United States

I. Introduction&lt;br/&gt;PMSM is widely used in industrial fields because of the advantages of high power density and high efficiency [1-3]. However, torque ripple of PMSM can cause vibration and noise, which are not conducive to the smooth operation of the motor. Consequently, this paper proposes segmented asymmetrical stator design, which can reduce torque ripple without significant drop of average torque.&lt;br/&gt;II. Segmented Asymmetrical Stator Design&lt;br/&gt;A 6-pole 9-slot PMSM is carried out to analyze the proposed stator design. Then segmented asymmetrical design is carried out to optimize the stator. The main parameters are &lt;i&gt;θ&lt;/i&gt; and &lt;i&gt;W&lt;/i&gt;. &lt;i&gt;θ&lt;/i&gt; is the degree from the middle of teeth to the middle of slot opening. W is the width of the slot opening.&lt;br/&gt;From the FEA analysis, it’s easy to find two torques which have opposite ripple phases. The first section is that when &lt;i&gt;θ&lt;/i&gt; is 14° and &lt;i&gt;W&lt;/i&gt; is 1.2 mm, and the second section is the mirroring of the first. The shapes of the sections and the torques are shown as Fig.1.&lt;br/&gt;According to the FFT analysis, the phases of sixth ripples of two sections are 65.9° and -109.3°, and the amplitudes are 0.1961Nm and 0.0763Nm. Adjusting the length ratio of the two sections to 2:5, then the amplitudes of sixth ripples are 0.056Nm and 0.0545Nm. The sixth ripples generated by two sections have the opposite phases and similar amplitudes, so the torque ripple of the whole motor can be decreased. The schematic of segmented asymmetrical stator and the torque waveforms are shown as Fig.2.&lt;br/&gt;III. Conclusion&lt;br/&gt;This paper proposes a segmented asymmetric stator structure. By optimizing the design parameters and adjusting the length of two stator segments, two torques with opposite ripple phases and similar ripple amplitudes can be obtained, so the two ripples can offset each other thus decreasing the torque ripple of the whole motor. This method doesn’t require PM shape optimization, so the average torque will not decrease significantly.


![](https://assets.underline.io/uploads/markdown_image/1/image/a728e6fa2214b0163d5f6e651ed53cfb.jpg)

Fig.1 Schematics of stator sections and waveform of torques


![](https://assets.underline.io/uploads/markdown_image/1/image/d1df39bc1bae3999d6a298bdff626d34.jpg)

Fig.2 Schematic of segmented asymmetrical stator and waveform of torques


2022 Joint MMM-INTERMAG

Segmented Asymmetrical Stator of PMSM for Torque Ripple Reduction

The 15th Joint MMM-INTERMAG Conference (2022 Joint) 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 plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag 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.

I. Introduction PMSM is widely used in industrial fields because of the advantages of high power density and high efficiency [1-3]. However, torque ripple of PMSM can cause vibration and noise, which are not conducive to the smooth operation of the motor. Consequently, this paper proposes segmented asymmetrical stator design, which can reduce torque ripple without significant drop of average torque. II. Segmented Asymmetrical Stator Design A 6-pole 9-slot PMSM is carried out to analyze the proposed stator design. Then segmented asymmetrical design is carried out to optimize the stator. The main parameters are θ and W. θ is the degree from the middle of teeth to the middle of slot opening. W is the width of the slot opening. From the FEA analysis, it’s easy to find two torques which have opposite ripple phases. The first section is that when θ is 14° and W is 1.2 mm, and the second section is the mirroring of the first. The shapes of the sections and the torques are shown as Fig.1. According to the FFT analysis, the phases of sixth ripples of two sections are 65.9° and -109.3°, and the amplitudes are 0.1961Nm and 0.0763Nm. Adjusting the length ratio of the two sections to 2:5, then the amplitudes of sixth ripples are 0.056Nm and 0.0545Nm. The sixth ripples generated by two sections have the opposite phases and similar amplitudes, so the torque ripple of the whole motor can be decreased. The schematic of segmented asymmetrical stator and the torque waveforms are shown as Fig.2. III. Conclusion This paper proposes a segmented asymmetric stator structure. By optimizing the design parameters and adjusting the length of two stator segments, two torques with opposite ripple phases and similar ripple amplitudes can be obtained, so the two ripples can offset each other thus decreasing the torque ripple of the whole motor. This method doesn’t require PM shape optimization, so the average torque will not decrease significantly.


![](https://assets.underline.io/uploads/markdown_image/1/image/a728e6fa2214b0163d5f6e651ed53cfb.jpg)

Fig.1 Schematics of stator sections and waveform of torques


![](https://assets.underline.io/uploads/markdown_image/1/image/d1df39bc1bae3999d6a298bdff626d34.jpg)

Fig.2 Schematic of segmented asymmetrical stator and waveform of torques

poster

Nowadays, permanent magnet synchronous machine (PMSM) has attracted more and more attention in wind power application with its inherent merits such as high-torque density and high efficiency [1-2]. However, with the fixed PM excitation, it is not easy for the PMSM to provide controllable airgap flux and extend speed range to capture more wind energy [3-4]. To extend the constant-power speed range and improve the machine efficiency, a new slot-PM-assisted hybrid magnet memory machine (SPMA-HMMM) is proposed, in which hybrid PMs, namely high coercive force (HCF) PMs and low coercive force (LCF) are artificially combined and inset into both stator yoke and slot opening. Especially, one pole of yoke PMs are made of HCF PMs, and the other pole of yoke PMs are composed of LCF PMs with flexible flux regulation ability. LCF PMs can be freely magnetized or demagnetized through DC current pulses supplied by the DC magnetizing coils wound on the LCF PMs. Therefore, during the high-speed operation, high efficiency of machine can be achieved with negligible field excitation loss. In addition, the HCF slot PMs can further enhance the torque/power density of machine with parallel excitation. Machine configuration Fig. 1 shows the configuration of SPMA-HMMM. It is composed of 28-pole outer rotor and 24-slot inner stator as denoted in Fig. 1. The rotor consists of only iron core, hence providing mechanical robustness. The stator comprises all excitation sources, including 3 pole-pair slot PMs, 3 pole-pair yoke PMs, armature winding and DC magnetizing coils. It is worth noting that the yoke PMs are formed by both HCF PMs and LCF PMs. Electromagnetic performance Fig. 2 shows electromagnetic performance of proposed SPMA-HMMM. As denoted in Fig. 2(a) and Fig. 2(b), the open-circuit flux-linkage and back-EMF can be effectively enhanced or weakened at different magnetization states via different DC magnetizing current pulses applying to LCF yoke PMs. Therefore, flexible flux regulation can be realized. As shown in Fig. 2(c), with the employment of slot PMs, the average torque is enhanced by 30.9% under flux-enhancing magnetization state.

![](https://assets.underline.io/uploads/markdown_image/1/image/056114d44fdf9028abfb9f3df5172d82.jpg)

Fig. 1. Configuration of SPMA-HMMM.

![](https://assets.underline.io/uploads/markdown_image/1/image/ee505f33e75ea49d09085daf20b05238.jpg)

Fig. 2. Electromagnetic performance of SPMA-HMMM.

A Novel Slot-PM-assisted Hybrid Magnet Memory Machine for Wind Power Generation

I.Introduction Recently, a variety of wave energy converters have been proposed with increasing concerns on low carbon electricity, of which direct drive wave energy converter (DD-WEC) requires fewer moving parts since the translator of the generator is coupled with the wave energy converter directly [1]. Permanent magnet linear generator (PMLG) is widely used for DD-WEC and permanent magnet transverse flux linear machine is a member of the variable reluctance PM linear machines family which are known to achieve high thrust density. So permanent magnet transverse flux linear generator (PMTFLG) is a good candidate in DD-WEC which is a typical low-speed high thrust application. Also, the air-gap flux can be adjusted by variable reluctance to extend the working range. Hence, in order to balance between extending the working range and achieving high thrust, more research should be done on PM positioning, number and shape of PMs and magnet material [2]. In this paper, a field-modulated transverse flux linear generator is proposed. By adjusting the machine topology and PM position, the generator can operate in a wide working range without sacrificing too much thrust density. II.Machine Topology and Operation Principle As shown in Fig. 1, the generator consists of outer stator, inner stator and moving translator. Some PMs and direct current field coils are placed in the inner stator, while the armature coils are placed in the outer stator slot and some PMs are inserted between the adjacent outer stator shoes. The moving part of the generator is translator and the moving direction is along z-axis. Silicon steel sheets and nonmagnetic sheets are arranged in the moving translator. The PMs which are inserted between the adjacent outer stator shoes can reduce the harmonics of back electromotive force (EMF). Fig. 1 III.Results Fig. 2 IV.conclusion Simulation results show that the air-gap flux can be adjusted by variable reluctance to extend the working range. The generator can operate in a wide working range without sacrificing too much thrust density.

![](https://assets.underline.io/uploads/markdown_image/1/image/93a8770a3fe2c80a6e7b3bdd2fa7f88e.jpg)

Fig. 1. Configuration of the proposed PMTFLG.

![](https://assets.underline.io/uploads/markdown_image/1/image/25ba2b9a683651ea55dcea34b5f1d0ec.jpg)

Fig. 2. Thrust of variable reluctance and variable reluctance and PM.

Analysis of a Variable Reluctance Field-modulated Transverse Flux Linear Generator

I. Introduction In recent years, dc excited multitooth flux-switching machines (DC-MFSMs) have attracted wide attention due to their excellent flux regulation capability and high reliability [1]. In this paper, a novel DC-MFSM is proposed by changing the winding configuration of the existing machine in literature [2]. Fig. 1 shows the topologies of the proposed and the existing DC-MFSMs, called model I and model II. The field winding of model I and model II employ concentrated winding on the same and adjacent stator, respectively. Corresponding, the magnetic polarities due to field windings of model I and model II close to the air gap can be respectively regarded as “N-S-S-N” and “N-N-S-S”. The two models are the same except for the configuration of field windings. II. Performance comparisons Fig. 2(a) and (b) present no-load back electromotive force (back-EMF) of two DC-MFSMs at the speed of 1500N/min and the corresponding finite-element analysis (FFT) results. It can be seen that the amplitude of fundamental back-EMFs of the model I is nearly 78% higher than that of model II. In terms of the total harmonic distortion (THD) of the back-EMF waveform, the model I is slightly larger than model II. Furthermore, Fig. 2(c) shows the torque waveforms when the armature current density (Ja) and excitation current density (Jf) of the two machines are both 5A/mm2. It can be observed that the average torque of model I and model II are 2.43 Nm and 2.29 Nm, respectively. Meanwhile, the torque ripple of model I is smaller. Due to unequal multitoothed distribution is adopted in model II during optimization, the peak-to-peak amplitude of model I (0.15Nm) is greater than that of model II (0.025 Nm), as shown in Fig. 2(d). Overall, the proposed novel DC-MFSM is superior to the conventional one since it exhibits much higher no-load back EMF and average torque, smaller torque ripple, and lower copper loss. The other performance, such as winding inductance, and efficiency, will be shown in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/36407c7e7ac02df9b479d3ef5d3388ed.jpg)

Fig.1. Topology of two dc excited MFSMs. (a) model I. (b) model II.

![](https://assets.underline.io/uploads/markdown_image/1/image/0c0c9bb24f9da7e35c459e4ee80b49f9.jpg)

Fig.2. Performance comparisons of two models. (a) Back-EMF waveforms at 1500r/min. (b) Harmonics of back-EMF. (c) Average torque. (d) Cogging torque.

Comparative Study on Two DC Exicited Multitooth Flux-Switching Machines

This work presents an approach to detect the inter-turn short circuit (ITSC) and demagnetization faults of permanent magnet synchronous machines (PMSMs) using maching learning. PMSMs possess advantages such as compact size, lightweight, high efficiency, high power density, and easy control. Therefore, they are a popular choice for traction motors of modern electric vehicles (EVs) and many high-performance industrial applications. With the widespread applications of PMSMs, their development should not be only focused on efficiency enhancement but also on fault detection to secure operation safety and cost. Therefore, preventive detection of motor failures is key to improve reliability and reduce damage or maintenance costs. Based on the research of Industry Applications Society (IAS) [1], the stator fault of electric motors is taking up to 37% of all sorts of faults, where ITSC fault occurs the most commonly. Demagnetization is also one of the major fault types in PMSMs. Taking EVs as an example, the high-power density and stochastic load conditions would risk the traction motors in potential ITSC or demagnetization. Among the previous studies regarding fault detection systems for PMSMs, the most frequently applied methods are mathematical modeling combined with the measurement of current or voltage signals. The drawback of these methods is that they are often not able to identify minor variations precisely and classify fault types and levels. Machine learning can be a good tool to improve fault classification capability. With the help of machine learning [2], this work is capable of detecting faults of ITSC and demagnetization in a preventive way so that the system can be ensured in healthy operation. Thus, the motors or components can be replaced before any collapses occur. The proposed algorithm has been trained with both simulation and test data (Fig. 1) with data collected from around 10000 tests. The effectiveness has also been tested with experimental data, and the results show a 97% - 99% accuracy (Fig 2).

![](https://assets.underline.io/uploads/markdown_image/1/image/a94c6021f9b8ff7a1b5885c9293721ea.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/6fc14da33b5f47434b542280f0b00bce.jpg)

Machine learning for fault detection in permanent magnet synchronous machines

1.Introduction The ANR RHU BioArt-Lung 2020 project aims to develop an extracorporeal artificial lung with reduced size and mass. An essential element of the system is its circulatory assist centrifugal pump, which ensures blood circulation. Our work focuses on this pump’s electric motor. Several papers present this medical technology [1-2]. In this article, we outline the electrical motor’s specifications and then present an initial dimensioning using a Design of Experiments. We then analyse the chosen structure using both 2D and 3D finite element (FE) methods. A prototype is then manufactured, and performance tests carried out. 2.Specifications and design The motor design should, therefore, be compact (adapted to the pump Fig.1 (a)). It must respect several medical, electrical, and mechanical constraints. The motor design specifications are provided in Table 1. The chosen structure is a radial flux motor with surface permanent magnets (Fig. 1 (b)). Two pairs of poles and its stator contains twelve slots with a concentrated winding. To study several structures, a method based on a Design of Experiments [3] is used. Effects of the variables (dimensions, geometrics) on the outputs: cost functions (torque, mass, efficiency) and constraints (current density, voltage level) are analysed. 3.Performance analysis The PMSM is modelled by both 2D and 3D Finite Element (FE) methods in FEMM and Comsol® Fig.1 (b). Both no-load and on-load analyses are performed. The machine can deliver torque under load with an average value of 60.9 mNm. The amplitude of the torque ripples remains acceptable (8%). The efficiency max of the PMSM is estimated to 85 %. Using iron loss model [4]. 4.PMSM prototype The prototype of the PMSM has been manufactured to test performance. Fig.1 (c) shows the active part of the engine prototype. In the final paper, a comparison will be presented to validate the simulation results. 5.Conclusion This article explores the design of a PMSM for the development of a portable artificial lung. Its pre-dimensioning is carried out using the Design of Experiments method. Details of the analysis and comparison will be described in the full paper.

Design of a Circulatory Assistance Actuator Applied to an Artificial Lung

The flux switching machine (FSM) and flux reversal machine (FRM) attract great attention because of simple structure of rotor, excellent heat dissipation and high reliability [1]. But both of the permanent magnets (PMs) and the armature windings placed in stator may decrease the space utilization, which limits the further torque production improvement [2]. Thus, the partitioned stator machines (PSMs) are developed, in which the armature windings and PMs are allocated in outer and inner stators to achieve high electromagnetic performances, respectively [3]. However, the existing PSMs with conventional PM arrays evolved from FSM or FRM can not provide high quality torque production. This paper proposes a new PSM with H-shape PM array (HPMPSM), which operates based on flux modulation effect and can offer high quality torque output and space utilization. In addition, the evolution process from conventional FSM and FRM to existing partitioned stator machines that operate based on flux modulation effect are described. H-shape PM (HPM) can be regarded as the combination of the interior PM array (IPM) in FSM and the surface mounted PM array in FRM, which could reduce the flux leakage and improve the flux density in airgaps effectively. HPM is composed of two tangentially magnetized PMs with opposite polarity and one radially magnetized PM. The polarity of the adjacent PMs in radial magnetization are opposite to form one-pole-pair PM excitation. The concentrated windings are adopted on outer stators for high efficiency, and the iron-pieces rotor is sandwiched between stators and has the merit of simple structure and high robustness. FSM, PSM with IPM, FRM, and PSM with surface mounted PM are designed and analyzed, which are simply referred as Models I, II, III, IV and V, respectively. By using finite element analysis (FEA), the electromagnetic performances of proposed HPMPSM are analyzed, containing back electromotive force (EMF), cogging torque, steady torque at rated condition and steady torque characteristics against current angle. The FEA-calculated result shows that the proposed HPMPSM can provide high back-EMF and high torque production with lowest torque ripple, which is desirable for electric vehicle application.

![](https://assets.underline.io/uploads/markdown_image/1/image/502f1a2dc15c22ee504c9e3e55b4a79e.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/4dd44069822e9d299c3f794948c6d6da.jpg)

A New Partitioned Stator Machine Based on Flux Modulation Effect

With the development of economy and social progress, people have higher requirements for environmental protection, travel comfort, energy saving and efficiency, so all-electric aircraft technology has been rapidly developed [1-4]. All-electric aircraft is powered by motor, and its performance requirements are higher than conventional motor. To be specific, the driving motor has the advantages of high power density, high torque overload capacity, and so on, which results in an extreme state of magnetic load and electrical load. Therefore, it is particularly important to research the accurate calculation and suppression technology of motor loss. In order to prevent stator core loss, B35A230 self-bonded silicon steel sheet is used as core material, which is a novel with the adhesive coating on the surface of the adhesive electrician ferromagnetic materials, and the coating on the surface of laminate is bonded together under a certain pressure and heat. The processed core can reduce the effect of the processing method on core loss, and the processed ring specimen is shown in Fig. 1. Conventional stator cores require to be welded on the outside and inside of the core to fix, as shown in Fig. 2, which makes the core loss worse. At the same time, the influence of core axial welding on iron loss is difficult to be calculated by theoretical analysis and finite element simulation. Therefore, the magnetic property of B35A230 ring core with and without weld path is experimentally tested by ring specimen method in this paper. The experimental test system is shown in Fig. 3. The ratio-loss curves at different frequency and different flux density, and the influence law of weld path on core loss are obtained. According to the experimental results of ring specimen method, the loss calculation model is adopted to improve the accuracy, considering processing factors, alternating and rotating magnetization modes and harmonic magnetic fields.

![](https://assets.underline.io/uploads/markdown_image/1/image/6e0da1daad2170226c1e04c6349ed21c.jpg)

Fig. 1 Ring sample of B35A230 self-bonded silicon steel sheet

![](https://assets.underline.io/uploads/markdown_image/1/image/c2dcb4e8233800d75514d652eb271b14.jpg)

Fig. 2 Fixing process of conventional core

Application Analysis of Self-bonded Silicon Steel Sheet in High Power Density SPMSM

A new hybrid flux consequent-pole permanent magnet memory Machine (CPPM-MM) with transverse field excitation is presented in Fig.1(a). Compared to conventional designs, the novel design has the following merits: (a) The machine can control the field with DC excitation pulses by using Alnico-PM's characteristics of low coercivity and high remanence, which improves the field regulation capability and enhances the efficiency. (b) With the unique configuration design, the Alnico-PM excitation flux is transverse to the main flux path, thus having minimum interferences with the main flux. The Alnico-PM is axially magnetized and artificially placed in the middle of the solid rotor yoke. A circumferential DC field winding is placed in the middle of the laminated stator yoke, inside the solid stator yoke, and outside the AC winding. The solid stator yoke and solid rotor yoke enable the axial excitation flux to turn into radial flux and flow to the rotor through the stator teeth. Fig.1(b) shows the demagnetizing mode. The Alnico-PM will be excited by the DC excitation pulse, making the iron poles adjacent to NdFeB-PMs in tangential direction have the same polarity. The main flux will path through the stator yoke and rotor yoke radially and axially. Because the field generated by the rotor remains constant, armature windings cannot have flux linkage with the rotor, thus realizing the flux weakening. Fig.1(c) shows the magnetizing mode. The iron pole adjacent to NdFeB-PMs in the axial direction will have the same polarity at this state. The main flux path will pass the stator yoke and rotor yoke tangentially. The machine in this state is like a normal PMSM. A 3-phase 30-slot 4-pole-pair model is designed and analyzed in ANSYS Maxwell 3D. The air gap flux distribution in the states of non-magnetized, fully-demagnetized, and fully-magnetized is shown in Fig.2(a) to Fig.2(c), and their back EMF comparison is shown in Fig.2(d). The results show that the machine has relatively outstanding field controllability.

![](https://assets.underline.io/uploads/markdown_image/1/image/310ad112013d6f3d8193f5e07acf803e.jpg)

Fig. 1. Structure and different magnetizing modes of CPPM-MM.


![](https://assets.underline.io/uploads/markdown_image/1/image/043feb7c6ccdc47f1e0bbdfff7abc68e.jpg)

Fig.2. Air gap flux distribution and back EMF comparison of three magnetization states.

Design and Analysis of a Novel Hybrid-Flux Consequent-Pole Permanent Magnet Memory Machine with Transverse Field Excitation

In high-speed electrical machines, centrifugal forces within the rotor can be first-order constraints on electromagnetic optimisation. This can be particularly acute, even at modest speeds, in interior permanent magnet (IPM) machines in which magnets are retained entirely by the rotor core with no additional mechanical containment. A close-up of one such IPM is shown in Figure 1 with key dimensions defined. The magnets, which are profiled to reduce stress concentrations, act as dead-weights which must be resisted by the single-piece core. The electromagnetic and mechanical design pinch-points are the thickness of the outer rib that closes off the magnet slot (h1) and the separation between magnets (h2). Increasing h1 or h2 enhances mechanical support but at the expense of greater leakage flux. A combined mechanical-electromagnetic optimisation was undertaken using 2D finite element analysis (FEA) to establish an optimal combination of rotor diameter, h1 and h2 to maximise torque density in an 8-pole, 100kW PM machine with a base speed of 4,000rpm and an extended speed range up to 12,000rpm. A maximum localised core stress limit of 240MPa was specified, this being 60% of the yield strength for NO20 alloy. The optimisation was done by systematic consideration of the design space rather than by formal optimisation methods. Rotor diameters from 120mm to 180mm in 15mm increments were considered, and for each diameter values of h1 and h2 which meet the mamximum stress limit at 12,000rpm were identified by structural FEA. For viable combinations of h1 and h2, torque was calculated by FEA for both 30 and 24 slot stators using FLUX2D. The axial length was then scaled to produce rated torque of 239Nm allowing the torque density to be calculated. The optimised rotor design diameter is 165mm and is 103mm long with a fractional-slot winding in a 30 slot stator. The overall machine has an active mass of 40.8kg with corresponds to ~2.5kW/kg. The paper described this optimisation study in detail and draws on the results to explore the nature of the design trade-offs in such rotors and impact of core properties.

![](https://assets.underline.io/uploads/markdown_image/1/image/82808e7b50ab87b074e0d5a79d86f4cb.jpg)

Figure 1 - Close up cross-section of the IPM machine type

![](https://assets.underline.io/uploads/markdown_image/1/image/f2d1a89fc0a74a7d03d6b2d345689207.jpg)

Figure 2 - Finite element predicted flux density at full-load

Combined electromagnetic and mechanical optimisation of an interior permanent magnet rotor

Introduction When permanent magnet synchronous machines (PMSMs) are running, electromagnetic forces acting on stator teeth excite vibrations. The electromagnetic forces can be decomposed into concentrated forces at different frequencies by FFT. If phase differences between the concentrated force are zero, zero-mode vibrations are excited. The zero-mode vibrations are generally dominant in PMSMs. Some approaches on optimizing the structure have been proposed for reducing the zero-mode vibrations. In addition, injecting harmonic currents into windings is also effective. However, almost existing methods aims to decrease the amplitude of concentrated forces. This study investigated the method of changing the phase difference between concentrated forces to transform zero-mode vibrations to nonzero-mode vibrations. Methodology The investigation used a finite-element model of surface mounted PMSM with 12 poles 36 slots. Its permanent magnets were optimized for decreasing the amplitude of concentrated forces. The main frequency of the zero-mode vibration of the model is 6 times fundamental frequency. So different 5th harmonic currents were injected into windings for changing phases of concentrated forces. Then, concentrated forces before and after the injection were calculated respectively, and its phase differences were analyzed. Finally, the validity of the injection was verified by calculating vibrations. Result The phase difference between concentrated force was changed from 0 degree to 120 degree after the harmonic injection. Fig.1 shows the vibration before the harmonic injection, and Fig. 2 shows the vibration after the harmonic injection. The zero-mode vibration became the nonzero-mode vibration after harmonic injection and its amplitude was reduced. Conclusion Combining the optimization and the harmonic injection not only reduced the amplitude of the concentrated force, but also changed the phase difference between them. Thus, zero-mode of vibrations can be transformed into nonzero-mode vibrations, and their amplitudes are reduced significantly.

![](https://assets.underline.io/uploads/markdown_image/1/image/afce0516c99d87098d474a957f252dae.jpg)

Fig.1 Acceleration of the core surface without harmonics


![](https://assets.underline.io/uploads/markdown_image/1/image/7888e7f00d1f09385a0829218aa4f9be.jpg)

Fig.2 Acceleration of the core surface with harmonics

Segmented Asymmetrical Stator of PMSM for Torque Ripple Reduction

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