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Permanent magnet synchronous motors (PMSMs) having high power density and high efficiency are rigorously researched in various premium applications. Among PMSMs, many studies have been conducted on interior permanent magnet synchronous motors (IPMSMs) to improve torque ripple [1-3], but its accurate estimation is not straightforward. Therefore, a six-pole nine-slot IPMSM is adopted as a base model due to its popularity in academia and industries. Other two pole/slot combinations (8p/12s, 10p/15s) having the same winding factor of 0.866 are additionally selected to investigate mainly the influence of a pole/slot combination on torque performance.&lt;br/&gt;Air gap force is separated into its radial and tangential components, and the tangential force density (F&lt;sub&gt;t&lt;/sub&gt;) is determined by two magnetic flux densities in air gap [4]. Due to proportional relation between F&lt;sub&gt;t &lt;/sub&gt;and the torque [4], torque performance is easily identified by analyzing. In case of maximum and minimum torque at the instant of t&lt;sub&gt;max&lt;/sub&gt; and t&lt;sub&gt;min&lt;/sub&gt;, respectively, the distribution of F&lt;sub&gt;t&lt;/sub&gt; along air gap is illustrated in Fig. 1 to analyze torque ripple. The biggest gap between F&lt;sub&gt;t&lt;/sub&gt;(Î¸&lt;sub&gt;m&lt;/sub&gt;, Ï‰t&lt;sub&gt;max&lt;/sub&gt;)and F&lt;sub&gt;t&lt;/sub&gt;(Î¸&lt;sub&gt;m&lt;/sub&gt;, Ï‰t&lt;sub&gt;min&lt;/sub&gt;) as indicated in red and blue, respectively, occurs around the right side of a stator pole surface as shaded in yellow in case of anticlockwise rotation. Since F&lt;sub&gt;t&lt;/sub&gt; is proportional to the product of B&lt;sub&gt;r&lt;/sub&gt; and B&lt;sub&gt;t &lt;/sub&gt;[4], magnetic flux densities in air gap have to be examined to analyze the variation of F&lt;sub&gt;t&lt;/sub&gt;. The moment of maximum torque is given in Fig. 2, and it is noted that the change of B&lt;sub&gt;t&lt;/sub&gt; in increasing a pole number is much greater than that of B&lt;sub&gt;r&lt;/sub&gt;. Compared to B&lt;sub&gt;t&lt;/sub&gt; of 6p/9s, in particular, that of 10p/15s is significantly reduced by 46% around the right side of a stator pole, and hence, torque ripple is improved in the 10p/15s combination. In conclusion, in varying pole and slot numbers, the impact of B&lt;sub&gt;t&lt;/sub&gt; is dominant on torque ripple. Especially, the change of B&lt;sub&gt;r&lt;/sub&gt; and B&lt;sub&gt;t&lt;/sub&gt; with respect to a pole/slot combination will be meticulously analyzed and explained in terms of its reason and relationship with torque ripple.

MMM 2022

Torque Analysis of a Permanent Magnet Synchronous Motor using Flux Densities in Air Gap

Permanent magnet synchronous motors (PMSMs) having high power density and high efficiency are rigorously researched in various premium applications. Among PMSMs, many studies have been conducted on interior permanent magnet synchronous motors (IPMSMs) to improve torque ripple [1-3], but its accurate estimation is not straightforward. Therefore, a six-pole nine-slot IPMSM is adopted as a base model due to its popularity in academia and industries. Other two pole/slot combinations (8p/12s, 10p/15s) having the same winding factor of 0.866 are additionally selected to investigate mainly the influence of a pole/slot combination on torque performance. Air gap force is separated into its radial and tangential components, and the tangential force density (Ft) is determined by two magnetic flux densities in air gap [4]. Due to proportional relation between Ft and the torque [4], torque performance is easily identified by analyzing. In case of maximum and minimum torque at the instant of tmax and tmin, respectively, the distribution of Ft along air gap is illustrated in Fig. 1 to analyze torque ripple. The biggest gap between Ft(Î¸m, Ï‰tmax)and Ft(Î¸m, Ï‰tmin) as indicated in red and blue, respectively, occurs around the right side of a stator pole surface as shaded in yellow in case of anticlockwise rotation. Since Ft is proportional to the product of Br and Bt [4], magnetic flux densities in air gap have to be examined to analyze the variation of Ft. The moment of maximum torque is given in Fig. 2, and it is noted that the change of Bt in increasing a pole number is much greater than that of Br. Compared to Bt of 6p/9s, in particular, that of 10p/15s is significantly reduced by 46% around the right side of a stator pole, and hence, torque ripple is improved in the 10p/15s combination. In conclusion, in varying pole and slot numbers, the impact of Bt is dominant on torque ripple. Especially, the change of Br and Bt with respect to a pole/slot combination will be meticulously analyzed and explained in terms of its reason and relationship with torque ripple.

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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The increase of power density in permanent magnet synchronous motors(PMSMs) has been getting more crucial these days, and there are two methods to improve the power of a PMSM. One is the increase of magnetic loading(ML) by changing the grade and/or size of permanent magnets [1]. The other is the change of electric loading(EL) by modifying winding design and/or current [2]. ML and EL leading to magnetic flux density in air gap affect electromagnetic and mechanical performance at the same time. Thus, Balance between ML and EL should be examined in terms of efficiency and vibration. In this paper, a sixteen-pole eighteen-slot PMSM for a vertical articulated robot is chosen as a reference model [3], and other two pole/slot combinations (20p/18s, 20p/24s) are together compared in terms of electrical and mechanical performance. In the electric motor, electromagnetic vibration is generated by air gap radial force(Pr) whose density is determined by radial and tangential magnetic flux densities. At a given instant of time, the flux densities are spatially distributed along air gap with respect to mechanical angle, and their spatial distribution changes by spinning the rotor. Pr distributed in a three-dimensional manner is decomposed into harmonics as Fig.1. In the case of 16p18s, the 16th radial force is dominant on the x-axis of a temporal harmonic order. Regarding the y-axis of a spatial harmonic order, the 2nd and 16th are important. The vibration displacement is calculated by the harmonics of Pr as Fig.2. At the frequency of 533.3Hz, the RMS of vibration acceleration of the 16th temporal order on the x-axis is 1.14m/s2, and the 2nd and 16th spatial harmonics have the portion of 83% and 9%, respectively, in vibration acceleration. The influence of ML and EL on the radial force density of the 2nd and 16th spatial harmonics is significantly different each other. In conclusion, balance between magnetic and electric loading has to be examined in terms of efficiency and vibration. Especially, trade-off between efficiency and vibration will be meticulously analyzed and explained during the increase of power in PMSMs.

Vibration Analysis of a Permanent Magnet Synchronous Motor by a Pole/Slot Combination

Recently, high-speed permanent magnet motors have been used in various fields by applying rare-earth permanent magnets. Because they rotate at high speeds, the effects of noise, vibration, and harshness (NVH) should be analyzed for mechanical stability. Based on many studies, electromagnetic-exciting sources affecting NVH are classified into cogging torque, torque ripple, electromagnetic force density distribution (MPF), and unbalanced electromagnetic force [1-2]. Therefore, an analysis reflecting the complex excitation source is required in designing a stable high-speed motor [3]. In this study, after analyzing the effect of carrier harmonics generated in the pulse-width modulation control method on the electromagnetic-exciting source through dynamic simulations, the unbalanced electromagnetic force was derived. Finally, the effect on the mechanical aspects was analyzed. Fig. 1(a) shows the 3D structure of the proposed model, and Fig. 1(b) shows the experimental set. Fig. 1(c) and (d) show the variations in the current and magneto-motive force (MMF) waveforms, respectively, according to carrier harmonics through dynamic simulation. Fig. 2(a) shows the UMF of the armature reaction, and Fig. 2(b) shows the harmonics of the torque. The NVH analysis results based on these effects are shown in Fig. 2(c) and (d). Fig. 2(c) shows the NVH when a sinusoidal current is applied, and Fig. 2(b) shows the NVH when the inverter generates a harmonic current. Based on the analysis results, it was confirmed that the higher the vibration order of the frequency related to the unbalanced electromagnetic force, the more significant its influence on the vibration and noise. These results indicate that vibration and noise analyses considering the inverter are essential in the design and performance analysis of high-speed motors. Detailed comparative analysis and experimental results will be presented in the complete paper.

Analysis and Measurements of Influence of Current Harmonics on Vibration of High Speed Motors with Rare

Soft magnetic composite (SMC) material is a relative new soft magnetic material, which has many advantages over traditional silicon sheets, however it has many disadvantages as well. For the better utilization of SMC material in developing electrical machines, some design guidelines should be followed, e.g., 3D magnetic flux path, high frequency operation, and permanent magnet excitation [1]. There are many electrical machines with SMC cores had been developed in the past decades. Based on global ring winding and 3D magnetic flux path, permanent magnet claw pole machine (PMCPM) has shown its high torque ability compared with other electrical machines [2]. For the most PMCPM, three same single phase PMCPM modules are required with shifting 120 degrees electrically each other to form three phase operation, and each one phase module has its own PM rotor thus the PM utilization is very low [3]. In this paper, for improving the PM rotor utilization a novel axial radial flux permanent magnet claw pole machine ARPMCPM is proposed and designed where there stators share one PM rotor. For the performance prediction, 3D finite element method (FEM) is used. Fig. 1 shows the main magnetic structure of the ARPMCPM. As shown, one radial flux claw pole stator and two axial flux claw pole stators are required, the global ring winding is adopted, and spoke PM configuration is adopted for the PM rotor. To form three phase operation, these three claw pole stators are shifted 120 degrees electrically to each other and the winding section area needs to be designed reasonably. Fig. 2 shows no load magnetic field distribution, parameters and main performance of ARPMCPM based on 3D FEM. Fig. 2(b) shows the no load PM flux linkage of winding A, B and C. As shown, A phase PM flux linkage higher than the other PM flux linkages as winding A is located on the radial flux claw pole stator. Fig. 2(c) shows the induced voltages. Fig. 2(d) shows the torque waveform under the current density of 6 A/mm2. Fig. 2(e) and (f) are the core loss and efficiency map. More details and design methods for the ARPMCPM will be presented in the full submission.

Development of a Novel Radial Axial Flux Permanent Magnet Claw Pole Machine with SMC Cores and Ferrite Magnets

I.Introduction
Nowadays, the field-modulated permanent magnet (FMPM) machines have attracted significant attention in direct-drive applications. However, the rare-earth PMs have fluctuation price
and unstable supply. Thus, the rare earth reduction of FMPM machine is extensively regarded as a candidate for electric vehicles [1]. It is investigated that the rotor consequent-pole PM
(R-CPM) machine exhibits higher torque capability than the stator CPM machine because of the fact that various rotor permeance harmonics are more involved in torque generation [2].
Based on the study, this paper designs and analyzes a new FMPM machine with one airgap, which adopts the half Halbach array PMs embedded in the rotor slot and possesses the merit of
high PM utilization ratio.
II.Topology and Operation Principle
As shown in Fig. 1, the proposed FMPM machine consists of rare earth PMs and windings, which are located in the rotor and stator respectively. Compared to the existing FMPM machine,
the key difference is that half Halbach array PMs are employed in rotor slot. The rotor teeth, which provide a mechanical support and better effect of heat dissipation for PMs, build the
routes for the fields of PM and armature winding.
III.Results
Fig. 2(a) presents the no-load phase back-EMFs of the existing and proposed FMPM machines under the same speed. It can be observed that the maximum back-EMF obtained by the
proposed HEFM machine is similar to the existing machine that excited by both rare earth PMs and ferrite PMs. Fig. 2(b) shows that the torque densities with the same rated armature
current of 5Arms. It is found that the torque density of the proposed machine is similar to the superposition of torque produced by the machines with rare earth PMs and ferrite PMs, while
the PM volume is only 66% of the existing one. It proves the effectiveness of the improved rotor structure. 

**References:** 

[1] C. Gong and F. Deng. Design and optimization of a high-torque-density low-torque-ripple vernier machine using ferrite magnets for direct-drive applications. IEEE Transactions on
Industrial Electronics, vol. 69, no. 6, pp. 5421-5431, June 2022. 

[2] Y. Li, H. Yang and H. Lin. Comparative study of torque production mechanisms in stator and rotor consequent-pole permanent magnet machines. IEEE Transactions on Transportation
Electrification, vol. 7, no. 4, pp. 2694-2704, Dec. 2021. 

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Design and Analysis of a New Field modulated Permanent Magnet Machine with an Improved PM Rotor

The magnetic-field-modulated permanent magnet (MFMPM) machines have attracted wide attention in hybrid electric vehicles. In order to improve the torque density, many MFMPM
machines employ two or three portions of PMs and two air gaps [1]. However, the structures with two air gaps increase the complexity and maintenance difficulty. To solve above
problems, alternative flux barriers and alternative flux bridges are introduced in the MFMPM machines with one air-gap [2]. In order to improve the utilizations of rotor space and torque
density per unit volume, this paper proposes a new MFMPM Machine with compound-structure PMs, in which both the spoke and Halbach array PMs are set in the rotor.
II.Topology and Operation Principle
Fig. 1 shows the configuration of the proposed MFMPM machine with the compound-structure Magnets. The stator contains flux-modulation tooth and slots which are filled with single
layer concentrated winding. The rotor is formed by the spoke PMs, Halbach array PMs and alternative flux bridges. The proposed MFMPM machine can be identified as the combination of
the spoke MFMPM machine and Halbach array MFMPM machine. Both the MFMPM machines work on the principle of field modulation effect. Besides, Halbach array PMs are inserted
between the flux bridge and spoke rare-earth PMs to reduce the flux leakage, resulting in improving the utilizations of spoke PMs field.
III.Results
Fig. 2(a) shows that the back EMF waves of proposed MFMPM machine. It can be seen that the proposed MFMPM machine can achieves 172 V which is almost equal to the sum of the
back-EMFs of spoke MFMPM machine and Halbach array MFMPM machine. The waveforms of torque can be obtained, as shown in Fig. 2(b). It reveals that the torque of proposed
machine can achieve 25N.m while the torques of the spoke MFMPM machine and Halbach array MFMPM machine are 19N.m and 7.3N.m respectively. It validates that proposed
compound-structure machine can realize the superposition of spoke PMs and Halbach array PMs. 

**References:** 

[1] G. Liu, P. Zheng, J. Bai, et al. Investigation of a dual-winding dual-flux-concentrated magnetic-field-modulated brushless compound-structure machine. IEEE Transactions on
Magnetics, vol. 58, no. 2, pp. 1-5, Feb. 2022, Art no. 8100505. 
[2] Y. Zhang, D. Li, P. Yan, et al. A high torque density claw-pole permanent-magnets vernier machine. IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 10, no.
2, pp. 1756-1765, April 2022. 

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A New Magnetic Field Modulated Machine with Compound

In general, three aspects of an entire electrical machine design task should be analyzed: electromagnetic, mechanical, and thermal. However, in practice, designers tend to
focus on the electromagnetic aspect and deal superficially with mechanical analysis and thermal analysis. It is necessary to perform mechanical and thermal analysis in applications for
high-speed and high-power machines.
The thermal analysis can be done using two approaches: the method using lumped-parameter thermal networks (LPTNs) also known as “thermal equivalent circuits,” and the analytical
method. The LPTN is a simple model that makes it possible to obtain quickly. However, defining one or two main heat-transfer paths is necessary first, so the final result is not highly
accurate. The analytical method based on complex differential equations and boundary conditions provides more reliable results.
In this study, a comprehensive thermal analysis model was developed and applied to an 8/12 permanent magnet synchronous motor prototype. Fig. 1 shows the manufactured model and
experimental setup. Fig. 2 illustrates an LPTN model according to the front view and side view in Figs. 2(a) and (b), respectively. Fig. 2(c) shows the simplified circuit in the winding, and
Fig. 2(d) shows the temperature results for some positions. The detailed work and experiment results will be presented in the full paper. 

**References:** 

1. A. Boglietti, A. Cavagnino, D. Staton, M. Shanel, M. Mueller and C. Mejuto, "Evolution and Modern Approaches for Thermal Analysis of Electrical Machines," in IEEE
Transactions on Industrial Electronics, vol. 56, no. 3, pp. 871-882, March 2009 
2. G. J. Li, J. Ojeda, E. Hoang, M. Lecrivain and M. Gabsi, "Comparative Studies Between Classical and Mutually Coupled Switched Reluctance Motors Using Thermal-Electromagnetic
Analysis for Driving Cycles," in IEEE Transactions on Magnetics, vol. 47, no. 4, pp. 839-847, April 2011 
3. D. Staton, A. Boglietti and A. Cavagnino, "Solving the more difficult aspects of electric motor thermal analysis in small and medium size industrial induction motors," in IEEE
Transactions on Energy Conversion, vol. 20, no. 3, pp. 620-628, Sept. 2005 

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Thermal Analysis and Experimental Verification of Permanent Magnet Synchronous Motor by Combining Lumped Parameter Thermal Networks with Analytical Method

I. Introduction
Double mechanical port permanent-magnet (DMP-PM) motor is one of the research highlights in motor field in recent years[1],[2].As shown in Fig. 1, this motor called NS-DRFSPM
machine.In this paper,the performances of NS-DRFSPM machine under several fault operation conditions are compared and analyzed.The simultaneous operation of two groups of
armature windings and the first group of permanent magnets is called state I,namely S1;The simultaneous operation of two groups of armature windings and the second group of permanent
magnets is called state II,namely S2;The first group of armature windings and two groups of permanent magnets operate at the same time,which is called state III,namely S3;The second
group of armature windings and two groups of permanent magnets operate at the same time,which is called state IV,namely S4.
II.Performance comparisons
A series of comparisons of electromagnetic performance of several fault operation states are conducted by finite element analysis (FEA).Fig.2(a) compares the no-load phase back-EMF per
turn waveforms of four fault operation states of the NS-DRFSPM machine at 1500r/min based on FEA.It can be seen that the back-EMF amplitude of the third operating state of the motor
is the smallest,and the second is the largest.Fig.2(b) shows the flux linkage waveforms of four fault operation states of the NS-DRFSPM machine.The cogging torque waveforms of four
fault operation states of NS-DRFSPM machine shown in Fig.2(c).The cogging torque waveforms of state III and state IV are almost the same,and the torque ripple is the smallest.Fig.2(d)
present the electromagnetic torque of the NS-DRFSPM machine under id=0 control with current densities Jsa=5A/mm2.The best performance of average torque and torque ripple of the NSDRFSPM
machine is state II(6.9Nm,42.1%).
III.Conclusion
The other performance,such as the FFT results analysis and simultaneous fault operation of single armature winding and magnet,will be shown in the full paper. 

**References:** 

[1]J. Bai,P. Zheng,C. Tong,Z. Song,and Q. Zhao,“Characteristic Analysis and Verification of the Magnetic-Field-Modulated Brushless Double-Rotor Machine,” IEEE Trans.
Ind. Electron.,vol. 62,no. 7,pp. 4023–4033,Jul. 2015. 
[2]X. Zhu,L. Chen,L. Quan,Y. Sun,W. Hua,and Z. Wang,“A new magnetic-planetary-geared permanent-magnet brushless machine for hybrid electric vehicle,”IEEE Trans. Magn.,vol.
48,no. 11,pp. 4642–4645,Nov. 2012. 

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Fault Operation Analysis Of A Novel Dual Three

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

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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Torque Analysis of a Permanent Magnet Synchronous Motor using Flux Densities in Air Gap

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