Определение длины плоской катушки в системах беспроводного заряда
DOI:
https://doi.org/10.24160/0013-5380-2026-2-84-89Ключевые слова:
беспроводная передача энергии, спиральная катушка, архимедова спираль, длина проводника, сопротивление, численное моделированиеАннотация
Область использования систем беспроводных зарядов расширяется с каждым годом. Наиболее перспективные сферы применения – зарядка беспилотных летательных аппаратов, автоматизированных нестационарных роботов и электромобилей. Ключевым этапом проектирования таких систем является точный расчёт параметров индуктивных катушек. Анализ литературных источников выявил отсутствие явной аналитической зависимости для определения длины проводника круглой плоской спиральной катушки, хотя данный параметр критически важен для вычисления её активного сопротивления. Целью работы является вывод точной формулы для расчёта длины проводника однослойной катушки в форме архимедовой спирали с равномерным шагом и её упрощения для практического использования. Достоверность выведенной формулы подтверждена сопоставлением с результатами численного моделирования электромагнитного поля в среде COMSOL Multiphysics: расхождение не превысило 0,1 %. Проведён сравнительный анализ с упрощёнными методиками расчёта на основе средней длины витка и модели в виде набора концентрических колец. Установлено, что первая из упрощённых методик обеспечивает погрешность менее 0,1 %, в то время как вторая приводит к отклонениям до 4 %. Полученные зависимости позволяют эффективно оценивать длину и омическое сопротивление катушек на предпроектной стадии без построения детальных трёхмерных моделей.
Библиографические ссылки
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1. Kim H. et al. Coil Design and Measurements of Automotive Magnetic Resonant Wireless Charging System for High-Efficiency and Low Magnetic Field Leakage. – IEEE Transactions on Microwave Theory and Techniques, 2016, vol. 64, No. 2, pp. 383–400, DOI: 10.1109/TMTT.2015.2513394.
2. Guo Y. et al. Rectifier Load Analysis for Electric Vehicle Wireless Charging System. – IEEE Transactions on Industrial Electronics, 2018, vol. 65, No. 9, pp. 6970–6982, DOI: 10.1109/TIE.2018.2793260.
3. Tiemann M. et al. Magnetic and Thermal Coupled Field Analysis of Wireless Charging Systems for Electric Vehicles. – IEEE Transactions on Magnetics, 2019, vol. 55, No. 6, DOI: 10.1109/TMAG.2019.2896780.
4. Nguyen M.Q. et al. Field Distribution Models of Spiral Coil for Misalignment Analysis in Wireless Power Transfer Systems. – IEEE Transactions on Microwave Theory and Techniques, 2014, vol. 62, No. 4, pp. 920–930, DOI: 10.1109/TMTT.2014.2302738.
5. Li Y. et al. Design and Optimization of Coupling Coils for Bidirectional Wireless Charging System of Unmanned Aerial Vehicle. – Electronics, 2020, vol. 9, No. 11, DOI: 10.3390/electronics9111964.
6. Hussain I., Woo D.K. Self-Inductance Calculation of the Archimedean Spiral Coil. – Energies, 2021, vol. 15, No. 1, DOI: 10. 3390/en15010253.
7. Chen Q. et al. Winding Loss Analysis of Planar Spiral Coil and Its Structure Optimization Technique in Wireless Power Transfer System. – Scientific Reports, 2022, vol. 12, No. 1, DOI: 10.1038/s41598-022-24006-x.
8. Paese E. et al. Simplified Mathematical Modeling for an Electromagnetic Forming System with Flat Spiral Coil as Actuator. – Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2011, vol. 33, pp. 324–331, DOI: 10.1590/S1678-58782011 000300008.
9. Krishnapriya S., Komaragiri R., Suja K.J. Fabrication, Characterization, and Modelling of a Novel Via-Less Single Metal Level Magnetic Microcoil Sensor for Biosensing Applications. – Sensors and Actuators A: Physical, 2019, vol. 290, pp. 190–197, DOI: 10.1016/j.sna.2019.02.025.
10. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, DOI: 10.7716/aem.v9i1.1346.
11. Ben Fadhel Y. et al. Model-Based Optimization of Spiral Coils for Improving Wireless Power Transfer. – Energies, 2023, vol. 16, No. 19, DOI: 10.3390/en16196886
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13. Jow U.M., Ghovanloo M. Modeling and Optimization of Printed Spiral Coils in Air, Saline, and Muscle Tissue Environments. – IEEE Transactions on Biomedical Circuits and Systems, 2009, vol. 3, No. 5, pp. 339–347, DOI: 10.1109/TBCAS.2009.2025366.
14. Biswal G., Dash S.K. Thermal Analysis of Constant Surface Area Tapered Helical Coils: Insights from Numerical Modelling. – Thermal Science and Engineering Progress, 2024, vol. 54, DOI: 10.1016/j.tsep.2024.102822.
15. Kadyrmjatov Y.R. et al. Application of COMSOL Multiphysics for Modeling Wireless Charging Systems. – 7th International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), 2025, DOI: 10.1109/REEPE63962.2025.10970942
