | 314.6 | 367.4 | 367.2 | 366.8 |

L_{vib, max} (dB) | 118.7 | 110.6 | 102.8 | 105.6 |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Asef, P.; Bargallo, R.; Lapthorn, A. Magnetic Noise Reduction of In-Wheel Permanent Magnet Synchronous Motors for Light-Duty Electric Vehicles. *Vehicles* **2020**, *2*, 156-172.
https://doi.org/10.3390/vehicles2010009

**AMA Style**

Asef P, Bargallo R, Lapthorn A. Magnetic Noise Reduction of In-Wheel Permanent Magnet Synchronous Motors for Light-Duty Electric Vehicles. *Vehicles*. 2020; 2(1):156-172.
https://doi.org/10.3390/vehicles2010009

**Chicago/Turabian Style**

Asef, Pedram, Ramon Bargallo, and Andrew Lapthorn. 2020. "Magnetic Noise Reduction of In-Wheel Permanent Magnet Synchronous Motors for Light-Duty Electric Vehicles" *Vehicles* 2, no. 1: 156-172.
https://doi.org/10.3390/vehicles2010009