基于Monte Carlo法和积分法的被动永磁轴承磁力计算
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摘要
以一种半定子环轴向充磁径向永磁轴承为例,建立轴承承载力的数学模型,分别采用数值积分法(四重for循环)和Monte Carlo法进行求解分析。结果表明:2种方法的计算结果吻合,且随着网格数量的增多,for循环方法的计算时间急剧增加,计算结果趋于稳定;Monte Carlo法的计算时间短,计算效率高。针对堆叠型永磁轴承提出了一种快速、方便的轴承承载力计算方法,为被动永磁体轴承的设计提供了理论指导。
A mathematical model is built for load capacity of axially polarized radial permanent magnetic bearings with semi-stator rings, and the numerical integration(quadruple for-loop) method and Monte Carlo method are used respectively for solution and analysis. The results show that the calculation results obtained by two methods are identical. The calculation time of for-loop method increases dramatically with increase of grid number, and the calculation results tend to be stable. The Monte Carlo method is characterized by short calculation time and high calculation efficiency. A fast and convenient calculation method is proposed for load capacity of stacked permanent magnetic bearings, which provides a theoretical guidance for design of passive permanent magnetic bearings.
A mathematical model is built for load capacity of axially polarized radial permanent magnetic bearings with semi-stator rings, and the numerical integration(quadruple for-loop) method and Monte Carlo method are used respectively for solution and analysis. The results show that the calculation results obtained by two methods are identical. The calculation time of for-loop method increases dramatically with increase of grid number, and the calculation results tend to be stable. The Monte Carlo method is characterized by short calculation time and high calculation efficiency. A fast and convenient calculation method is proposed for load capacity of stacked permanent magnetic bearings, which provides a theoretical guidance for design of passive permanent magnetic bearings.
引文
[1] SAFAEIAN R,HEYDARI H.Comprehensive comparison of different structures of passive permanent magnet bearings[J].IET Electric Power Applications,2018,12(2):179-187.
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[11] HIRANI H,SAMANTA P.Hybrid (hydrodynamic+permanent magnetic) journal bearings[J].Proceedings of The Institution of Mechanical Engineers,Part J:J Engineering Tribology,2007,221 (8):881-891.
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[13] 张钢,张坚,张海龙,等.基于等效磁荷法用蒙特卡洛法计算永磁轴承磁力[J].轴承,2013(10):1-4.
[14] LIJESH K P,HIRANI H.Development of analytical equations for design and optimization of axially polarized radial passive magnetic bearing[J].Journal of Tribology,2015,137:011103-1-9.
[15] PADEN B,GROOM N,ANTAKI J F.Design formulas for permanent-magnet bearings[J].Journal of Mechanical Design,Transactions of the ASME,2003,125:734-738.
[2] YONNET J P.Permanent magnet bearings and couplings[J].IEEE Transactions on Magnetics,1981,17(1):1169-1173.
[3] FANG J,LE Y,SUN J,et al.Analysis and design of passive magnetic bearing and damping system for high-speed compressor[J].IEEE Transactions on Magnetics,2012,48(9):2528-2537.
[4] ELKIN R,GUILHERME G S,JANAINA G O,et al.Designing,simulations and experiments of a passive permanent magnet bearing[J].International Journal of Applied Electromagnetics and Mechanics,2016,51:131-149.
[5] MAGNUS H,ABRAHAMSSON J,JESUS J L,et al.Eddy currents in a passive magnetic axial thrust bearing for a flywheel energy storage system[J].International Journal of Applied Electromagnetics and Mechanics,2017,54:389-404.
[6] SIDDAPPA I BL,SADANAND S K,SOUMENDU J.A hybrid (permanent magnet and foil) bearing set for complete passive levitation of high-speed rotors[J].Proceedings of The Institution of Mechanical Engineers,Part C:J Mechanical Engineering Science,2017,231(20):3679-3689.
[7] TAN Q,LI W,LIU B.Investigations on a permanent magnetic-hydrodynamic hybrid journal bearing[J].Tribology International,2002,35(7):443-448.
[8] BEKINAL S I,ANIL T R,JANA S.Analysis of axially magnetized permanent magnet bearing characteristics[J].Progress in Electromagnetics Research B,2012,44:327-343.
[9] SUN J J,WANG C E,LE Y.Research on a novel high stiffness axial passive magnetic bearing for DGMSCMG[J].Journal of Magnetism and Magnetic Materials,2016,412:147-155.
[10] TANG J Q,XIANG B,ZHANG Y B.Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing[J].ISA Transactions,2014,53:1357-1365.
[11] HIRANI H,SAMANTA P.Hybrid (hydrodynamic+permanent magnetic) journal bearings[J].Proceedings of The Institution of Mechanical Engineers,Part J:J Engineering Tribology,2007,221 (8):881-891.
[12] SIDDAPPA I B,SOUMENDU J.Generalized three-dimensional mathematical models for force and stiffness in axially,radially,and perpendicularly magnetized passive magnetic bearings with “n” number of ring pairs[J].Journal of Tribology,2016,138:031105-1-9.
[13] 张钢,张坚,张海龙,等.基于等效磁荷法用蒙特卡洛法计算永磁轴承磁力[J].轴承,2013(10):1-4.
[14] LIJESH K P,HIRANI H.Development of analytical equations for design and optimization of axially polarized radial passive magnetic bearing[J].Journal of Tribology,2015,137:011103-1-9.
[15] PADEN B,GROOM N,ANTAKI J F.Design formulas for permanent-magnet bearings[J].Journal of Mechanical Design,Transactions of the ASME,2003,125:734-738.