Design and analysis of superconducting magnets of a new mixed Maglev model *

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1 716 Fang et al. / J Zhejiang Univ SCI 25 6A(7): Journal of Zhejiang Universit SCIENCE ISSN jus@ju.edu.cn Design and analsis of superconducting magnets of a new mied Maglev model * FANG You-tong ( 方攸同 ) 1, GAO Chong-ang ( 高重阳 ) 2, YAO Ying-ing ( 姚缨英 ) 1 ( 1 School of Electrical Engineering, Zhejiang Universit, Hanghou 3127, China) ( 2 School of Mechanical and Energ Engineering, Zhejiang Universit, Hanghou 3127, China) outong@ju.edu.cn Received Feb. 1, 25; revision accepted Apr. 26, 25 Abstract: A new electromagnetic suspension model using a combination of high temperature superconductors (HTS) and copper conductors is proposed in this paper. A feasibilit stud showed that the magnets of our model can generate the 25 kg vertical suspension force. Three dimensional FEM and Design Sensitivit Analsis using the levitation gap length and cross sectional dimensions of the HTS magnets as design parameters were conducted to obtain the optimal shape of the cross section and the configuration of the HTS magnet. It was found that the gap length when optimied HTS magnet was used was much larger than that when copper conductor magnet was used, while the HTS coil volume was minimum, and the perpendicular field along the outer surface of the HTS coil was less than.12 T. Ke words: HTS, Maglev, Magnet, FEM doi:1.1631/jus.25.a716 Document code: A CLC number: U266 INTRODUCTION An electromagnetic suspension transportation sstem (EMS-MAGLEV) with cruising speed up to 43 km/h has been set into commercial operation in Shanghai, China since the end of 22. This shows that research and development of EMS-MAGLEV technologies have alread reached mature stage. The magnets used in the above sstem depicted in Fig.1 were made of copper conductors (Zhou and Siniscalchi, 23), and its suspending gap is so small that qualit requirements for track manufacturing and maintenance are ver high. These disadvantages make it necessar to develop new designs of the magnet. Wang et al.(22) achieved remarkable progress in high-t c super-conducting applications in transportation engineering. The high current densit and * Project (No ) supported b the National Natural Science Foundation of China no loss properties of super-conducting magnet allow larger levitation gap. Manufacturing cost and maintenance costs are lower for the same transportation capabilit. Various eperimental and theoretical studies have been conducted for superconducting magnet, and a growing number of eperts are tring to produce it b various approaches. Some optimal designs of high temperature superconductors (HTS) magnets in SMES and MRI were presented previousl in (Noguchi et al., 22; Jo et al., 22). Common features of these designs include coreless magnets, arbitrar cross sectional shapes of HTS magnets, minimum volume of consumed HTS tape, and the anisotropic characteristic of HTS tape. To take the advantage of the HTS concept, a new EMS-MAGLEV model with mied HTS and copper conductor is proposed in this paper, as shown in Fig.2. With normal iron core, HTS coils fabricated b using HTS Bi-2223 for levitation and copper conductor coils for controller were selected in the design. To assess the efficienc, a 3D analsis code based on

2 Fang et al. / J Zhejiang Univ SCI 25 6A(7): FEM (finite element method) of reduced magnetic vector potential with Biot-Savart s law was developed. Using our approach, satisfactor solutions, as shown in the computation results, could be obtained with lower computational efforts. In addition, our Design Sensitivit Analsis ielded the optimied superconductive coil with anisotropic characteristic (J c -B c -T c curve), larger gap, and smaller volume. punched in it and three-phase stator windings embedded in it is simplified as a laminated flat plate. The region containing half pole and half window in terms of the periodicit, as shown in Fig.4 where is copper coil and is superconducting coil, are chosen to be the 3D region for finite-element analsis. Carriage Elevated guidewa Long-stator Levitation magnet Bearing Fig.1 Suspensive and propulsive magnets in Shanghai EMS-MAGLEV commercial line Control coil Superconducting coil Iron core Fig.3 Structure of Maglev sstem magnet Copper conducting coil magnet; Superconducting coil magnet Fig.2 Hbrid EMS-MAGLEV model In our model, because the levitating force is mainl provided b the HTS magnet, the electrical power for the same levitation will be much less than that of other designs. On the other hand, in contrast to the full superconducting model (Zhang et al., 24), the manufacturing of the HTS magnets in our model is much easier due to lower current frequenc in the superconducting coils. However, an AC crogenerator-free HTS magnet suffers from heat load caused b the AC loss. Iron track Iron core Iron track Iron track 3D FINITE ELEMENT ANALYSIS OF EMS-MAGLEV MAGNET Phsical model Two tpical configurations of magnets made of copper conductor coil and HTS coil, are illustrated in Figs.3a and 3b respectivel, assuming that the have the same iron core. The upper iron track with slots Iron core Fig.4 The 3D solving region of the investigated magnet Copper coil magnet; Superconducting coil magnet

3 718 Fang et al. / J Zhejiang Univ SCI 25 6A(7): D magnetic field formulation of reduced magnetic vector potential The three dimensional magnetic field in space is computed b a reduced magnetic vector potential method which is effective and has man advantages (Biro and Preis, 2). Using the method, complicated coil structures do not have to be meshed and the field caused b the coils can be calculated eactl b integration. In nuclear magnetic resonance magnet simulations, the field can be evaluated with ver high accurac because the source fields dominate and are calculated without discretiation error. Total and reduced magnetic vector in the edge elements has been successfull used in the computation of the edd currents occurring in ships (Xu and Simkin, 24). In this work, a 3D nonlinear magnetostatic code was developed using reduced magnetic vector potential as follows. The reduced magnetic vector potential A r is defined b B = A= As + Ar = µ Hs + Ar (1) where the impressed field H s and the impressed vector potential A s describing the effect of the eciting coils can be calculated as follows b Biot-Savart law µ Js As = dv 4 π V r r H 1 ( ) = dv 4 π J r r r r s s V 3 (2) (3) Therefore, it is possible to avoid modelling the comple sources in the finite element meshes. The governing equations for the reduced vector potential are then ( ν A ) ( ν A ) = Ω r r air ( ν A ) ( ν A ) = ( νµ H ) Ω (4) r r s iron Γai ( As n) Nd s = ( As N ) Ω ν ν dν iron (5) where Γ ai is the interface between Ω air and Ω iron, n is the outer normal of Ω iron, N is the weighting function, and ν denotes the reluctivit of the field. Optimal design of superconducting coil With iron core, iron track and average magnetic flu densit in the air gap being the same as those of the copper coil magnet, the superconducting magnet is designed to minimie cost and maimie air gap. In the optimiation process, the air gap length δ and cross sectional dimensions r and of the HTS coil in Fig.5 are chosen as the design parameters. The mathematical problem can be epressed as follows: min F obj = πr(2r +r) sub. to ma{b j }.12 T j=1,2,,m D U p p p i=1,2,,n (6) i i i where the objective function F obj stands for the volume of HTS coils; p D i and U p i are the lower and upper bounds of the design variable, respectivel; p i, r and are the radial thickness and aial half height of the coi; r is the inner radii of the coil; and B j is the perpendicular field of the jth point on the tape flat surface of the HTS coil. (mm) r r Fig.5 The cross sectional dimensions of HTS coil r (mm) Appling the Galerkin method to the differential equations in Eq.(4) and considering the continuit of the interface field ield the following equation: ( ν ν ) Ar N + Ar N dω Ωair + ( ν Ar N + ν Ar N ) dω Ω iron Fig.6 shows the anisotropic characteristics of the I c (35 K)/I c (77 K) curves of Bi-2223 HTS tape. In the design, it is desired that the maimal value of perpendicular fields is kept at less than.12 T. Here perpendicular fields refer to the magnetic flu penetrating through the tape flat surface, in contrast to the parallel field which represents the magnetic flu

4 Fang et al. / J Zhejiang Univ SCI 25 6A(7): parallel to the same surface. The width and thickness of consumed HTS Bi-2223 tape were.25 mm and 4 mm respectivel (including the thickness of insulation laers), and so, 2 mm, r.25 mm. The eciting current in HTS coil is AT. Current I c (35 K)/I c (77 K) Perpendicular field Parallel field B (T) Fig.6 The I c -B c curves of Bi-2223 HTS tape Design Sensitivit Analsis was successfull applied to different kinds of 3D shape optimiation problems (Yao et al., 24a; 24b; 24c). Utiliing the normal FE analsis results, the calculation of the adjoint variable was carried out onl once. With the help of the adjoint variable, design sensitivit of the objective function with respect to the design variables can be obtained easil. The required computation increases ver little as the number of design variables increases. The topologicall constant mesh regeneration method based on the deformation theor of the elastic bod makes it possible to integrate geometric modeling, finite element mesh regenerator and optimiation algorithms into a universal sstem to achieve optimal design automaticall. In this paper, A r method is incorporated into the above optimal design scheme to search for the preferable shape of the HTS coil. was set to 1 mm, and the thickness of upper iron track was set to 13 mm. The copper coil eciting current was AT. The flu linkage distributed on the smmetric surfaces is shown in Fig.7. The average flu densit in the air gap was.696 T for 3D computation and.857 T for the case of 2D. The magnetic field of this kind of magnet should be computed b 3D code due to the prominent fringe effects. Then, with the same iron core, the suspensive magnet in our mied Maglev sstem was designed b using Design Sensitivit Analsis. The optimied dimensions and parameters are listed in Table 1. Fig.8 and Fig.9 illustrate the magnetic field distributions on the smmetrical surfaces during the optimiation, respectivel. Fig.1 and Fig.11 show the perpendicular fields (B ) distributed in a partial region of the HTS coil magnet. It is obvious that the maimum of the perpendicular fields is less than.12 T. CONCLUSION A novel strateg is presented in this paper for analing the static magnetic field of the Maglev ss- Table 1 Parameters of designed HTS coil Item Data Levitation gap length (mm) 14. Inner, outer radii and Height of HTS coil (mm) 83, 138, 16 Rated DC current and turns in HTS coil (A, Turn) 1.5, 88 Pole width Pole length (mm 2 ) Core width Core height (mm 2 ) OPTIMAL DESIGN RESULTS OF THE EMS-MAGLEV MODEL The magnetic field of normal EMS magnet shown in Fig.2 was calculated in both 2D and 3D. The cross sections of its pole and iron core were (13 mm 13 mm) and (65 mm 13 mm), respectivel. The half width and height of iron core window were 5 mm and 85 mm respectivel. The air gap length δ Fig.7 The flu linkage distributed on the smmetric surfaces of the copper coil magnet

5 72 Fang et al. / J Zhejiang Univ SCI 25 6A(7): Fig.8 The flu densit distributed on the smmetric surfaces of the HTS coil magnet =; = Fig.9 The flu linkage distributed on the smmetric surfaces of the HTS coil magnet Fig.1 The contour of flu densit components distributed in the partial region of o surface in Fig.3b. B contour; B contour Fig.11 The contour of flu densit components distributed in the partial region of o surface in Fig.3b. B contour; B contour tems magnet. The 3D magnetic fields were computed b utiliing reduced magnetic vector potential. With the help of Biot-Savart s law, the magnetic field generated b the coils can be easil calculated. Due to its smaller volume and larger suspending gap, the proposed HTS magnet designed for the mied Maglev sstem is preferable to that of the EMS-MAGLEV model.

6 Fang et al. / J Zhejiang Univ SCI 25 6A(7): ACKNOWLEDGEMENT The authors would like to thank Prof. Li-Sheng Wang from National Taiwan Universit for his ver helpful comments. References Biro, O., Preis, K., 2. An edge finite element edd current formulation using a reduced magnetic and a current vector potential. IEEE Trans. on Magnetics, 36(5): Jo, Y., Kwon, Y., Kim, Y., Hong, J., 22. Design of high temperature superconducting magnet. IEEE Trans. Appl. Superconduct., 12(1): Noguchi, S., Yamashita, H., Ishiama, A., 22. An optimal design method for SMES coils using HTS tape. IEEE Trans. Appl. Superconduct., 12(1): Wang, J.S., Wang, S.Y., Ren, Z.Y., Jiang, H., Zhu, M., Wang, X.R., Shen, X.M., Song, H.H., 22. Eperimental Results of High Temperature Superconducting Maglev Vehicle. Superconductors for Practical Applications (SPA 22), Xi an, China. Xu, E., Simkin, J., 24. Total and reduced magnetic vector potentials and electrical scalar potential for edd current calculation. IEEE Trans. on Magnetics, 4(2): Yao, Y., Ru, J.S., Koh, C.S., Xie, D., 24a. Utiliing design sensitivit analsis for 3D optimiation of transformer tank shields considering edd current. COMPEL, 23(2): Yao, Y., Ru, J.S., Koh, C.S., Xie, D., 24b. 3D optimal shape design of magnetic pole in permanent magnet assembl for MRI taking account of edd current. IEEE Trans. on Magnetics, 4(2): Yao, Y., Ru, J.S., Koh, C.S., Xie, D., 24c. A novel mesh regeneration using structural deformation analsis for 3D shape optimiation of electromagnetic devices. IEEE Trans. on Magnetics, 4(2): Zhang, G., Fang, Y., Song, F., Zhu, G., Wang, Z., 24. Optimal design and FEM analsis of the superconducting magnets of EMS-MAGLEV models using Bi-2223 tapes. IEEE Trans. on Appl. Superconduct., 14(2): Zhou, W., Siniscalchi, G., 23. EMS-MAGLEV train took off from Shanghai. Newton Magaine, (2):6-12 (in Chinese). Welcome contributions from all over the world The Journal aims to present the latest development and achievement in scientific research in China and overseas to the world's scientific communit; JZUS is edited b an international board of distinguished foreign and Chinese scientists. And an internationalied standard peer review sstem is an essential tool for this Journal's development; JZUS has been accepted b CA, Ei Compende, SA, AJ, ZM, CABI, BIOSIS (ZR), IM/MEDLINE, CSA (ASF/CE/CIS/Corr/EC/EM/ESPM/MD/MTE/O/SSS*/WR) for abstracting and indeing respectivel, since started in 2; JZUS will feature Science & Engineering subjects in Vol. A, 12 issues/ear, and Life Science & Biotechnolog subjects in Vol. B, 12 issues/ear; JZUS has launched this new column Science Letters and warml welcome scientists all over the world to publish their latest research notes in less than 3 4 pages. And assure them these Letters to be published in about 3 das; JZUS has linked its website ( to CrossRef: (doi:1.1631/jus.25.); MEDLINE: High- Wire: Princeton Universit Librar: