Analysis on the Axial Magnetic Field of Multi-layer Finite Solenoid Based on the Equivalent Current Density Model
LI Zesong1,HUANG Feili1,WANG Yimin1,YU Shancheng1,JIN Bo2
1. Ningbo Institute of Measurement and Testing,Ningbo, Zhejiang 315048, China
2. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang 310027, China
Abstract：In order to resolve the calibrating problem of axial Hall magnetic probe with short rob, a portable finite solenoid was proposed as the reference magnetic field generator. The axial magnetic filed was calculated to obtain its distribution based on the Biot-Savart law and superposition principle of magnetic field, by establishing the solenoid model in a cylindrical coordinate system. In addition, a finite element model (FEM) was established for the multi-layer finite solenoid to analyze its spatial magnetic filed with given exciting current. A solenoid prototype with 100mT central magnetic intensity was designed according to above theoretical analysis. The data from the ECD model, FEM and prototype testing were compared, and the results show that at the solenoid center the deviation between theoretical calculation and FEM is less than 0.1%, and its less than 0.8% between theoretical calculation and prototype testing. Its demonstrated that the ECD model is effective to analyze solenoid axial magnetic field. This method is suggested to be applied in designing and optimizing parameters of a finite solenoid more efficiently and accurately.
李泽松,黄腓力,王一民,余善成,金波. 基于等效电流密度模型的多层有限长螺线管轴线磁场分析[J]. 计量学报, 2024, 45(9): 1378-1383.
LI Zesong,HUANG Feili,WANG Yimin,YU Shancheng,JIN Bo. Analysis on the Axial Magnetic Field of Multi-layer Finite Solenoid Based on the Equivalent Current Density Model. Acta Metrologica Sinica, 2024, 45(9): 1378-1383.
JIANG Q, ZHOU X Y, CHIN J Y, et al. Design and realization of a two-dimensional spatial magnetic field mapping apparatus to measure magnetic fields of metamaterials［J］. Journal of Applied Physics, 2011, 110(2): 024903
RENALLA D P, SPASIC S, UGHINI R, et al. Accurate 3-axis measurement of inhomogenous magnetic fields［J］. TM-technisches Messen, 2019, 86(10): 599-608.
［3］
YANG Z Y, SONG J C, CAI W, et al. Analysis of the influence of a solenoid magnetic field in the azimuth transmission system［J］. Scientific Reports, 2021, 11(1): 16242.
GUAN Z C, SU H F, JIA Z D. Analysis on magnetic field Distribution generated by axisymmetric hollow coils systems ［J］. High Voltage Engineering, 2009, 35(11): 2735-2740.
CAO B Z, CUI C, QIAO L. Two new methods for accurately solving magnetic field distribution around infinite solenoid and their simulation verification ［J］. Experimental Technology and Management, 2021, 38(4): 141-145, 149.
ZHANG M R, GUO X F, REN W J, et al. Simulation and optimization of solenoid magnetic system in magnetic separation column ［J］. Metal Mine, 2021, 544(10): 162-166.
BEHTOUEI M, FAILLACE L, SPATARO B, et al. A novel exact analytical expression for the magnetic field of a solenoid［J］. Waves in Random and Complex Media, 2022, 32(4): 1977-1991.
ZHANG M X, LIU Z Y. The magnetic field distribution of electrified solenoid ［J］. Journal of Liaoning University, 2021, 48(4): 359-364.
XU Y, CAO Y, CHEN G Y. et al. Calibration of 1mT~2. 5T Magnetometers ［J］. Acta Metrogica Sinica, 2019, 40(6A): 84-88.
DING Y, DONG Q L, ZHAO W X, et al. Research on magnetic uniformity performance of two kinds of saddle coils for magnetic shielding ［J］. Acta Metrogica Sinica, 2016, 37(6): 638-643.
［12］
GRANUM P, MADSEN M L, McKENNA J T K, et al. Efficient calculations of magnetic fields of solenoids for simulations［J］. Nuclear Inst. and Methods in Physics Research, A, 2022, 1034: 166706.
［13］
ZUO F L. Axial component of the magnetic field produced by a straight solenoid: Application of the solid angle concept［J］. American Journal of Physics, 2019, 87(6): 449-451
［15］
LIN Q G. An approach to the magnetic field of a finite solenoid with a circular cross-section ［J］. European Journal of Physics, 2021, 42(3): 035206.
HE X R, RONG C C, LIU M H. Optimization design of Multi-coil structure parameters based on wireless power transfer system ［J］. Transactions of China Electrotechnical Society, 2021, 36(S2): 404-411.
LI X, ZHANG W. The establishment of magneometer calibration device ［J］. Electrical Measurement & Instrumentation, 2012, 49(10A): 33-35.
［18］
HUANG L, LEE S. Study on Magnetic field mapping method in the center volume of the air-core solenoid ［J］. IEEE Transaction Applied Superconductivity, 2016, 26(4): 4900104.
PENG L, YANG Z H, HU Q. Finite element computation of 2-D magnetic field of solenoid with current ［J］. High Power Laser and Particle Bems, 2011, 23(8): 2151-2156.
2024, Vol. 45 
