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Keywords = surface permanent magnet (SPM) motor

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13 pages, 5435 KiB  
Article
Design, Analysis, and Comparison of Electric Vehicle Electric Oil Pump Motor Rotors Using Ferrite Magnet
by Huai-Cong Liu
World Electr. Veh. J. 2025, 16(1), 50; https://doi.org/10.3390/wevj16010050 - 20 Jan 2025
Viewed by 1422
Abstract
With the recent proliferation of electric vehicles, there is increasing attention on drive motors that are powerful and efficient, with a higher power density. To meet such high power density requirements, the cooling technology used for drive motors is particularly important. To further [...] Read more.
With the recent proliferation of electric vehicles, there is increasing attention on drive motors that are powerful and efficient, with a higher power density. To meet such high power density requirements, the cooling technology used for drive motors is particularly important. To further optimize the cooling effects, the use of direct oil-cooling technology for drive motors is gaining more attention, especially regarding the requirements for electric vehicle electric oil pumps (EOPs) in motor cooling. In such high-temperature environments, it is also necessary for the EOP to maintain its performance under high temperatures. This research explores the feasibility of using high-temperature-resistant ferrite magnets in the rotors of EOPs. For a 150 W EOP motor with the same stator size, three different rotor configurations are proposed: a surface permanent magnet (SPM) rotor, an interior permanent magnet (IPM) rotor, and a spoke-type IPM rotor. While the rotor sizes are the same, to maximize the power density while meeting the rotor’s mechanical strength requirements, the different rotor configurations make the most use of ferrite magnets (weighing 58 g, 51.8 g, and 46.3 g, respectively). Finite element analysis (FEA) was used to compare the performance of these models with that of the basic rotor design, considering factors such as the no-load back electromotive force, no-load voltage harmonics (<10%), cogging torque (<0.1 Nm), load torque, motor loss, and efficiency (>80%). Additionally, a comprehensive analysis of the system efficiency and energy loss was conducted based on hypothetical electric vehicle traction motor parameters. Finally, by manufacturing a prototype motor and conducting experiments, the effectiveness and superiority of the finite element method (FEM) design results were confirmed. Full article
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15 pages, 8783 KiB  
Article
Comprehensive Analysis of Dual-Rotor Yokeless Axial-Flux Motor with Surface-Mounted and Halbach Permanent Magnet Array for Urban Air Mobility
by Do-Kwan Hong, Jang-Hyun Park and Yeon-Ho Jeong
Energies 2024, 17(1), 30; https://doi.org/10.3390/en17010030 - 20 Dec 2023
Cited by 6 | Viewed by 4622
Abstract
A dual-rotor yokeless and segmented armature (YASA)-type axial-flux permanent magnet (AFPM) motor with a surface-mounted permanent magnet (SPM) array type was developed for urban air mobility (UAM) aircraft in this work. The proposed AFPM motor had rated and peak output powers of 75.5 [...] Read more.
A dual-rotor yokeless and segmented armature (YASA)-type axial-flux permanent magnet (AFPM) motor with a surface-mounted permanent magnet (SPM) array type was developed for urban air mobility (UAM) aircraft in this work. The proposed AFPM motor had rated and peak output powers of 75.5 and 104 kW, respectively, with rated and peak rotational speeds of 1800 rpm. To achieve a high torque, a cobalt–iron alloy core material was used for the stator core. The prototype AFPM motor, developed by KSEP in the Republic of Korea, was successfully manufactured and verified through experimentation. Additionally, the thermal stability of the winding and permanent magnets (PMs) was confirmed with a water-cooling system. A structure analysis of the proposed AFPM motor was conducted due to the detachment of an uneven air-gap length in the prototype AFPM motor. An output performance comparison based on core materials for the stator and rotor was carried out to explore the material cost reduction. Subsequently, the design for performance improvement by applying a Halbach permanent magnet (HPM) array type was investigated for further research. Full article
(This article belongs to the Section F: Electrical Engineering)
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21 pages, 7886 KiB  
Article
Performance Improvement of Permanent-Magnet-Synchronous Motors through Rotor Shape Optimization of Marine Blowing System with High-Speed Rotation
by Keun-Young Yoon and Sang-Taek Lee
Energies 2023, 16(14), 5486; https://doi.org/10.3390/en16145486 - 19 Jul 2023
Cited by 8 | Viewed by 3309
Abstract
Currently, research is being carried out on the performance improvement of permanent-magnet-synchronous motors (PMSM) used in air conditioning and blowing systems for marine, as well as structural research, regarding their high-speed operation. Surface-mounted permanent magnet (SPM) motors used in marine propulsion and air-conditioning [...] Read more.
Currently, research is being carried out on the performance improvement of permanent-magnet-synchronous motors (PMSM) used in air conditioning and blowing systems for marine, as well as structural research, regarding their high-speed operation. Surface-mounted permanent magnet (SPM) motors used in marine propulsion and air-conditioning systems have the advantages of easy rotor manufacturing and a simple structure. However, owing to the structural characteristics associated with attaching a permanent magnet to the surface of the rotor, there is a risk of permanent magnet scattering when turning a rated load at high speed, and the rotor assembly is directly affected by the heat generated in the stator winding. Therefore, in this study, additional protrusions were proposed to prevent rotor scattering during high-speed operations. Additionally, optimization was performed to reduce the torque ripple at the rated load and the total harmonic distortion (THD) of the no-load-induced electromotive-force waveform generated by the protrusion. Consequently, the risk of scattering at high speeds was improved by securing the bonding force of the permanent magnet using the proposed structure, and the THD and torque ripple were reduced compared with those of the basic model through optimization. In addition, rotor structural stress analyses were conducted to solve the problem of scattering at high speeds and eigenmode analysis. Full article
(This article belongs to the Section F: Electrical Engineering)
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21 pages, 18826 KiB  
Article
Design of a High Torque Density Robot Joint and Analysis of Force Control Method Applied for a Light Exoskeleton
by Gan Zhang, Qing Tong, Taixun Zhang, Jinxin Tao and Anjian Qiu
Electronics 2023, 12(2), 397; https://doi.org/10.3390/electronics12020397 - 12 Jan 2023
Cited by 8 | Viewed by 5042
Abstract
In many robotic applications, the joint is required to have a small volume, low weight and high torque output. In this paper, based on the finite element analysis (FEA), a 36-slot 40-pole outer rotor surface-mounted permanent magnet (OR-SPM) motor with concentrated winding is [...] Read more.
In many robotic applications, the joint is required to have a small volume, low weight and high torque output. In this paper, based on the finite element analysis (FEA), a 36-slot 40-pole outer rotor surface-mounted permanent magnet (OR-SPM) motor with concentrated winding is designed for the exoskeleton robot. The fractional slot concentrated winding (FSCW) is employed to reduce end winding height, leading better portability. Since the motor is relatively flat, the 3D end effect is critical to the electromagnetic performances. Special attention is paid to 3D end effect during the multi-objective optimization of the OR–SPM motor. In order to increase the ending torque output, the planetary reducer is located between OR–SPM motor and load, and then system level optimization covering motor and reducer is carried out to achieve best torque output. In addition, the force impendence control method with parameter self-adaptive capability is proposed to improve user experience of the exoskeleton robot, where the key parameters in the algorithm vary according to different actions of the exoskeleton. In addition, the inertia of load is calculated using the parameter identification based on least squares method. Finally, the prototype of the joint is fabricated and tested to validate the above FEA results and control method. The user experience of the exoskeleton robot is also covered. Full article
(This article belongs to the Section Power Electronics)
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13 pages, 7481 KiB  
Article
A Novel High-Speed Permanent Magnet Synchronous Motor for Hydrogen Recirculation Side Channel Pumps in Fuel Cell Systems
by Kang Ma, Ye Liu, Ziqiang Wei, Jianfei Yang and Baocheng Guo
Energies 2022, 15(23), 8913; https://doi.org/10.3390/en15238913 - 25 Nov 2022
Cited by 1 | Viewed by 2237
Abstract
In hydrogen recirculation side channel pumps, the motor rotor is exposed to a high-pressure mixture of steam and hydrogen, which makes hydrogen embrittlement occur in permanent magnets (PMs). A protective coating is necessary for the PMs in high-pressure hydrogen. However, in the process [...] Read more.
In hydrogen recirculation side channel pumps, the motor rotor is exposed to a high-pressure mixture of steam and hydrogen, which makes hydrogen embrittlement occur in permanent magnets (PMs). A protective coating is necessary for the PMs in high-pressure hydrogen. However, in the process of sleeve interference installation, the protective coating of the PMs is easily damaged. This paper proposes two surface-mounted insert permanent magnet (SIPM) synchronous motor topologies, SIPM1 and SIPM2, in which the retaining sleeves can be eliminated and the PM protective coating is safe in the assembling process. A dovetail PM and rotor core structure is used to protect the PM with higher rotor strength without retaining the sleeve. The electromagnetic performance of the motors with different rotors, including airgap flux density, output torque, torque ripple, and energy efficiency is compared and optimized. It is concluded that the output torque of the SIPM motor can be promoted by 22.4% and torque ripple can be reduced by 2.9%, while the PM volume remains the same as that of the conventional SPM motor. At the same time, the SIPM motor can have lower harmonic contents of back electromotive force (EMF) and rotor loss compared to the SPM motor with a retaining sleeve. Furthermore, the stress of the PM is analyzed under conditions of PM glue action and failure. The proposed SIPM2 has the ability to operate safely at high-speed and high-temperature operating conditions when the PM glue fails. Full article
(This article belongs to the Topic Advanced Electrical Machines and Drives Technologies)
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25 pages, 10917 KiB  
Article
Mathematical Model Derivation and Experimental Verification of Novel Consequent-Pole Adjustable Speed PM Motor
by Akihisa Hattori, Toshihiko Noguchi and Kazuhiro Murakami
Energies 2022, 15(17), 6147; https://doi.org/10.3390/en15176147 - 24 Aug 2022
Cited by 2 | Viewed by 2157
Abstract
This paper proposes a novel consequent-pole-type PM motor having a structure different from that of conventional consequent-pole-type PM motors. The proposed rotor structure is composed of a magnetic pole pair using a permanent magnet and an image-pole pair using a high permeability core. [...] Read more.
This paper proposes a novel consequent-pole-type PM motor having a structure different from that of conventional consequent-pole-type PM motors. The proposed rotor structure is composed of a magnetic pole pair using a permanent magnet and an image-pole pair using a high permeability core. The windings facing the magnetic pole pair and the image-pole pair are connected in series in the rotor structure, the three-phase synchronous impedance is balanced, and the d-axis inductance is increased. Therefore, compared with the conventional consequent-pole type, the field weakening operation can be performed efficiently with a lower d-axis current. These advantages make it possible to expand the operating range during field weakening. Furthermore, to fix the driving control method of the proposed consequent-pole PM motor, the voltage equation of the proposed motor is derived and verified by analysis and experiment. In addition, the essential characteristics of the proposed motor were compared with that of a standard surface permanent magnet (SPM) motor and a conventional consequent-pole PM motor. Full article
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20 pages, 11845 KiB  
Article
Multi-Physics Comparison of Surface-Mounted and Interior Permanent Magnet Synchronous Motor for High-Speed Applications
by Guanghui Du, Niumei Li, Qixun Zhou, Wentao Gao, Lu Wang and Tao Pu
Machines 2022, 10(8), 700; https://doi.org/10.3390/machines10080700 - 17 Aug 2022
Cited by 14 | Viewed by 8536
Abstract
For high-speed permanent magnet machines (HSPMMs), two different rotor structures are widely used: surface-mounted permanent magnet (SPM) and interior permanent magnet (IPM). The two different rotor structures have a large impact on the comprehensive performance in multiple physical fields of HSPMMs, including mechanical [...] Read more.
For high-speed permanent magnet machines (HSPMMs), two different rotor structures are widely used: surface-mounted permanent magnet (SPM) and interior permanent magnet (IPM). The two different rotor structures have a large impact on the comprehensive performance in multiple physical fields of HSPMMs, including mechanical stress, electromagnetic characteristics, and temperature distribution. However, the multi-physics comparison of two different rotor structures is rare in the existing literature, which makes it difficult for designers to choose a suitable rotor structure. Therefore, in this paper, the comprehensive performance of multi-physics for SPM and IPM is comprehensively compared and analyzed. Firstly, the SPM and IPM were designed under 60 kW and 30,000 rpm with the condition of the same stator structure, winding type and volume. Secondly, to ensure that the two rotor structures meet the stress-field constraints, a finite element model (FEM) was built in Ansys Workbench. The influence of different parameters on the rotor stress was analyzed. Following this, the electromagnetic characteristics and temperature distributions of the two motors were compared and analyzed comprehensively through the FEM. Finally, a prototype of an SPM rotor structure is selected and manufactured. The validity of the multi-physics analysis and design was verified through experimental measurements. The above analysis will provide a reference when a designer chooses a rotor structure for an HSPMM. Full article
(This article belongs to the Special Issue Advances and Trends in PM-Free or Rare-Earth-Free PM Motors)
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16 pages, 8026 KiB  
Article
Solid Rotor Core vs. Lamination Rotor Core in Fractional-Slot PMSM Motor with High Power Density
by Tomasz Wolnik and Tomasz Jarek
Energies 2022, 15(15), 5729; https://doi.org/10.3390/en15155729 - 6 Aug 2022
Cited by 8 | Viewed by 3988
Abstract
Fractional-slot PMSM motors allow for obtaining high values of power density factors, but at the same time, they are characterized by high values of rotor losses—in the rotor core and permanent magnets. The main causes of rotor losses in this type of motor [...] Read more.
Fractional-slot PMSM motors allow for obtaining high values of power density factors, but at the same time, they are characterized by high values of rotor losses—in the rotor core and permanent magnets. The main causes of rotor losses in this type of motor are subharmonics and a high content of higher harmonics in the distribution of the magnetomotive force MMF. The use of a solid rotor core simplifies the construction and technology of the rotor but eddy current losses in the core account for a significant percentage of the total rotor losses. It is well known that a laminated core reduces eddy currents, while for motors with an outer rotor, it complicates the construction and increases weight. Thus, the question arises about the necessity to use a laminated core in a high power density motor and the real benefits of this. The article presents a comparison of the motors with a solid rotor core and a laminated rotor core, considering the value of rotor losses, power density factor, efficiency and the range of rotational speed and range of current load. The analysis was carried out for various types of sheets for laminated core and solid steel and SMC (Soft Magnetic Composite) material for solid rotor core. FEM models were used in the analysis, and the results were partially verified with the results of laboratory tests of motor models. The object of the analysis is a fractional-slot PMSM motor with an external rotor with surface permanent magnets (SPM). Motor weight is about 10 kg, and the maximum power is 50 kW at 4800 rpm. Full article
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24 pages, 4583 KiB  
Article
Study on the Selection of the Number of Magnetic Poles and the Slot-Pole Combinations in Fractional Slot PMSM Motor with a High Power Density
by Tomasz Wolnik, Vítezslav Styskala and Tomas Mlcak
Energies 2022, 15(1), 215; https://doi.org/10.3390/en15010215 - 29 Dec 2021
Cited by 18 | Viewed by 7900
Abstract
Fractional slot, PMSM motors with a properly designed electromagnetic circuit allow for obtaining high power density factors (more than 4 kW per 1 kg of total motor weight). The selection of the number of magnetic poles to the specific dimensions and operating conditions [...] Read more.
Fractional slot, PMSM motors with a properly designed electromagnetic circuit allow for obtaining high power density factors (more than 4 kW per 1 kg of total motor weight). The selection of the number of magnetic poles to the specific dimensions and operating conditions of the motor, as well as the number of slots for the selected number of magnetic poles is the subject of the analysis in this article. This issue is extremely important because it affects the mass of the motor, the value of shaft torque, shaft power and the value of rotor losses. The aim of the work is to select solutions with the highest values of power density factor and, at the same time, the lowest values of rotor losses. The object of the study is a fractional slot PMSM motor with an external solid rotor core with surface permanent magnets (SPM). Motor weight is approximately 10 kg, outer diameter is 200 mm and a maximum power is 50 kW at 4800 r/min. The article analyzes the selection of magnetic poles in the range from 2p = 12 to 2p = 24 and various slot-pole combinations for individual magnetic poles. The target function of the objective was achieved and the calculations results were verified on the physical model. The best solutions were 20-pole, 30-slots (highest efficiency and lowest rotor loss) and 24-pole, 27 slots (highest power density). Full article
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22 pages, 20802 KiB  
Article
Optimal Design of A 12-Slot/10-Pole Six-Phase SPM Machine with Different Winding Layouts for Integrated On-Board EV Battery Charging
by Ahmed Hemeida, Mohamed Y. Metwly, Ayman S. Abdel-Khalik and Shehab Ahmed
Energies 2021, 14(7), 1848; https://doi.org/10.3390/en14071848 - 26 Mar 2021
Cited by 16 | Viewed by 5038
Abstract
The transition to electric vehicles (EVs) has received global support as initiatives and legislation are introduced in support of a zero-emissions future envisaged for transportation. Integrated on-board battery chargers (OBCs), which exploit the EV drivetrain elements into the charging process, are considered an [...] Read more.
The transition to electric vehicles (EVs) has received global support as initiatives and legislation are introduced in support of a zero-emissions future envisaged for transportation. Integrated on-board battery chargers (OBCs), which exploit the EV drivetrain elements into the charging process, are considered an elegant solution to achieve this widespread adoption of EVs. Surface-mounted permanent-magnet (SPM) machines have emerged as plausible candidates for EV traction due to their nonsalient characteristics and ease of manufacturing. From an electric machine design perspective, parasitic torque ripple and core losses need to be minimized in integrated OBCs during both propulsion and charging modes. The optimal design of EV propulsion motors has been extensively presented in the literature; however, the performance of the optimal traction machine under the charging mode of operation for integrated OBCs has not received much attention in the literature thus far. This paper investigates the optimal design of a six-phase SPM machine employed in an integrated OBC with two possible winding layouts, namely, dual three-phase or asymmetrical six-phase winding arrangements. First, the sizing equation and optimized geometrical parameters of a six-phase 12-slot/10-pole fractional slot concentrated winding (FSCW)-based SPM machine are introduced. Then, variations in the output average torque, parasitic torque ripple, and parasitic core losses with the slot opening width and the PM width-to-pole pitch ratio are further investigated for the two proposed winding layouts under various operation modes. Eventually, the optimally designed machine is simulated using analytical magnetic equivalent circuit (MEC) models. The obtained results are validated using 2D finite element (FE) analysis. Full article
(This article belongs to the Section F: Electrical Engineering)
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11 pages, 2489 KiB  
Article
Torque Ripple Minimization of the Permanent Magnet Synchronous Machine by Modulation of the Phase Currents
by Cezary Jędryczka, Dawid Danielczyk and Wojciech Szeląg
Sensors 2020, 20(8), 2406; https://doi.org/10.3390/s20082406 - 23 Apr 2020
Cited by 18 | Viewed by 7219
Abstract
This paper deals with the torque ripple minimization method based on the modulation of the phase currents of the permanent-magnet synchronous motor (PMSM) drive. The shape of the supply current waveforms reducing the torque ripple of the machine considered was determined on the [...] Read more.
This paper deals with the torque ripple minimization method based on the modulation of the phase currents of the permanent-magnet synchronous motor (PMSM) drive. The shape of the supply current waveforms reducing the torque ripple of the machine considered was determined on the basis of finite element analysis (FEA). In the proposed approach, the machine is supplied by a six-leg inverter in order to allow for the injection of zero sequence current harmonics. Two test PMSMs with fractional-slot concentrated windings (FSCW) and surface-mounted permanent magnets (SPMs) have been examined as a case study problem. Wide-range fractional analyses were performed using developed numerical models of the electromagnetic field distribution in the considered machines. The results obtained show that the level of torque ripple in FSCW PMSMs can be effectively reduced by the modulation of the phase currents under the six-leg inverter supply. Full article
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16 pages, 13631 KiB  
Article
Tolerance-Insensitive Design of the Magnet Shape for a Surface Permanent Magnet Synchronous Motor
by Chung-Seong Lee, Kyoung-Soo Cha, Jin-Cheol Park and Myung-Seop Lim
Energies 2020, 13(6), 1311; https://doi.org/10.3390/en13061311 - 11 Mar 2020
Cited by 7 | Viewed by 3557
Abstract
Many studies have been conducted to reduce the cogging torque of electric power steering motors. However, in the mass production of such motors, it is essential to enhance performance robustness in relation to tolerances. For such motors, this work analyzes performance robustness in [...] Read more.
Many studies have been conducted to reduce the cogging torque of electric power steering motors. However, in the mass production of such motors, it is essential to enhance performance robustness in relation to tolerances. For such motors, this work analyzes performance robustness in relation to tolerances by applying a cycloid curve to the surface magnet of the rotor. Applying a cycloid curve to the magnet surface of the rotor is one of several ways to reduce cogging torque. To evaluate the performance of the cycloid curve, we compare it with an eccentric curve. The two curves are compared for the same specifications and evaluated using the indicator, tolerance insensitivity rate, which is used to assess performance robustness in relation to tolerances. The cycloid curve was evaluated to be more robust in relation to tolerances, as compared with the eccentric curve. Finally, an experiment was conducted to validate the robustness of the cycloid curve. Full article
(This article belongs to the Special Issue Permanent Magnet Electrical Machines)
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12 pages, 12571 KiB  
Article
Stator Core Shape Design for Low Core Loss and High Power Density of a Small Surface-Mounted Permanent Motor
by Naoya Soda and Masato Enokizono
Sensors 2020, 20(5), 1418; https://doi.org/10.3390/s20051418 - 5 Mar 2020
Cited by 2 | Viewed by 7931
Abstract
In this paper, a stator core shape design method is proposed for an improvement in the power density of a small surface-mounted permanent magnet (SPM) motor. In order to improve the power density of a motor, it is necessary to increase its torque [...] Read more.
In this paper, a stator core shape design method is proposed for an improvement in the power density of a small surface-mounted permanent magnet (SPM) motor. In order to improve the power density of a motor, it is necessary to increase its torque or reduce its weight. However, when a stator core shape is miniaturized to reduce the weight of the motor, the winding regions in a motor frequently decrease. Our stator core shape design method improves the power density of a motor by reducing its weight without decreasing the torque and keeping the winding regions constant. Moreover, the core loss of a motor also decreases when using our method. A Bezier curve is used for the determination of a stator core shape. The finite element method in consideration of the vector magnetic properties is used to evaluate the core loss of the motor shaped by our method. As a result, the power density of an SPM motor is improved, and the core loss of the motor decreases. Full article
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24 pages, 7131 KiB  
Article
An Analytical Subdomain Model of Torque Dense Halbach Array Motors
by Moadh Mallek, Yingjie Tang, Jaecheol Lee, Taoufik Wassar, Matthew A. Franchek and Jay Pickett
Energies 2018, 11(12), 3254; https://doi.org/10.3390/en11123254 - 22 Nov 2018
Cited by 4 | Viewed by 7785
Abstract
A two-dimensional mathematical model estimating the torque of a Halbach Array surface permanent magnet (SPM) motor with a non-overlapping winding layout is developed. The magnetic field domain for the two-dimensional (2-D) motor model is divided into five regions: slots, slot openings, air gap, [...] Read more.
A two-dimensional mathematical model estimating the torque of a Halbach Array surface permanent magnet (SPM) motor with a non-overlapping winding layout is developed. The magnetic field domain for the two-dimensional (2-D) motor model is divided into five regions: slots, slot openings, air gap, rotor magnets and rotor back iron. Applying the separation of variable method, an expression of magnetic vector potential distribution can be represented as Fourier series. By considering the interface and boundary conditions connecting the proposed regions, the Fourier series constants are determined. The proposed model offers a computationally efficient approach to analyze SPM motor designs including those having a Halbach Array. Since the tooth-tip and slots parameters are included in the model, the electromagnetic performance of an SPM motor, described using the cogging torque, back-EMF and electromagnetic torque, can be calculated as function of the slots and tooth-tips effects. The proposed analytical predictions are compared with results obtained from finite-element analysis. Finally, a performance comparison between a conventional and Halbach Array SPM motor is performed. Full article
(This article belongs to the Special Issue Energy Efficiency in Electric Devices, Machines and Drives)
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16 pages, 19287 KiB  
Article
Tolerance Sensitivity Analysis and Robust Optimal Design Method of a Surface-Mounted Permanent Magnet Motor by Using a Hybrid Response Surface Method Considering Manufacturing Tolerances
by Cha-Seung Jun, Byung-Il Kwon and Ohbong Kwon
Energies 2018, 11(5), 1159; https://doi.org/10.3390/en11051159 - 5 May 2018
Cited by 12 | Viewed by 3643
Abstract
This paper presents a robust optimal design method using a hybrid response surface method (H-RSM) which directly finds an optimal point satisfying a target Z-value or a probability of failure. Through three steps, this paper achieves the goal that is to increase the [...] Read more.
This paper presents a robust optimal design method using a hybrid response surface method (H-RSM) which directly finds an optimal point satisfying a target Z-value or a probability of failure. Through three steps, this paper achieves the goal that is to increase the open-circuit airgap flux (OCAF) in a surface-mounted permanent magnet motor and decrease its variation caused by variations of the airgap lengths including an additional one between permanent magnets and rotor back yoke. First, the OCAF equation is derived from the magnetic equivalent circuit (MEC) considering the additional airgap. Then, the equation is validated by comparing its results with those of the finite element method (FEM) modeled by the slotless stator. Next, the tolerance sensitivity analysis, using the partial derivative of the OCAF equation with respect to the airgap length, is performed to investigate the effects of design variables on the OCAF. It is shown that increasing the magnet thickness is effective for both increasing mean of the OCAF and reducing its variation. Finally, robust optimal design is performed using the H-RSM, in which all data are obtained from the FEM modeled by the slotted stator. The results of the robust optimal design are verified using the FEM. Full article
(This article belongs to the Section F: Electrical Engineering)
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