United States

Surface Permanent magnet (SPM) motors are generally used in small traction applications due to high power density, simple designing and easy manufacturing processes.
SPM motors dominates the market particularly for small permanent magnet motors.However, the major concern with the SPM motors is their higher demagnetization risks due to close
exposure of PM to the stator windings [1]. In order to avoid demagnetization risks, such motors use the critical rare-earth permanent magnets (REPMs) which are prone to supply disruption
and critical availability, hence poses a long-time sustainability challenge [2]. Many attempts have been made [3-4], for reduction of critical REPMs in permanent magnet motors. However,
most of these attempts focus on the interior permanent magnet motors but rarely on SPM motors.
This work proposes a reduced rare-earth sandwich surface permanent magnet (SSPM) motor, which uses cost-effective and abundant ferrite permanent magnets (FPM, (BH)max=3 MGOe)
between two high-energy product rare-earth PM (Nd-Fe-B, (BH)max =33 MGOe) layers. The main idea of such a magnet structure is that the REPM drives the FPM to operate at higher
flux density which reduces demagnetization susceptibilities of the FPM without degrading torque capability of the motor. Equivalent magnetic circuit (EMC) approach is applied to
investigate the SSPM motor and the approach can also be applied to represent a sandwiched multiple type magnet structure with an equivalent single magnet. The performance of
sandwich-type magnets is carried out on a small traction motor (1.75 kW, 640 rpm motor) [5]. The output torque and demagnetization performance of the motor with different magnets are
given in Table-I and Fig.1. The present work offers a way to reduce the consumption of critical REPM materials in PM motors without significant performance degradation.
This research was supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy,
Advanced Manufacturing Office.&lt;br&gt;

**References:**&lt;br&gt;


[1] A. M. El-Refaie. T. M. Jahns, and D. W. Novotny, IEEE Trans. Magn., vol. 21, pp. 34-43, 2006.&lt;br&gt;
[2] R. T. Nguyen, D. D. Imholte, A. C. Matthews, and W. D. Swank, Waste Management, vol. 83, Pp. 209-217, 2019,&lt;br&gt;
[3] W. Wu, X. Zhu, L. Quan, Y. Du, Z. Xiang and X. Zhu, IEEE Transactions on Applied Superconductivity, vol. 28, pp. 1-6, 2018.&lt;br&gt;
[4] Y. Chen, T. Cai, X. Zhu, D. Fan and Q. Wang, IEEE Transactions on Applied Superconductivity, vol. 30, pp. 1-6, 2020.&lt;br&gt;
[5] N. Y. Braiwish, F. J. Anayi, A. A. Fahmy and E. E. Eldukhri, 49th International Universities Power Engineering Conference (UPEC-2014), pp. 1-5, 2014.&lt;br&gt;

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MMM 2022

Design and Analysis of Reduced Rare Earth Magnet Surface Permanent Magnet Motor using Sandwich Magnets

Surface Permanent magnet (SPM) motors are generally used in small traction applications due to high power density, simple designing and easy manufacturing processes.
SPM motors dominates the market particularly for small permanent magnet motors.However, the major concern with the SPM motors is their higher demagnetization risks due to close
exposure of PM to the stator windings [1]. In order to avoid demagnetization risks, such motors use the critical rare-earth permanent magnets (REPMs) which are prone to supply disruption
and critical availability, hence poses a long-time sustainability challenge [2]. Many attempts have been made [3-4], for reduction of critical REPMs in permanent magnet motors. However,
most of these attempts focus on the interior permanent magnet motors but rarely on SPM motors.
This work proposes a reduced rare-earth sandwich surface permanent magnet (SSPM) motor, which uses cost-effective and abundant ferrite permanent magnets (FPM, (BH)max=3 MGOe)
between two high-energy product rare-earth PM (Nd-Fe-B, (BH)max =33 MGOe) layers. The main idea of such a magnet structure is that the REPM drives the FPM to operate at higher
flux density which reduces demagnetization susceptibilities of the FPM without degrading torque capability of the motor. Equivalent magnetic circuit (EMC) approach is applied to
investigate the SSPM motor and the approach can also be applied to represent a sandwiched multiple type magnet structure with an equivalent single magnet. The performance of
sandwich-type magnets is carried out on a small traction motor (1.75 kW, 640 rpm motor) [5]. The output torque and demagnetization performance of the motor with different magnets are
given in Table-I and Fig.1. The present work offers a way to reduce the consumption of critical REPM materials in PM motors without significant performance degradation.
This research was supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy,
Advanced Manufacturing Office. 

**References:** 


[1] A. M. El-Refaie. T. M. Jahns, and D. W. Novotny, IEEE Trans. Magn., vol. 21, pp. 34-43, 2006. 
[2] R. T. Nguyen, D. D. Imholte, A. C. Matthews, and W. D. Swank, Waste Management, vol. 83, Pp. 209-217, 2019, 
[3] W. Wu, X. Zhu, L. Quan, Y. Du, Z. Xiang and X. Zhu, IEEE Transactions on Applied Superconductivity, vol. 28, pp. 1-6, 2018. 
[4] Y. Chen, T. Cai, X. Zhu, D. Fan and Q. Wang, IEEE Transactions on Applied Superconductivity, vol. 30, pp. 1-6, 2020. 
[5] N. Y. Braiwish, F. J. Anayi, A. A. Fahmy and E. E. Eldukhri, 49th International Universities Power Engineering Conference (UPEC-2014), pp. 1-5, 2014. 

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poster

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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For tickets to the event, please register at the following link: https://magnetism.org/registration

Please register for the MMM 2022 conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Compared with non-grain-oriented silicon sheet (NGO), the grain-oriented silicon sheet (GO) has superior magnetic characteristic along its rolling direction, but bad
characteristic along other directions. GO silicon sheet is a popular material used in transformers [1]. For electrical machines, it can be only used to design the stator teeth [2]. While,
reasonable design and optimization of joint part between the GO silicon sheets and NGO silicon sheets is very important, otherwise the main performance of electrical machine with hybrid
GO - NGO cores will be reduced. In the pasts, optimizing main dimensions is a main mainstream however shape optimization of the joint part was neglected. In this paper, the shape design
optimization method is adopted for obtaining the best joint shape between the GO and NGO silicon sheets based on an 12 slot 8 pole (12s8p) interior permanent magnet machine (IPMSM)
as shown in Fig. 1(a). For achieving better machine performance, the magnetic barrier shape are optimized as well. Specifically, the GO silicon sheets are used for building the stator teeth,
and the others are made by NGO silicon sheets. By using finite element method (FEM), the main performance of the IPMSM with different GO silicon sheets can be obtained. Piecewise
linear interpolation method is used to establish the GO silicon sheets and rotor barrier shape, as shown in Fig. 1(b) and (c). Fig. 1(d) shows the obtained new rotor barrier shape after
optimization. For benchmark comparison the optimized traditional IPMSM with 12s8p and IPMSM with 48s8p with NGO silicon sheets are adopted. Fig 2 shows the performance
comparison of 12s8p IPMSM using NGO (NGO-IPMSM (12 Slot)), 12s8p IPMSM using GO teeth (GO-IPMSM (12 Slot)), 12s8p IPMSM using GO teeth and new magnetic flux barriers
(GO-B-IPMSM (12 Slot)), and 48s8p IPMSM using NGO (NGO-IPMSM (48 Slot)). More results will be presented in the final submission. 


**References:** 

[1] S. Magdaleno-Adame, T. D. Kefalas, A. Fakhravar and J. C. Olivares-Galvan, "Comparative Study of Grain Oriented and Non–Oriented Electrical Steels in Magnetic 
Shunts of Power Transformers," 2018 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), 2018, pp. 1-7. 
[2] Y. Tsuchiya and K. Akatsu, "A Study of the Switched Reluctance Motor using Grain-Oriented Electrical Steel Sheets," 2020 IEEE Energy Conversion Congress and Exposition
(ECCE), 2020, pp. 3623-3628. 

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Shape Design Optimization of Interior Permanent Magnet Synchronous Machine with Hybrid GO and NGO Silicon Sheet Cores

Bolting or sleeve are applied to permanent magnet synchronous generators (PMSGs) to prevent shattering permanent magnet (PM)-generated defects[1],[2]. Of these,
bolting is more useful than a sleeve during manufacturing. However, as the magnetic flux is reduced due to the material characteristics of the bolting, overhang structure is often used for
PM machines to compensate for the flux reduction[2]. Therefore, the axial length of the rotor must be considered during the overhang structure-based 3D analysis[2]. However, the analysis
of a 3D model with diverse and complex design variables is time-intensive[2].
In this study, we analyzed a PMSG considering the bolting and overhang structure based on an analytical method. Preferably, the initial design process must consider several variables, and
the analysis time of a PMSG with a complex structure must be reduced[2]. Characteristic analyses using a semi-3D method have been employed previously. However, there is a limit to the
variation of 2D design variables to ensure that they are not saturated when considering a 3D shape. Therefore, we propose analytical methods using electromagnetic transfer relations[3]. It
was used to analytical method considering the operating point of the PM calculated through magnetic energy analyses of the overhang and 3D models [2]–[4]. These were applied to the
region of PMs with the overhang[1],[2]. Performance analysis of the separated overhang and bolting regions was conducted based on the superposition principle[1],[2]. A circuit parameter
was derived based on the predicted results and applied to the equivalent circuit of the generator[2]. The performance results were compared with the 3D model and experimental results.
Figs. 1(a)–(c) and 2(a) illustrate the manufactured and analysis models, respectively. Fig. 2(b) depicts the variation in the operating point of the PM. Figs. 2(c) and (d) illustrate the results
obtained from the comparison of 3D, analytical, and experiment models. The results appear to be in near agreement. 

**References:** 

[1] K.H Shin, J.Y. Choi, "Electromagnetic Analysis of Permanent Magnet Synchronous Generator Considering Permanent Magnet Bolting" KOSMEE, pp. 154-154, 2018. 
[2] J.S. Hong, K.H. Shin, J.Y. Choi.,"Semi-3D Analysis of a Permanent Magnet Synchronous Generator Considering Bolting and Overhang Structure." Energies 15, no. 12: 4374.2022. 
[3] S. Jang, M. Koo, J. Choi, "Characteristic Analysis of Permanent Magnet Synchronous Machines Under Different Construction Conditions of Rotor Magnetic Circuits by Using 
Electromagnetic Transfer Relations," in IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 3665-3668, Oct. 2011. 
[4] J. Song, J. H. Lee, S. Jung, "Computational Method of Effective Remanence Flux Density to Consider PM Overhang Effect for Spoke-Type PM Motor With 2-D Analysis Using 
Magnetic Energy," in IEEE Transactions on Magnetics, vol. 52, no. 3, pp. 1-4, March 2016. 

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Characteristic Analysis of a Permanent Magnet Synchronous Generator Considering Overhang and Bolting Structure Based on Analytical Method

In-wheel motor technology is committed to provide a better travel for electric vehicles (EVs), which leads the way to innovation for a new generation of EVs. Quite
excitingly, the in-wheel motor generates power directly in vehicle wheel. It means that improved power performance and operation efficiency can be achieved potentially for the EVs with
in-wheel drive. Generally, the motor torque guarantees general drive requirements, while the loss determines operation efficiency. It is noted that, during the design process of motor, there
is relatively complex association between the two performances. Hence, how to obtain a capability of excellent low-speed large-torque and low loss characteristic is the essential entry point
for the study of in-wheel motor [1],[2].
In this paper, the research on improvement of torque and loss characteristics is presented for a spoke-type in-wheel PM (SIW-PM) motor. In the perspective of flux modulation, a concept
of featured airgap harmonic is introduced into the motor design. By purposely designing the featured harmonic, a well tradeoff is realized between the torque and loss of SIW-PM motor.
Fig. 1 shows the topology of the motor. Fig. 2 shows an analysis of the amplitude of main harmonics, the torque contribution of harmonics, and the rotor magnetic density, in which the 5th
harmonic produces positive loss and negative torque. Reducing the amplitude of the fifth harmonic can effectively reduce rotor loss and improve the output torque. As is shown in Fig. 3,
sensitivity analysis is used to find the parameters with high sensitivity to 5th flux density harmonic amplitude [3]. Fig. 4 shows Pareto front of harmonic amplitude generated by parameter
optimization, in which optimal sample is selected as optimization results. Fig. 5 shows the rotor core loss distribution before and after optimization. The comparison of torque and rotor loss
before and after optimization is given, as shown in Fig. 6 and Fig. 7. The results show that the rotor core loss is reduced and the output torque is increased by suppressing the amplitude of
the 5th harmonic.
More detailed analysis and experimental verification will be presented in the full paper. 


**References:** 

[1] Z. Q. Zhu and J. T. Chen, IEEE Trans. Magn., vol. 46, no. 6, pp. 1447-1453, Jun. 2010. 
[2] X. Zhou, X. Zhu and W. Wu, IEEE Transactions on Industrial Electronics., vol. 68, no. 8, pp. 6516-6526, Aug. 2021. 
[3] G. Lei, C. Liu, and J. Zhu, IEEE Transactions on Energy Conversion., vol. 30, no. 4, pp. 1574-1584, Dec. 2015. 

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Research on Improvement of Torque and Loss Characteristics for an In Wheel Permanent Magnet Motor Considering Featured

Electromagnetic interference (EMI) causes various serious problems such as data loss, misinterpretation of data, and cross-talk between electronic devices. Thus, the
materials with high shielding effectiveness (SE) have been quested to attenuate or reflect EM waves. Various materials and compositions and synthetic methods have been investigated,
optimized, and adapted to achieve the desired SE (> 30 dB) [1-4]. These approaches can provide the optimal SE of the material of interest but are costly due to a long period of optimization
and expensive characterization of investigated materials.
To reduce EMI materials development time and effort, we propose Artificial Intelligence (AI)-based modeling, predicting the SE of materials. We used MATLAB to create random input
parameters, Simulink to calculate SE, and Classification Learner to determine data reliability. We take the following nine input parameters to estimate SE of FINEMET (Fe-Si-Nb-Cu-BCr-
Mn-Ni-Co), MnZn-ferrite, and NiZn-ferrite: incoming electric field, transmission (TC) and reflection (RC) coefficients, thickness, frequency, and real and imaginary parts of
permeability (μr) and permittivity (εr). Fig. 1 shows the Simulink block diagram for calculating SE. First, we sampled 200 random TC and RC of the materials and then calculate the SEs
with seven fixed input parameters. Among calculated SEs (Fig. 2e), the reliable SEs (Fig. 2f) are determined using AI. Our preliminary results show that the reliability was 19.5%, meaning
that 39 of 200 samples are reliable. The estimated SE was compared with the experimental SE [1] to assess the accuracy of the developed AI modeling. The estimated and experimental
maximum SEs are 31.87 dB and 30.61 dB, respectively, as shown in Fig. 2 (d,f,g). Accordingly, the effectiveness of our proposed method is validated. We will present how to predict the
SE of EMI materials in detail.
*This work was supported in part by the National Science Foundation (NSF) IUCRC under Grant No. 2137275. 

**References:** 

[1] Anatoly B. Rinkevich, Dmitry V Perov, and Yuriy I Ryabkov, Materials, 14, 3499 (2021). 
[2] Isa ARAZ, Turkish Journal of Electrical Engineering & Computer Sciences, 26, 2996 (2018). 
[3] Jing Li, yao-Jiang Zhang, Aleksandr Gafarov, Soumya De, Marina Y. Koledintseva, Joel Marchand, David Hess, Todd Durant, Eric Nickerson, James L. Drewniak, and Jun Fan, 2012 
IEEE International Symposium on Electromagnetic Compatibility, 646, (2012).
[4] Jae Man Song, Dong Il Kim, and Kyeung Jin O, Journal of the Korea Electromagnetic Engineering Society 6, 71, (2006). 

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EMI Materials Design for High Shielding Effectiveness using AI (Machine Learning)

Magnetic microrobots actuated by a magnetic navigation system (MNS) have gained importance as a versatile device with minimally invasive and wireless manipulation
abilities in various biomedical applications [1, 2]. Generally, MNSs are composed of multiple numbers of coils and massive turns of wires to generate a sufficiently strong magnetic field to
manipulate the microrobots’ mechanical motions. In our previous research, we proposed a geometrically compact and magnetically efficient MNS composed of a triad of electromagnetic
coils (TEC), as shown in Fig. 1 [3, 4]. In the TEC, there are only three control variables (three coil currents) for manipulating two-dimensional (2D) microrobots. In this research, we
investigated a new magnetic field generation method to improve the TEC’s magnetic efficiency in generating 2D microrobot motions. Based on the physical property of a magnetic coil that
acts as a pulling magnet for a microrobot, we established a process and several equations by which one can maneuver the 2D microrobot motions via the selective control of only two coil
currents of the TEC. We also employed a closed-loop controller for the method so that the microrobot can move along a programmed pathway actuated by the TEC. We then constructed an
experimental setup to demonstrate and validate the controlled motions of the microrobot using the proposed method. The experimental results shown in Fig. 2 state that the combination of
only two coils of the TEC can also generate relatively complex 2D motions of a microrobot. This research can contribute to developing an optimal MNS and strategy that can be used to
manipulate 2D magnetic microrobots for various biomedical and biological applications, including minimally invasive surgery, targeted drug and cargo delivery, microfluidic control, etc. 

**References:** 

[1] L. Wang, Z. Meng, Y. Chen and Y. Zheng, “Engineering magnetic micro/nanorobots for versatile biomedical applications.,” Advanced Intelligent Systems., vol. 3, no. 9, pp.
2000267, 2021. 
[2] T. Xu, J. Yu, X. Yan, H. S. Choi and L. Zhang, “Magnetic actuation based motion control for microrobots: An overview.,” Micromachines., vol. 6, no. 9, pp. 1346-1364, 2015. 
[3] H. Lee and S. Jeon, “Two-dimensional manipulation of a magnetic robot using a triad of electromagnetic coils.,” AIP Advances., vol. 10, no. 1, pp. 015003, 2020. 
[4] H. Lee, D. Lee, and S. Jeon, “A two-dimensional manipulation method for a magnetic microrobot with a large region of interest using a triad of electromagnetic coils.,”
Micromachines., vol. 13, no. 3, pp. 416, 2022. 

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A Selective Magnetic Field Generation Method for the Manipulation of Two Dimensional Magnetic Microrobots Using a Triad of Electromagnetic Coils

Recently, interior permanent magnet motors have been widely employed in various commercial electric vehicles. To expand the cruising range of EVs, the analysis and
improvement of efficiency for the IPM motors have attracted increasing attention [1]. For the IPM motors, a large current is often required to weaken the PM magnetic field to increase the
speed range, which inevitably increases the copper and iron losses of the motor, resulting in a decrease in efficiency under high speed [2]. Consequently, it is necessary and full of
challenges to research and expands the high-efficiency region of the IPM motor, especially at high speed. In this paper, by introducing the new magnetic field variable effect into an interior
PM motor, the variable magnetic field can be obtained under different operation conditions, which not only helps to reduce the copper and core losses under different operation conditions
but also widens high-efficiency region.[3]
Fig 1 shows the topology of the proposed VMF motor and the structure of the corresponding variable magnetic field. To explore the performance advantage of the proposed VMF motor,
three operation points are selected to investigated, which can be classified into two operation conditions, as shown in Fig. 2. By the purposeful design of variable magnetic field structure,
the increased efficiency of high-speed operation point and the expanded high-efficiency region can be realized. Fig 3 shows the comparison of the performance of the VMF and IPM motor,
including no-load flux density and back-EMF. Fig 4 shows the flux density distributions of the VMF motor under different operation condition. Furthermore, the loss distributions of the
IPM and VMF motor under different conditions are shown in Fig 5. As can be seen from the Table I and Fig6, the efficiency of the motor has been improved and broadened, especially at
point C, the efficiency has increased to 96.5%. Consequently, it is noted that the efficiency of the VMF motor is improved and the high-efficiency region is widened, which verifies the
effectiveness of the VMF motor design proposed in this paper.
More detailed analysis and experimental verification will be presented in the full paper. 

References [1] W. Jiang, S. Feng and Z. Zhang, IEEE Transactions on Magnetics., vol. 54, no. 11, pp. 1-5, Nov. 2018, Art no. 8108005. 
[2] H. Hua and Z. Q. Zhu, IEEE Trans. Energy Convers, vol. 32, no. 2, pp. 495-504, June 2017. 
[3] A. Athavale, T. Fukushige and T. Kato, IEEE Trans. Ind. Appl., vol. 52, no. 1, pp. 234-241, Jan.-Feb. 2016. 

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Research on High efficiency Region of Interior Permanent Magnet Synchronous Motor with Variable Magnetic Field Effect

Permanent magnet (PM) motors have been widely applicable for electric vehicles due to their excellent power density and efficiency. Yet, due to the relatively constant
airgap magnetic field, the motor always suffers from a limited speed range. So, the achievement of a wide speed range is one of the hot research orientations for PM motors. In recent years,
a type of leakage-flux-controllable (LFC) motor has attracted some interest and attention of researchers, where the magnetic bridge and flux barrier are purposely designed in PM rotor for
forming the controllable leakage flux[1]. Based on this, the LFC-PM motor possesses the potential advantages of speed regulation[2]. It is noted that to realize the condition of no leakage
flux in motor drive process, a relatively strong armature field is usually required to be applied at this time, and, correspondingly, the magnetic saturation comes with that. It means that the
torque capability of LFC PM motor is worthy of attention and full of challenge, especially on the drive requirements of low-speed large torque.
In this study, a V-typed leakage-flux-controllable PM (VFLC-PM) motor with multiple functional magnetic flux barrier units is proposed, which can provide relatively high output torque
and a wide speed range. The motor topology and magnetic barrier structure analysis are shown in Fig. 1. The magnetic field distributions under different operating conditions are shown in
Fig. 2. At no load, the flux leakage barrier guides parts of PM flux into the flux leakage path and reduces the air gap effective flux. As the armature current increases, the flux focusing
barrier guides the PM flux to pass through the air gap rather than flux leakage path, and the main flux is enhanced. And then, a response surface method is adopted to optimize the key
parameters related to the magnetic flux barrier units in Fig. 3. After optimization, the torque performances of the motor are significantly improved both at different operating conditions as
shown in Fig. 4. Finally, the torque characteristics of the motor are verified through experiments in Fig. 5. The experimental results are in good agreement with the simulation results,
which verifies the effectiveness of the motor design. 

**References:** 

[1] T. Kato, T. Matsuura and K. Sasaki, Proc. IEEE Energy Convers. Congr. Expo., 2017, pp. 5803–5810. 

[2] X. Zhou, X. Zhu and W. Wu, IEEE Trans. Ind. Electron., vol. 68, no. 8, pp. 6516–6526, Aug. 2021. 

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Design and Analysis of a V Shaped Leakage

In recent years, variable leakage flux permanent magnet (VLF-PM) motors, which can realize different operation conditions, have attracted increasing attention [1]. In this
kind of motors, by the purposeful design of flux barriers and PMs, design requirements of different operation conditions can be satisfied [2]. It is noted that, under different working
conditions, different flux density distribution often leads to significant changes in radial electromagnetic force distribution and characteristics of vibration noise [3]. Thus, it is necessary to
design and analyze the characteristic of vibration noise of VLF-PM motor under multiple working conditions. In this paper, the characteristics of electromagnetic vibration of VLF-PM
motor under different working conditions are researched. And, an low vibration design method is proposed for VLF-PM motors, considering multiple working conditions.
Fig. 1 shows the proposed VLF-PM motor and operation principle under different operation conditions. Fig. 2 presents the characteristics of electromagnetic vibration of the VLF-PM
motor in different working regions. According to the operation principle, two typical working points are selected for analysis. The sensitivity of design parameters to the desired
optimization objective are depicted in Fig. 3, and the selected sensitive parameters are marked. The characteristics of sensitive design parameters are illustrated in Fig. 4. The basic
electromagnetic performances under two working points are shown in Fig. 5. It can be seen that under the two working conditions, the output torque of the two motors is almost the same,
and the torque ripple of the optimal motor is obviously reduced. Fig. 6 shows the vibration characteristics of VLF-PM motor. Due to the lower amplitudes of low-order radial force density,
especially, 4th, the vibration and noise characteristics of the optimal VLF-PM motor is preferred under the two working points, which verifies the effectiveness of the low vibration design
of the VLF-PM motor proposed in this paper.
More detailed analysis and experimental verification will be presented in the full paper. 


**References:** 

[1] H. Hu, Z. Xiang and X. Zhu, IEEE Transactions on Magnetics, vol. 58, no. 2, pp. 1-6, Feb. 2022, Art no. 8102606. 
[2] X. Zhou, X. Zhu and W. Wu, IEEE Transactions on Industrial Electronics, vol. 68, no. 8, pp. 6516-6526, Aug. 2021. 
[3] M. S. Islam, R. Islam and T. Sebastian, IEEE Transactions on Industry Applications, vol. 50, no. 5, pp. 3214-3222, Sept.-Oct. 2014. 

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Low Vibration Design of Variable Leakage Flux Permanent Magnet Motor Considering Multiple Working Conditions

Due to the advantage of high torque at low speed, permanent magnet vernier (PMV) motor has become an excellent candidate for low-speed direct-drive applications [1],
such as electric vehicles. With the increasing critical demand for electric vehicle drives, multiple design requirements have also been proposed for performance of electric vehicle drive
motors, including output torque and torque ripple [2]. Recently, many researchers have contributed to improving torque performances of PMV, mainly by the design of permanent magnet
and stator teeth [3][4]. Yet, it is noted that, current literature on improving motor performances would either increase output torque or reduce torque ripple, while the comprehensive
improvement of torque performances can hardly be achieved. Thus, in this paper, an airgap-harmonic-orientated partitioned design method is newly proposed for PMV motors. In the
proposed design method, considering the effect of different harmonics on torque performance, the torque designed region of rotor is artfully divided into torque enhanced region and ripple
reduced region. And, by the purposeful design of these two regions, output torque is increased while torque ripple is reduced effectively.
Fig. 1 shows the configurations of proposed and initial PMV motors. The airgap-harmonic-orientated partitioned design principle is presented in Fig. 2, providing theoretical guidance for
motor torque performance improvement. Fig. 3 shows the magnetic field and flux distributions of proposed motor. Meanwhile, based on partition design principle, the airgap flux density
waveforms, and the main airgap harmonic variations related to output torque and torque ripple are presented in Fig. 4 and Fig. 5 respectively. It can be seen from Fig. 6 that, by the
reasonable design of torque enhanced region and ripple reduced region, output torque of motor is significantly increased by 82.6% while torque ripple is reduced by 61.1% efficiently as
expected. Thus, by the proposed airgap-harmonic-orientated partition design method, improved output torque and reduced torque ripple can be realized effectively. The detailed theoretical
analysis and simulation results will be presented in the full paper. 

**References:** 

[1] Y. Ma and W. Fu, IEEE Trans. Magn, vol. 57, no. 6, pp. 1-5, June 2021. 
[2] B. Lee, Z. Zhu and L. Huang, IEEE Trans. Ind. Appl, vol. 55, no. 3, pp. 2510-2518, May-June 2019. 
[3] X. Zhu, M. Jiang and Z. Xiang, IEEE Trans. Ind. Electron, vol. 67, no. 7, pp. 5337-5348, July 2020. 
[4] L. Fang, D. Li and X. Ren, IEEE Trans. Ind. Electron, vol. 69, no. 6, pp. 6058-6068, June 2022. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d1ba1888bd574b1a4cae6b3c1787b3c4.png) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/98b1d340459bae9fae75cd6f1b31e2a8.png)

Airgap Harmonic

Recently, flux modulated permanent magnet motors have aroused considerable attention, due to the merits of relatively high output torque at low speed. To further improve
motor torque output capability, double stator vernier permanent magnet (DS-VPM) motors have attracted increasing attention [1]. However, due to the relatively complicated relationship
among airgap flux harmonic, motor structure and performances, the difficulty and time burden of the optimization design of DSVPM motor is increased significantly [2]. Besides, during
actual motor manufacturing process, there exists many unavoidable design uncertainties, which would result in motor performance degradation [3]. Thus, it has been a hot but challenging
issue on how to realize high-efficiency optimization design of DS-VPM motor consider parameter fluctuation. In this paper, an airgap-harmonic-based multi-level robust optimization
design method is proposed for DS-VPM motor. By the proposed optimization method, motor performances can be improved comprehensively considering parameter fluctuation.
The structure of the investigated DS-VPM motor is shown in Fig. 1 (a), and corresponding design parameters of DS-VPM motor are presented in Fig. 1 (b). The flowchart of the proposed
airgap-harmonic-based multi-level robust optimization method is presented in Fig. 2. Firstly, the detailed relationship among design parameters, design parameters, and motor performances
are investigated, as shown in Fig. 3 and Fig. 4. Then, based on multi-objective genetic algorithm and response surface method, deterministic optimal design of DS-VPM motor is
determined. Furthermore, robust optimization method is utilized to achieve the robust optimal motor deign. Electromagnetic performances of the optimal DS-VPM motor are presented in
Fig. 5 and Fig. 6, while the normal distribution of the initial and final motor performances is presented in Fig. 7. Consequently, it is noted that that not only motor performances are
improved effectively, but the fluctuations of the motor performances are reduced significantly which verifies the effectiveness of the proposed robust multi-level optimization method.
More simulation and experimental results will be presented in the full paper. 

**References:** 

[1] W. Zhao, T. A. Lipo and B. -I. Kwon, IEEE Trans. Magn, vol. 51, no. 11, pp. 1-4, Nov 2015. 
[2] X. Zhu, M. Jiang and Z. Xiang, IEEE Trans. Ind. Electron, vol. 67, no. 7, pp. 5337-5348, July 2020. 
[3] M.-M. Koo, J.-Y. Choi and K. Hong, IEEE Trans. Magn, vol. 51, no.11, pp. 1-4, Nov 2015. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a568762d8fd475568ea902f3f8c63996.png)

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