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Keywords = magnetic equivalent circuit

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18 pages, 5389 KiB  
Article
Novel Method of Estimating Iron Loss Equivalent Resistance of Laminated Core Winding at Various Frequencies
by Maxime Colin, Thierry Boileau, Noureddine Takorabet and Stéphane Charmoille
Energies 2025, 18(15), 4099; https://doi.org/10.3390/en18154099 (registering DOI) - 1 Aug 2025
Abstract
Electromagnetic and magnetic devices are increasingly prevalent in sectors such as transportation, industry, and renewable energy due to the ongoing electrification trend. These devices exhibit nonlinear behavior, particularly under signals rich in harmonics. They require precise and appropriate modeling for accurate sizing. Identifying [...] Read more.
Electromagnetic and magnetic devices are increasingly prevalent in sectors such as transportation, industry, and renewable energy due to the ongoing electrification trend. These devices exhibit nonlinear behavior, particularly under signals rich in harmonics. They require precise and appropriate modeling for accurate sizing. Identifying model-specific parameters, which depend on frequency, is crucial. This article focuses on a specific frequency range where a circuit model with series resistance and inductance, along with a parallel resistance to account for iron losses (Riron), is applicable. While the determination of series elements is well documented, the determination of Riron remains complex and debated, with traditional methods neglecting operating conditions such as magnetic saturation. To address these limitations, an innovative experimental method is proposed, comprising two main steps: determining the complex impedance of the magnetic device and extracting Riron from the model. This method aims to provide a more precise and representative estimation of Riron, improving the reliability and accuracy of electromagnetic and magnetic device simulations and designs. The obtained values of the iron loss equivalent resistance are different by at least 300% than those obtained by an impedance analyzer. The proposed method is expected to advance the understanding and modeling of losses in electromagnetic and magnetic devices, offering more robust tools for engineers and researchers in optimizing device performance and efficiency. Full article
(This article belongs to the Section F1: Electrical Power System)
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13 pages, 13107 KiB  
Article
Ceramic Isolated High-Torque Permanent Magnet Coupling for Deep-Sea Applications
by Liying Sun, Xiaohui Gao and Yongguang Liu
J. Mar. Sci. Eng. 2025, 13(8), 1474; https://doi.org/10.3390/jmse13081474 - 31 Jul 2025
Abstract
Permanent magnetic couplings provide critical advantages for deep-sea systems through static-sealed, contactless power transmission. However, conventional metallic isolation sleeves incur significant eddy current losses, limiting efficiency and high-speed operation. Limited torque capacities fail to meet the operational demands of harsh marine environments. This [...] Read more.
Permanent magnetic couplings provide critical advantages for deep-sea systems through static-sealed, contactless power transmission. However, conventional metallic isolation sleeves incur significant eddy current losses, limiting efficiency and high-speed operation. Limited torque capacities fail to meet the operational demands of harsh marine environments. This study presents a novel permanent magnet coupling featuring a ceramic isolation sleeve engineered for deep-sea cryogenic ammonia submersible pumps. The ceramic sleeve eliminates eddy current losses and provides exceptional corrosion resistance in acidic/alkaline environments. To withstand 3.5 MPa hydrostatic pressure, a 6-mm-thick sleeve necessitates a 10 mm operational air gap, challenging magnetic circuit efficiency. To address this limitation, an improved 3D magnetic equivalent circuit (MEC) model was developed that explicitly accounts for flux leakage and axial end-effects, enabling the accurate characterization of large air gap fields. Leveraging this model, a Taguchi method-based optimization framework was implemented by balancing key parameters to maximize the torque density. This co-design strategy achieved a 21% increase in torque density, enabling higher torque transfer per unit volume. Experimental validation demonstrated a maximum torque of 920 Nm, with stable performance under simulated deep-sea conditions. This design establishes a new paradigm for high-power leak-free transmission in corrosive, high-pressure marine environments, advancing applications from deep-sea propulsion to offshore energy systems. Full article
(This article belongs to the Section Ocean Engineering)
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17 pages, 2283 KiB  
Article
Application of High Efficiency and High Precision Network Algorithm in Thermal Capacity Design of Modular Permanent Magnet Fault-Tolerant Motor
by Yunlong Yi, Sheng Ma, Bo Zhang and Wei Feng
Energies 2025, 18(15), 3967; https://doi.org/10.3390/en18153967 - 24 Jul 2025
Viewed by 183
Abstract
Aiming at the problems of low thermal analysis efficiency and high computational cost of traditional computational fluid dynamics (CFD) methods for modular fault-tolerant permanent magnet synchronous motors (MFT-PMSMs) under complex working conditions, this paper proposes a fast modeling and calculation method of motor [...] Read more.
Aiming at the problems of low thermal analysis efficiency and high computational cost of traditional computational fluid dynamics (CFD) methods for modular fault-tolerant permanent magnet synchronous motors (MFT-PMSMs) under complex working conditions, this paper proposes a fast modeling and calculation method of motor temperature field based on a high-efficiency and high-precision network algorithm. In this method, the physical structure of the motor is equivalent to a parameterized network model, and the computational efficiency is significantly improved by model partitioning and Fourth-order Runge Kutta method. The temperature change of the cooling medium is further considered, and the temperature rise change of the motor at different spatial positions is effectively considered. Based on the finite element method (FEM), the space loss distribution under rated, single-phase open circuit and overload conditions is obtained and mapped to the thermal network nodes. Through the transient thermal network solution, the rapid calculation of the temperature rise law of key components such as windings and permanent magnets is realized. The accuracy of the thermal network model was verified by using fluid-structure coupling simulation and prototype test for temperature analysis. This method provides an efficient tool for thermal safety assessment and optimization in the motor fault-tolerant design stage, especially for heat capacity check under extreme conditions and fault modes. Full article
(This article belongs to the Special Issue Linear/Planar Motors and Other Special Motors)
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20 pages, 3000 KiB  
Article
Non-Linear Analytical Model for Bread-Loaf Linear PM Motor
by Ferhat Turun, Tunahan Sapmaz, Yasemin Öner, Salman Ali and Fabrizio Marignetti
Energies 2025, 18(15), 3940; https://doi.org/10.3390/en18153940 - 24 Jul 2025
Viewed by 318
Abstract
This article presents a non-linear MEC for a linear PM motor, and its experimental validation. In the MEC model, winding flux leakage and iron saturation are considered. In addition, two different linear PM motor models (bread-loaf and surface-type) are examined for linear PM [...] Read more.
This article presents a non-linear MEC for a linear PM motor, and its experimental validation. In the MEC model, winding flux leakage and iron saturation are considered. In addition, two different linear PM motor models (bread-loaf and surface-type) are examined for linear PM motors. An iterative method is used to predict the magnetic behavior of saturated magnetic steel. The proposed MEC for linear PM motors is compared with finite element analysis (FEA) to determine its accuracy and suitability. FEA is widely regarded as a highly accurate and reliable tool for analyzing linear PM motors. However, its primary limitation lies in its considerable computational time requirement. This disadvantage becomes particularly problematic during the early stages of the design process. Therefore, the proposed model addresses this limitation. Also, experimental results validate the practicality of the MEC. Finally, the proposed model can be a tool for different slot/pole combinations. Thus, the model can be considered suitable for both bread-loaf and surface-type PM motors. Full article
(This article belongs to the Special Issue Condition Monitoring of Electrical Machines Based on Models)
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20 pages, 67621 KiB  
Article
Magnetic Induction Spectroscopy-Based Non-Contact Assessment of Avocado Fruit Condition
by Tianyang Lu, Adam D. Fletcher, Richard John Colgan and Michael D. O’Toole
Sensors 2025, 25(13), 4195; https://doi.org/10.3390/s25134195 - 5 Jul 2025
Viewed by 335
Abstract
This study demonstrates that the ripeness of avocado fruits can be analyzed using frequency-dependent electrical conductivity and permittivity through a non-invasive Magnetic Induction Spectroscopy (MIS) method. Utilizing an MIS system for conductivity and permittivity measurements of a large sample set ( [...] Read more.
This study demonstrates that the ripeness of avocado fruits can be analyzed using frequency-dependent electrical conductivity and permittivity through a non-invasive Magnetic Induction Spectroscopy (MIS) method. Utilizing an MIS system for conductivity and permittivity measurements of a large sample set (N=60) of avocado fruits across multiple frequencies from 100 kHz to 3 MHz enables clear observation of their dispersion behavior and the evolution of their spectra over ripening time in a completely non-contact manner. For the entire sample batch, the conductivity spectrum exhibits a general upward shift and spectral flattening over ripening time. To further quantify these features, normalized gradient analysis and equivalent circuit modeling were employed, and statistical analysis confirmed the correlations between electrical parameters and ripening stages. The trend characteristics of the normalized gradient parameter Py provide a basis for defining the three ripening stages within the 22-day period: early pre-ripe stage (0–5 days), ripe stage (5–15 days), and overripe stage (after 15 days). The equivalent circuit model, which is both physically interpretable and fitted to experimental data, revealed that the ripening process of avocado fruits is characterized by a weakening of capacitive structures and an increase in extracellular solution conductivity, suggesting changes in cellular integrity and extracellular composition, respectively. The results also highlight significant inter-sample variability, which is inherent to biological samples. To further investigate individual conductivity variation trends, Gaussian Mixture Model (GMM) clustering and Principal Component Analysis (PCA) was conducted for exploratory sample classification and visualization. Through this approach, the sample set was classified into three categories, each corresponding to distinct conductivity variation patterns. Full article
(This article belongs to the Special Issue Application of Sensors Technologies in Agricultural Engineering)
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15 pages, 3135 KiB  
Article
Resonance Circuit Design Eliminating RX-Side Series Capacitor in LCC-LCC WPT Systems Using an RX Shield Coil
by Yujun Shin, Jaewon Rhee and Seongho Woo
Electronics 2025, 14(13), 2686; https://doi.org/10.3390/electronics14132686 - 2 Jul 2025
Viewed by 216
Abstract
This paper presents a new resonance circuit design method for LCC-LCC wireless power transfer (WPT) systems that incorporate reactive shielding (SH) coils on the receiver (RX) side to suppress the electromagnetic field (EMF). While reactive SH coils are known to reduce leakage magnetic [...] Read more.
This paper presents a new resonance circuit design method for LCC-LCC wireless power transfer (WPT) systems that incorporate reactive shielding (SH) coils on the receiver (RX) side to suppress the electromagnetic field (EMF). While reactive SH coils are known to reduce leakage magnetic fields, they alter the equivalent inductance of the system, thereby disrupting resonance conditions. To address this, we derive the changes in the equivalent inductance caused by SH coils and propose a method to re-select the series capacitor on both the RX and TX sides. Furthermore, we investigate the adjustment of the required input voltage to maintain output power with the SH coils. The proposed methodology eliminates the need for a series capacitor on the RX side, simplifies the network, and reduces the magnetic leakage field by up to 55.6%, as verified by the simulation and measurement results. This study provides a new pathway toward compact, EMF-conscious and LCC-based WPT systems. Full article
(This article belongs to the Special Issue Wireless Power Transfer Systems and Applications)
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15 pages, 4864 KiB  
Article
The Systematic Design of Voice Coil Motor Structures for Rapid Zoom Optical Lens
by Junqiang Gong, Dameng Liu and Jianbin Luo
Actuators 2025, 14(7), 332; https://doi.org/10.3390/act14070332 - 2 Jul 2025
Viewed by 271
Abstract
In order to solve the zoom delay issue for high-magnification zoom optical systems, a voice coil motor (VCM) is used to achieve rapid zooming. In this paper, the structural design of VCMs is systematically analyzed through magnetic field numerical computations. Firstly, finite element [...] Read more.
In order to solve the zoom delay issue for high-magnification zoom optical systems, a voice coil motor (VCM) is used to achieve rapid zooming. In this paper, the structural design of VCMs is systematically analyzed through magnetic field numerical computations. Firstly, finite element method (FEM) is used to analyze magnetic field of single magnets, and simulations correspond to experimental results. Both FEM and equivalent magnetic charge (EMC) results confirm that increasing magnet thickness while reducing its lateral dimensions will contribute to magnetic enhancement. Furthermore, the influence of structural parameters VCM is analyzed, validating the yoke’s critical role in suppressing edge effects and optimizing magnetic circuit efficiency, and optimal yoke thickness and magnet width range are determined. Moreover, a simple EMC calculation method is proposed for rapid and accurate determination of the magnetic field distribution in the VCM air gap. Optimal structural parameters of VCM are determined for a 40× rapid zoom lens with cost and space limitations. Driving force Fdrive = 5.58 N is about 5 times the demand force Fd = 1.06 N, and the prototype fabrication of the rapid zoom lens is successfully accomplished. Moving group reaches 35.4 mm destination within 0.18 s, and photographs confirm that the rapid zoom system achieves 100-ms-level short/long-focus transition. Rapid zoom lens shows great potential in applications including security surveillance, industrial visual inspection, and intelligent logistics management. Full article
(This article belongs to the Special Issue Actuators in 2025)
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28 pages, 3951 KiB  
Article
An Iterative Error Correction Procedure for Single Sheet Testers Using FEM 3D Model
by Robert Krobot and Martin Dadić
Sensors 2025, 25(12), 3813; https://doi.org/10.3390/s25123813 - 18 Jun 2025
Viewed by 341
Abstract
Determination of single-valued BH curve and power loss curve of electric steels is an important parameter in the design of electrical machines and transformers. This paper proposes a correction procedure for the measurement of anhysteretic BH curve and power losses, based on the [...] Read more.
Determination of single-valued BH curve and power loss curve of electric steels is an important parameter in the design of electrical machines and transformers. This paper proposes a correction procedure for the measurement of anhysteretic BH curve and power losses, based on the finite element model (FEM) and SST apparatus. A 3D finite element model (FEM) of the SST (Single Sheet Tester) was developed with respect to the IEC 60404-3 standard. The measurement results obtained with a standardized SST apparatus are fed to its FEM and used to iteratively correct initial BH and power loss curves, obtained using magnetic equivalent circuits theory. The proposed iterative correction procedure is based on the steepest descent algorithm, while the stopping criteria were based on the difference between simulated and measured global variables (power loss, induced voltage, and primary current). After correction, root mean squared errors were decreased from 1.85 A/m to 42.88 × 10−3 A/m for the BH curve, and from 44.5 × 10−4 W/kg to 7.28 × 10−4 W/kg for the power loss curve. Full article
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20 pages, 2957 KiB  
Article
Magnetic Field Analytical Calculation of No-Load Electromagnetic Performance of Line-Start Explosion-Proof Permanent Magnet Synchronous Motors Considering Saturation Effect
by Jinhui Liu, Yunbo Shi, Yang Zheng and Minghui Wang
Actuators 2025, 14(6), 294; https://doi.org/10.3390/act14060294 - 17 Jun 2025
Viewed by 311
Abstract
This paper proposes an improved analytical model for a line-start explosion-proof magnet synchronous motor that considers the effect of magnetic bridge saturation. Under the condition of maintaining the air-gap magnetic field unchanged, and taking into account the topological structures of embedded magnets, squirrel [...] Read more.
This paper proposes an improved analytical model for a line-start explosion-proof magnet synchronous motor that considers the effect of magnetic bridge saturation. Under the condition of maintaining the air-gap magnetic field unchanged, and taking into account the topological structures of embedded magnets, squirrel cages, and rotor slot openings, a subdomain model partitioning method is systematically investigated. Considering the saturation effect of the magnetic bridge of the rotor, the equivalent magnetic circuit method was utilized to calculate the permeance of the saturated region. It not only facilitates the establishment of subdomain equations and corresponding subdomain boundary conditions, but also ensures the maximum accuracy of the equivalence by maintaining the topology of the rotor. The motor was partitioned into subdomains, and in conjunction with the boundary conditions, the Poisson equation and Laplace equation are solved to obtain the electromagnetic performance of the motor. The accuracy of the analytical model is verified through finite element analysis. The accuracy of the analytical model is verified through finite element analysis (FEA). Compared to the FEA, the improved model maintains high precision while reducing computational time and exhibiting better generality, making it suitable for the initial design and optimization of industrial motors. Full article
(This article belongs to the Section Actuators for Manufacturing Systems)
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24 pages, 6162 KiB  
Article
Thermal Behavior of Plated Electrical Connectors Under High-Power and High-Frequency Excitation
by Yuqi Zhou, Jinchun Gao, Tianmeng Zhang and Jie Lei
Electronics 2025, 14(12), 2353; https://doi.org/10.3390/electronics14122353 - 8 Jun 2025
Viewed by 512
Abstract
The temperature variations of interconnected coaxial connectors in RF circuits are strongly influenced by the contact surface characteristics and the ferromagnetic properties of the electroplated materials. In this study, specially structured N-DIN connectors with either magnetic or non-magnetic plating were designed. A dedicated [...] Read more.
The temperature variations of interconnected coaxial connectors in RF circuits are strongly influenced by the contact surface characteristics and the ferromagnetic properties of the electroplated materials. In this study, specially structured N-DIN connectors with either magnetic or non-magnetic plating were designed. A dedicated high-frequency, high-power RF experimental platform was set up to monitor and measure the temperature and power of the connectors. Finite element analysis (FEA) was employed to simulate the current density and temperature distribution across the samples. Furthermore, an equivalent circuit model of the central conductor was established by integrating electrical contact theory with the magnetic hysteresis effect. Based on the voltage–temperature (V–T) relation and the derived magnetic field–magnetoresistance (H–M) relation, a predictive model for the temperature rise of the central conductor was formulated. Experimental results demonstrated good agreement with simulation predictions, validating the proposed model and highlighting the critical role of plating material properties in high-power RF connectors’ thermal effect. Full article
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23 pages, 7744 KiB  
Article
Optimization and Design of Built-In U-Shaped Permanent Magnet and Salient-Pole Electromagnetic Hybrid Excitation Generator for Vehicles
by Keqi Chen, Shilun Ma, Changwei Li, Yongyi Wu and Jianwei Ma
Symmetry 2025, 17(6), 897; https://doi.org/10.3390/sym17060897 - 6 Jun 2025
Cited by 1 | Viewed by 383
Abstract
In this paper, the concept of symmetry is utilized to optimize the structural parameters and output characteristics of the generator design—that is, the construction and solution of the equivalent magnetic circuit method for the hybrid excitation generator are symmetrical. To address the issues [...] Read more.
In this paper, the concept of symmetry is utilized to optimize the structural parameters and output characteristics of the generator design—that is, the construction and solution of the equivalent magnetic circuit method for the hybrid excitation generator are symmetrical. To address the issues of high excitation loss and low power density in purely electrically excited generators, as well as the difficulty in adjusting the magnetic field in purely permanent magnet generators, a new topology for a built-in permanent magnet and salient-pole electromagnetic hybrid excitation generator is proposed. Firstly, an equivalent magnetic circuit model of the generator is established. Secondly, expressions are derived to describe the relationships between the dimensions of the salient-pole rotor and the permanent magnets and the generator’s no-load induced electromotive force, cogging torque, and air gap flux density. These expressions are then used to analyze the structural parameters that influence the generator’s performance. Thirdly, optimization targets are selected through sensitivity analysis, with the no-load induced electromotive force, cogging torque, and air gap flux density serving as the optimization objectives. A multi-objective genetic algorithm is employed to optimize these parameters and determine the optimal structural matching parameters for the generator. As a result, the optimized no-load induced electromotive force increased from 18.96 V to 20.14 V, representing a 6.22% improvement; the cogging torque decreased from 177.08 mN·m to 90.52 mN·m, a 48.88% reduction; the air gap flux density increased from 0.789 T to 0.829 T, a 5.07% improvement; and the air gap flux density waveform distortion rate decreased from 6.22% to 2.38%, a 39.3% reduction. Finally, a prototype is fabricated and experimentally tested, validating the accuracy of the simulation analysis, the feasibility of the optimization method, and the rationality of the generator design. Therefore, the proposed topology and optimization method can effectively enhance the output performance of the generator, providing a valuable theoretical reference for the design of hybrid excitation generators for vehicles. Full article
(This article belongs to the Section Engineering and Materials)
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14 pages, 12187 KiB  
Article
Magnetic Field Simulation and Torque-Speed Performance of a Single-Phase Squirrel-Cage Induction Motor: An FEM and Experimental Approach
by Jhonny Barzola and Jonathan Chandi
Machines 2025, 13(6), 492; https://doi.org/10.3390/machines13060492 - 5 Jun 2025
Viewed by 517
Abstract
This study presents a detailed investigation of the torque-speed characteristics of a WEG single-phase squirrel-cage induction motor (SPSCIM) of (1/2 hp), 110/220 V at 60 Hz. The primary objective was to derive the motor’s equivalent circuit and validate its performance curves through finite [...] Read more.
This study presents a detailed investigation of the torque-speed characteristics of a WEG single-phase squirrel-cage induction motor (SPSCIM) of (1/2 hp), 110/220 V at 60 Hz. The primary objective was to derive the motor’s equivalent circuit and validate its performance curves through finite element analysis (FEA), simulation using MATLAB®/Simulink®, and experimental testing. Finite element simulations were conducted using the software FEMM (Finite Element Method Magnetics) to model the magnetic flux distribution within the motor’s stator and rotor. These simulations, based on the motor’s dimensions and nameplate data, provided essential insights into the electromagnetic behavior, including flux density and saturation effects, which are crucial for accurate torque-speed curve predictions. For experimental validation, tests were performed under open-circuit and locked-rotor conditions through a universal machine as a load emulator. The torque-speed characteristics were determined using the Suhr method and the classical approach, with the resulting curves compared to experimental measurements. Voltage and current were measured using AC PZEM-004T and DC PZEM-017 meters, while rotor speed was monitored with a Hall effect sensor (A3144). The results revealed strong agreement between the FEM simulations, Surh method, and experimental data, demonstrating the reliability and accuracy of the combined simulation and analytical methods for modeling the motor’s performance. The estimations using classical and Suhr methods, Simulink simulations, and FEMM yielded low error percentages, mostly below 2%. However, in the FEMM simulation, rotor resistance showed a higher error of around 20% due to unavailable data on the exact number of windings turns, a modifiable parameter that can be corrected through further adjustments in the simulation. The torque-speed curves obtained at different voltage levels showed an excellent correlation, confirming the effectiveness of the proposed approach in characterizing the motor’s operational behavior. Full article
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17 pages, 6604 KiB  
Article
Research on Torque Modeling of the Reluctance Spherical Motor Based on Magnetic Equivalent Circuit Method
by Lufeng Ju, Honglei Liu, Guoli Li, Qunjing Wang and Kangjian Zha
Energies 2025, 18(11), 2882; https://doi.org/10.3390/en18112882 - 30 May 2025
Viewed by 302
Abstract
Torque modeling is an important research aspect of multi-degree of freedom (multi-DOF) spherical motors, and it is the key to realizing the accurate control of multi-DOF spherical motors. In this paper, a torque modeling method of the reluctance spherical motor (RSPM) based on [...] Read more.
Torque modeling is an important research aspect of multi-degree of freedom (multi-DOF) spherical motors, and it is the key to realizing the accurate control of multi-DOF spherical motors. In this paper, a torque modeling method of the reluctance spherical motor (RSPM) based on the magnetic equivalent circuit (MEC) method is proposed. Firstly, the structure of the RSPM is introduced, and the MEC topology of the RSPM is obtained. The calculation formulas of the reluctances in this topology are given. Then the magnetic flux of the RSPM is solved by the mesh analysis method, and the torque is calculated based on the magnetic field energy storage. Finally, the calculated torque is verified by the finite element method (FEM). The verification results show that the torque modeling of the RSPM based on the MEC method is correct, which consumes less memory and time than the three-dimensional finite element method. Full article
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18 pages, 4153 KiB  
Article
Analysis of Electromagnetic Characteristics of Outer Rotor Type BLDC Motor Based on Analytical Method and Optimal Design Using NSGA-II
by Tae-Seong Kim, Jun-Won Yang, Kyung-Hun Shin, Gang-Hyeon Jang, Cheol Han and Jang-Young Choi
Machines 2025, 13(6), 440; https://doi.org/10.3390/machines13060440 - 22 May 2025
Viewed by 497
Abstract
This study investigates the electromagnetic analysis and optimal design of outer rotor type brushless DC (BLDC) motors for fan filter applications. The primary objective is to develop a method that integrates three-dimensional (3D) structural effects with efficient two-dimensional (2D) equivalent analysis. This study [...] Read more.
This study investigates the electromagnetic analysis and optimal design of outer rotor type brushless DC (BLDC) motors for fan filter applications. The primary objective is to develop a method that integrates three-dimensional (3D) structural effects with efficient two-dimensional (2D) equivalent analysis. This study proposes a 2D equivalent analysis method that addresses the unique features of outer rotor type BLDC motors, particularly the permanent magnet (PM) overhang structure. This approach transforms the operating point on the B–H curve to facilitate accurate modeling in a 2D framework, overcoming traditional analysis limitations. An analytical method using spatial harmonics is introduced to derive essential electromagnetic quantities, namely flux linkage and back electromotive force (EMF). The method compensates for slot effects using the Carter coefficient, ensuring precise evaluation of circuit parameters and electromagnetic losses. To optimize motor performance, a multi-objective optimization technique is implemented using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), aiming to maximize both efficiency and power density. The research validates the proposed analytical approach against the finite element analysis method (FEM) results to confirm its accuracy. Full article
(This article belongs to the Special Issue Recent Developments in Machine Design, Automation and Robotics)
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22 pages, 1739 KiB  
Article
Design of a Lorentz Force Magnetic Bearing Group Steering Law Based on an Adaptive Weighted Pseudo-Inverse Law
by Chenyu Wang, Lei Li, Weijie Wang, Yanbin Zhao, Baiqi Li and Yuan Ren
Sensors 2025, 25(10), 3242; https://doi.org/10.3390/s25103242 - 21 May 2025
Viewed by 479
Abstract
Aiming at the high-precision torque output and saturation singularity avoidance problems in Lorentz force magnetic bearing (LFMB) swarms for magnetic levitation spacecraft, this study designs a manipulation law based on an adaptive weighted pseudo-inverse law. The system monitors each magnetic bearing’s working state [...] Read more.
Aiming at the high-precision torque output and saturation singularity avoidance problems in Lorentz force magnetic bearing (LFMB) swarms for magnetic levitation spacecraft, this study designs a manipulation law based on an adaptive weighted pseudo-inverse law. The system monitors each magnetic bearing’s working state in real time using high-precision position and current sensors. As the key input for the adaptive weighted pseudo-inverse control law, the sensor data’s measurement accuracy directly determines torque distribution effectiveness and attitude control precision. First, considering electromagnetic back-EMF effects, individual LFMB dynamics are modeled via the equivalent magnetic circuit method, with working principles elucidated. Subsequently, saturation coefficients for LFMB swarms are designed. Incorporating spacecraft maneuvering requirements, a genetic optimization algorithm establishes the optimal mounting configuration under task constraints. Considering the LFMB swarm configuration characteristics, this study proposes an adaptive weighted pseudo-inverse maneuvering law tailored to operational constraints. By designing an adaptive weighting matrix, the maneuvering law adjusts each LFMB’s torque output in real time, reducing residual saturation effects on attitude control speed and accuracy. Simulation results demonstrate that the proposed mounting configuration and adaptive weighted pseudo-inverse maneuvering law effectively mitigate saturation singularity’s impact on attitude control accuracy while reducing total energy consumption by 22%, validating the method’s effectiveness and superiority. Full article
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