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Keywords = coreless motor

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17 pages, 5415 KB  
Article
Magnetic Equivalent Circuit-Based Performance Evaluation of Modular PCB AFPM Motor for Electric Water Pumps
by Do-Hyeon Choi, Won-Ho Kim and Hyungkwan Jang
Actuators 2026, 15(2), 87; https://doi.org/10.3390/act15020087 (registering DOI) - 1 Feb 2026
Abstract
Electric Water Pumps (EWPs) are being adopted more widely to improve thermal management in internal combustion engines and electrified powertrain systems. In this context, the drive motor must deliver high efficiency and reliability despite a strict volume constraint. This paper addresses a key [...] Read more.
Electric Water Pumps (EWPs) are being adopted more widely to improve thermal management in internal combustion engines and electrified powertrain systems. In this context, the drive motor must deliver high efficiency and reliability despite a strict volume constraint. This paper addresses a key drawback of coreless printed circuit board (PCB) stator axial-flux permanent-magnet machines for EWP use: the PCB traces are directly exposed to the magnet flux, which increases AC loss, while the required phase resistance also leads to non-negligible DC copper loss. To mitigate both loss components within the same conductor design space, a pyramid trace concept is introduced. A magnetic equivalent circuit (MEC) based model is first used to estimate the baseline performance as the number of PCB stator modules changes, and the resulting scalability is examined in terms of module commonality. The final design then applies the pyramid trace layout with a layer-dependent trace width that is narrower on the layers closer to the magnets and wider on the layers farther away—the trade-off between AC loss and DC loss is optimized using 3D finite element analysis. Torque predictions from the simplified MEC model are cross-checked against 3D finite element analysis (FEA), and finally, a prototype is built to validate the analysis with experimental measurements; for the final selected model, the torque prediction error is 2.37% compared with the validation result. Full article
(This article belongs to the Section High Torque/Power Density Actuators)
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25 pages, 23143 KB  
Article
Experimental Characterization of Miniature DC Motors for Robotics in High Magnetic Field Environments
by Francesco Mazzei, Luca Bernardi, Paolo Francesco Scaramuzzino, Corrado Gargiulo and Fabio Curti
Robotics 2025, 14(12), 172; https://doi.org/10.3390/robotics14120172 - 21 Nov 2025
Viewed by 986
Abstract
The deployment of robotic systems in hazardous and magnetically intense environments requires careful assessment of their performance under external disturbances. In particular, electromagnetic motors used for actuation may interact with strong magnetic fields, potentially impairing their functionality. This study investigates the behaviour of [...] Read more.
The deployment of robotic systems in hazardous and magnetically intense environments requires careful assessment of their performance under external disturbances. In particular, electromagnetic motors used for actuation may interact with strong magnetic fields, potentially impairing their functionality. This study investigates the behaviour of miniature brushed coreless Direct Current (DC) motors for small Unmanned Aerial Vehicle (UAV) applications in magnetically harsh environments, such as underground accelerator facilities like the Large Hadron Collider (LHC) at CERN. Experimental tests were conducted measuring four main physical quantities: the torque components acting along the axes orthogonal to the shaft, the torque about the shaft axis, variations in angular speed, and electrical current consumption. The results showed that the motors were able to operate under external magnetic field intensities up to 0.4 T, although measurable torques acted on the internal permanent magnet and on the ferromagnetic housing material. Some discrepancies and speed fluctuations were observed during operation and were attributed to mobility of the internal permanent magnet. Overall, the findings demonstrate that the tested miniature motors exhibit resilience in high magnetic fields but suffer from manufacturing variability, suggesting that higher-quality motors with more consistent characteristics would be preferable for reliable robotic operation in harsh environments. Full article
(This article belongs to the Section Intelligent Robots and Mechatronics)
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22 pages, 6317 KB  
Article
Simulation Study on the Magnetic Field Characteristics of a Permanent Magnet Motor for a Rim-Driven Device
by Chao Jiang, Changgeng Shuai and Mingzhong Qiao
Appl. Sci. 2025, 15(20), 11129; https://doi.org/10.3390/app152011129 - 17 Oct 2025
Viewed by 442
Abstract
The rim-driven device (RDD) integrates the motor and the impeller, which can achieve shaftless, modular, and integrated operation of the turbomachinery system and has broad application prospects. To reduce the axial length and radial thickness of the RDD, a motor with a thin-yoke [...] Read more.
The rim-driven device (RDD) integrates the motor and the impeller, which can achieve shaftless, modular, and integrated operation of the turbomachinery system and has broad application prospects. To reduce the axial length and radial thickness of the RDD, a motor with a thin-yoke wide-tooth fractional slot concentrated winding stator and a coreless Halbach permanent magnet array rotor is designed. Theoretical and finite element simulation analyses of its air gap magnetic field characteristics were carried out. The results show that, for the thin-yoke wide-tooth fractional slot concentrated winding permanent magnet motor, the harmonic magnetic field generated by the magnetic poles should mainly consider the magnetic field components produced by the interaction between the harmonic magnetomotive force of the magnetic poles and the constant air gap specific magnetic permeability, as well as the magnetic field components generated by the interaction between the fundamental magnetomotive force of the magnetic poles and the fundamental and second-order harmonic air gap specific magnetic permeability. The harmonic magnetic field generated by the current should mainly consider the magnetic field components produced by the interaction between the harmonic magnetomotive force with a small number of pole pairs (NOPP) and large amplitude generated by the current and the constant air gap specific magnetic permeability. Compared with radial magnetic flux density, tangential magnetic flux density has the same NOPP and frequency components, with a phase difference of 90°. The fundamental amplitude difference between them is larger, while the harmonic amplitude difference between them is smaller. Full article
(This article belongs to the Section Applied Physics General)
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16 pages, 5272 KB  
Article
Performance Comparison of Coreless PCB AFPM Topologies for Duct Fan
by Seung-Hoon Ko, Min-Ki Hong, Na-Rim Jo, Ye-Seo Lee and Won-Ho Kim
Energies 2025, 18(17), 4600; https://doi.org/10.3390/en18174600 - 29 Aug 2025
Viewed by 1072
Abstract
Duct fan motors must provide high torque within limited space to maintain airflow while requiring low vibration characteristics to minimize fluid resistance caused by fan oscillation. Axial Flux Permanent Magnet Motor (AFPM) offers higher torque performance than Radial Flux Permanent Magnet Motor (RFPM) [...] Read more.
Duct fan motors must provide high torque within limited space to maintain airflow while requiring low vibration characteristics to minimize fluid resistance caused by fan oscillation. Axial Flux Permanent Magnet Motor (AFPM) offers higher torque performance than Radial Flux Permanent Magnet Motor (RFPM) due to their large radial and short axial dimensions. In particular, the coreless AFPM structure enables superior low-vibration performance. Conventional AFPM typically employs a core-type stator, which presents manufacturing difficulties. In core-type AFPM, applying a multi-stator configuration linearly increases winding takt time in proportion to the number of stators. Conversely, a Printed Circuit Board (PCB) stator AFPM significantly reduces stator production time, making it favorable for implementing multi-stator topologies. The use of multi-stator structures enables various topological configurations depending on (1) stator placement, (2) magnetization pattern of permanent magnets, and (3) rotor arrangement—each offering specific advantages. This study evaluates and analyzes the performance of different topologies based on efficient arrangements of magnets and stators, aiming to identify the optimal structure for duct fan applications. The validity of the proposed approach and design was verified through three-dimensional finite element analysis (FEA). Full article
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25 pages, 18306 KB  
Article
Rapid Design of a Coreless Axial Flux Motor Based on the Magnetic Charge Method
by Guoqing Zhu, Zhihui Jin and Jian Luo
Energies 2025, 18(13), 3520; https://doi.org/10.3390/en18133520 - 3 Jul 2025
Cited by 2 | Viewed by 1820
Abstract
Axial flux motors have attracted significant attention in recent years due to their advantages such as shorter axial length and high torque density. However, the optimization of axial flux motors is an extremely time-consuming process. To reduce the computational time required for motor [...] Read more.
Axial flux motors have attracted significant attention in recent years due to their advantages such as shorter axial length and high torque density. However, the optimization of axial flux motors is an extremely time-consuming process. To reduce the computational time required for motor optimization, this study employed a magnetic charge model to establish a coreless axial flux motor model and analyzed the advantages of this approach. This method is applicable to coreless axial flux motor optimizations with surface-mounted rotors and concentrated windings. Parameter optimization was subsequently performed based on the theoretical model. In terms of seeking optimal solutions, the torque obtained through the magnetic charge method (MCM) reached 99.67% of the finite element method (FEM) results. Finally, a prototype was fabricated, and a test platform was constructed based on the optimization results. The experimental torque showed a 4% deviation from simulations, validating the accuracy of the optimization. Full article
(This article belongs to the Section E: Electric Vehicles)
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27 pages, 4210 KB  
Article
Magnetic Field Distribution and Energy Losses in a Permanent Magnet Linear Synchronous Motor Under Stick-Slip Friction
by Paweł Olejnik, Yared D. Desta and Marcin Mydłowski
Energies 2025, 18(1), 191; https://doi.org/10.3390/en18010191 - 4 Jan 2025
Cited by 5 | Viewed by 3032
Abstract
This study investigates the modeling and dynamic analysis of three coupled electromechanical systems, emphasizing interactions between a magnetic linear drive and frictional contact with flat springs. The experimental setup includes a table driven by a three-phase permanent magnet linear synchronous motor (PMLSM) using [...] Read more.
This study investigates the modeling and dynamic analysis of three coupled electromechanical systems, emphasizing interactions between a magnetic linear drive and frictional contact with flat springs. The experimental setup includes a table driven by a three-phase permanent magnet linear synchronous motor (PMLSM) using an LMCA4 inductor, LMCAS3 magnetic track, and Xenus XTL controller. Mechanical phenomena such as stick-slip friction and impulsive loads are observed, particularly due to the rapid buckling of flat springs. These springs transition between sliding friction and fixation, impacting the motor’s operation during reciprocating velocity trajectories and generating acoustic emissions. Numerical simulations using COMSOL Multiphysics evaluate the magnetic field and system geometry in two- and three-dimensional spaces. Key findings include mechanical stick-slip vibrations, numerical modeling of the linear drive, and comparative analysis of experimental and simulated inductor current variations. Additionally, energy loss mechanisms under irregular loading conditions are assessed. The results highlight the coupling between friction-induced current changes and magnetic field variations, elucidating their impact on motor efficiency, vibration propagation, and acoustic emissions. The study provides insights into optimizing the design and reliability of coreless linear motors for precision applications under discontinuous loading. Full article
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15 pages, 14638 KB  
Article
Control Strategy for Disc Coreless Permanent Magnet Synchronous Motor with LC Filter
by Hong Tian and Min Kang
Electronics 2024, 13(22), 4572; https://doi.org/10.3390/electronics13224572 - 20 Nov 2024
Cited by 2 | Viewed by 1617
Abstract
The disc coreless permanent magnet synchronous motor has the advantages of a short axial size, high power density, and small volume. Due to the coreless structure, its inductance is very small, which results in a serious current ripple and an unacceptable torque ripple [...] Read more.
The disc coreless permanent magnet synchronous motor has the advantages of a short axial size, high power density, and small volume. Due to the coreless structure, its inductance is very small, which results in a serious current ripple and an unacceptable torque ripple if driven from a conventional inverter. This can be solved by installing an LC filter between the inverter and the motor. However, an undesirable resonance phenomenon is induced by the LC filter. In this paper, a new capacitive current feedback active damping (CCFAD) strategy is proposed. Instead of current sensors in the capacitor branch, a state observer is introduced to estimate the capacitance current. The observer is designed with double sliding mode surfaces, which reduces the order of the system. Compared to conventional capacitive current feedback, no additional current sensors are required, reducing the system cost. Besides the resonant harmonics, the phase current contains obvious fifth and seventh harmonics due to the special plane structure of the rotor. The proportional-integral-resonance (PIR) controller, instead of the traditional PI controller, is designed to suppress lower order harmonics. The experiment results show that current ripples due to resonance and rotor structure are suppressed significantly. Full article
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14 pages, 2390 KB  
Article
Study on the Influences of an Outer-Coreless-Rotor Permanent Magnet Synchronous Machine Using Halbach Magnet Array
by Cong Xu, Hao Wu, Yuchao Shi, Ning Wang and Liwei Song
Energies 2024, 17(13), 3108; https://doi.org/10.3390/en17133108 - 24 Jun 2024
Cited by 2 | Viewed by 2229
Abstract
In order to evaluate the influences of the topology design of a Halbach Magnet Array (HA) on the performance of a motor, a PMSM with an outer coreless rotor using a Halbach Magnet Array (HAORPMSM) is proposed in this article. The design parameters [...] Read more.
In order to evaluate the influences of the topology design of a Halbach Magnet Array (HA) on the performance of a motor, a PMSM with an outer coreless rotor using a Halbach Magnet Array (HAORPMSM) is proposed in this article. The design parameters of the HA could be separated into dividing methods per pole, magnet thickness, and initial magnetization direction angle. The phase Back-EMF under constant mechanical speed is chosen as the index to measure the performance of the motor. To start with, different dividing methods of the HA are evaluated. After that, the influence of thickness considering the utilization of the magnet is studied. Lastly, the relationship between initial magnetization direction and motor manufacturing is represented. The results show that the HA design meets the optimized performance considering the balance of the amount of magnet usage and manufacturing when using specific HA parameters. Full article
(This article belongs to the Special Issue Linear/Planar Motors and Other Special Motors)
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17 pages, 17265 KB  
Article
Design, Analysis and Experimental Verification of a Coreless Permanent Magnet Synchronous Motor
by Wojciech Szelag, Cezary Jedryczka, Mariusz Baranski and Milena Kurzawa
Energies 2024, 17(7), 1664; https://doi.org/10.3390/en17071664 - 30 Mar 2024
Cited by 3 | Viewed by 3111
Abstract
The paper presents a new cost-effective magnetic circuit structure of a coreless permanent magnet synchronous motor (PMSM) with 16 poles and 12 coils for a mass production fan drive unit. 2D and 3D numerical models of the coreless PMSM were developed. Optimisation calculations [...] Read more.
The paper presents a new cost-effective magnetic circuit structure of a coreless permanent magnet synchronous motor (PMSM) with 16 poles and 12 coils for a mass production fan drive unit. 2D and 3D numerical models of the coreless PMSM were developed. Optimisation calculations were carried out using the field model of the machine. Multistage calculations were performed using the professional FEM package, ANSYS Maxwell and the author’s proprietary finite element method (FEM) code. On the basis of the conducted tests and analysis of the obtained results, the “optimal” magnetic circuit structure of the PMSM motor was selected. The prototype motor was subjected to measurement to verify the developed models and the proposed design approach that takes advantage of finite element analysis (FEA). Full article
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16 pages, 5382 KB  
Article
Eddy Current Braking Force Analysis of a Water-Cooled Ironless Linear Permanent Magnet Synchronous Motor
by Mengyao Wang, Lu Zhang, Kai Yang, Junjie Xu and Chunyu Du
Energies 2023, 16(15), 5826; https://doi.org/10.3390/en16155826 - 6 Aug 2023
Cited by 1 | Viewed by 2191
Abstract
The ironless linear permanent magnet synchronous motor (ILPMSM) is highly compact, easy to control, and exhibits minimal thrust fluctuations, making it an ideal choice for direct loading applications requiring precise positioning accuracy in linear motor test rigs. To address the issue of temperature [...] Read more.
The ironless linear permanent magnet synchronous motor (ILPMSM) is highly compact, easy to control, and exhibits minimal thrust fluctuations, making it an ideal choice for direct loading applications requiring precise positioning accuracy in linear motor test rigs. To address the issue of temperature rise resulting from increased primary winding current and to simultaneously enhance thrust density while minimizing thrust fluctuations, this paper introduces a bilateral-type ILPMSM with a cooling water jacket integrated between the dual-layer windings of the primary movers. The primary winding of the motor adopts a dual-layer coreless structure where the upper and lower windings are closely spaced and cooled by a non-conductive metal cooling water jacket, while the dual-sided secondary employs a Halbach permanent magnet array. The motor’s overall braking force is a combination of the electromagnetic braking force generated by the energized windings and the eddy current braking force induced on the cooling water jacket. This paper specifically focuses on the analysis of the eddy current braking force. Initially, the motor’s geometry and working principle are presented. Subsequently, the equivalent magnetization intensity method is employed to determine the no-load air gap magnetic density resulting from the Halbach array. An analytical model is then developed to derive expressions for the eddy current density and braking force induced in the water-cooling jacket. The accuracy of the analytical method is validated through finite element analysis. Then, a comparative analysis of the braking forces in two primary cooling structures, namely the inter-cooled type and the two-side cooled type ILPMSM, is conducted. Moreover, the characteristics of the eddy current braking force are thoroughly examined concerning motor size parameters and operating conditions. This paper provides a solid theoretical foundation for the subsequent optimization design of the proposed motor. Full article
(This article belongs to the Special Issue Advanced Permanent-Magnet Machines for Electric Vehicles)
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16 pages, 8537 KB  
Article
A Comprehensive Investigation of Winding Eddy and Circulating Current Losses of Stator Iron Coreless PMBLDC Motors
by Liu Yang, Jing Zhao, Wenqi Fu, Xiangdong Liu, Jianguo Zhu and Chao Ai
Energies 2023, 16(14), 5523; https://doi.org/10.3390/en16145523 - 21 Jul 2023
Cited by 6 | Viewed by 3108
Abstract
A method is proposed to comprehensively study the eddy and circulating current losses of stator winding wound by multiple parallel strands, to further improve the power density of stator iron coreless permanent magnet brushless DC (PMBLDC) motors. Analytical models of the eddy and [...] Read more.
A method is proposed to comprehensively study the eddy and circulating current losses of stator winding wound by multiple parallel strands, to further improve the power density of stator iron coreless permanent magnet brushless DC (PMBLDC) motors. Analytical models of the eddy and circulating current losses in stator winding are deduced firstly to explicitly express the influencing factors of these two losses. As is shown, these factors are mutually contradicting. While the eddy current loss can be greatly reduced by using multiple parallel conductor strands, the circulating current loss will be extensively increased. The factors influencing these two winding losses, such as the strand diameter, magnetization types, and rotating speed, are investigated. A prototype of stator iron coreless PMBLDC motor without an inner rotor core is manufactured and tested to validate the theory. The experimental results of winding eddy and circulating current losses with different combinations of strand diameters and parallel numbers agree well with the theoretical results. Full article
(This article belongs to the Topic Advanced Electrical Machine Design and Optimization Ⅱ)
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14 pages, 4773 KB  
Article
Multi-Parameter Optimization of Stator Coreless Disc Motor Based on Orthogonal Response Surface Method
by Huiqin Sun, Ying Li, Lucheng Zhang, Zezhao Xue, Weiguang Hu, Guoshuai Li and Yingjun Guo
Electronics 2023, 12(14), 3020; https://doi.org/10.3390/electronics12143020 - 10 Jul 2023
Cited by 3 | Viewed by 2024
Abstract
In response to the structural optimization problem of PCB stator coreless disc motors, the orthogonal response surface method was used to optimize the motor structure, preliminarily determine the basic parameters of the motor, and conduct orthogonal experiments on the motor parameters based on [...] Read more.
In response to the structural optimization problem of PCB stator coreless disc motors, the orthogonal response surface method was used to optimize the motor structure, preliminarily determine the basic parameters of the motor, and conduct orthogonal experiments on the motor parameters based on the optimization design objectives. The optimization factors were the quantity of the magnetic pole of the motor rotor p, the ratio of the main/auxiliary pole sizes Rnd, the thickness Tm of the permanent magnet, and the air gap length δ. The motor torque Td, the amplitude of the magnetic density of the air gap Bδ, and the waveform distortion rate THD were used as optimization objectives. The motor parameters that cause the motor torque to reach a maximum cause the air gap magnetic density to reach a maximum and the waveform distortion rate to reach a minimum. Due to the use of PCB plates instead of motor stator cores in the PCB coreless disc motors, the service life of the PCB board during motor operation will be reduced with the temperature increase generated by the stator winding. To solve this problem, a response surface analysis of the motor was carried out to reduce the increase in the temperature of the stator windings during the operation of the motor. The PCB board and stator winding are the main factors affecting the motor’s temperature increase. Taking the thickness of the PCB board, the hole diameter on the board, and the uneven width of the stator winding as optimization factors, the motor parameters with the lowest increase in the temperature of the motor winding were obtained. A simulation analysis was conducted using Ansys/Maxwell software, and the results prove the feasibility of the optimization. Full article
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11 pages, 4683 KB  
Communication
Design of a Single-Sided, Coreless, Flat-Type Linear Voice Coil Motor
by Wei Zhang, He Zhang, Junren Mu and Song Wang
Actuators 2023, 12(2), 77; https://doi.org/10.3390/act12020077 - 11 Feb 2023
Cited by 4 | Viewed by 4014
Abstract
A voice coil motor is a type of permanent magnet linear motor, which is based on the Ampere force theorem. It has the following advantages: a simple structure, a small size, no cogging force, and a fast response time. In this study, a [...] Read more.
A voice coil motor is a type of permanent magnet linear motor, which is based on the Ampere force theorem. It has the following advantages: a simple structure, a small size, no cogging force, and a fast response time. In this study, a voice coil motor was designed to provide x-directional thrust in the magnetically levitated cable table of a lithography machine. The voice coil motor designed in this study was based on the Halbach permanent magnet array, and adopted a single-sided, coreless, flat-type structure. First, the magnetic field distribution was analyzed based on the magnetic charge method to obtain an expression for the magnetic field and the thrust. The results of this analysis agreed very well with the finite element simulation results. Next, the main parameters of the motor, including the number of turns made by the coil, the size of the wire, and the size of the permanent magnets, were selected and optimized to increase the force density. Finally, two double-layer, serpentine waterway water-cooling plate configurations were designed for this voice coil motor. The validity of this water-cooling structure was verified for two different winding equivalent models. This provided feasibility to further upgrade the windings’ current density. Full article
(This article belongs to the Section Actuators for Medical Instruments)
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11 pages, 2997 KB  
Article
Speed Tracking Performance for a Coreless Linear Motor Servo System Based on a Fitted Adaptive Fuzzy Controller
by Meizhu Luo, Ji-an Duan and Zhaoxi Yi
Energies 2023, 16(3), 1259; https://doi.org/10.3390/en16031259 - 24 Jan 2023
Cited by 4 | Viewed by 1732
Abstract
Fuzzy control is widely used in linear motor servo systems. However, simple fuzzy rules reduce the control accuracy of the servo system, while complex fuzzy rules reduce the speed of its decision making. This paper proposes a fitted adaptive fuzzy controller (FAFC) to [...] Read more.
Fuzzy control is widely used in linear motor servo systems. However, simple fuzzy rules reduce the control accuracy of the servo system, while complex fuzzy rules reduce the speed of its decision making. This paper proposes a fitted adaptive fuzzy controller (FAFC) to improve the speed tracking performance of a coreless linear motor servo system. The FAFC took a planned curve as a motion target. The planned curve is compounded by multiple performance curves of fuzzy control under the same given input. These multiple performance curves cover the variation range of motor parameters, which are offline-obtained. The performance of the planned curve is ensured by the multiple offline performance curves. The FAFC only needs simple fuzzy rules to fit the planned curve, and achieves high control accuracy without affecting the decision speed. The experimental results verified the feasibility of an FAFC. This research shows that an FAFC can effectively shorten the online calculation time of complex algorithms and keep the consistency of performance. Full article
(This article belongs to the Special Issue Advanced Modeling and Optimization of Electrical Drives Technology)
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12 pages, 9702 KB  
Article
Research on Air Gap Magnetic Field Characteristics of Trapezoidal Halbach Permanent Magnet Linear Synchronous Motor Based on Improved Equivalent Surface Current Method
by Bo Li, Jun’an Zhang, Xiaolong Zhao, Bo Liu and Hao Dong
Energies 2023, 16(2), 793; https://doi.org/10.3390/en16020793 - 10 Jan 2023
Cited by 11 | Viewed by 2705
Abstract
Accurate analysis of the air gap magnetic field is the focus of research in the field of precision permanent magnet linear synchronous motors. In this paper, the two-dimensional air gap magnetic field of a secondary trapezoidal Halbach permanent magnet array coreless permanent magnet [...] Read more.
Accurate analysis of the air gap magnetic field is the focus of research in the field of precision permanent magnet linear synchronous motors. In this paper, the two-dimensional air gap magnetic field of a secondary trapezoidal Halbach permanent magnet array coreless permanent magnet linear synchronous motor (PMLSM) was taken as our research object. On the basis of the equivalent surface current method, we proposed an improved equivalent analytical algorithm with a trapezoidal side length unit. The equivalent analytical model of the magnetic induction vector of the two-dimensional air gap was established, and the air gap magnetic field of the trapezoidal Halbach array coreless PMLSM was calculated. At the same time, we analyzed the influence of the bottom angle α of a trapezoidal permanent magnet equivalent width coefficient αw, pole height coefficient αh, and air gap height coefficient αg on the amplitude (Bpeak) and total harmonic distortion (THDB) of the central magnetic field in the air gap. The results show that α and αw have a significant influence on the Bpeak and THDB of the central magnetic field air gap. With the synergy of α and αw, we identified the “flux convergence” effect, which makes the maximum range of Bpeak α > 90° and αw < 0.5. We also found the “equilateral” effect, which causes the minimum region of THDB to change linearly. The calculation results of the improved equivalent surface current analytical model established in this paper agree with those verified by the finite element method. The calculation is convenient, and the accuracy of the result is high. This research provides a new method for analyzing the air gap magnetic field of a permanent magnet with a nonrectangular cross-section and lays a theoretical foundation for optimizing the PMLSM pole model. Full article
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