Skip to main content

Advertisement

SpringerLink
Log in

Numerical Simulations on the Vertical Dynamic Characteristics of High-Temperature Superconducting Bulk

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

High-temperature superconducting (HTS) maglev, owing to its unique self-stability characteristic, has a wide range of application prospect in flywheel energy storage, magnetic levitation bearing, rail transportation, and other fields. As the important foundation of the engineering application, researches on the dynamic characteristics of HTS maglev have attracted more and more attention. As most of existing models adopted the power exponential function to approximately fit the relationship between the force and displacement, which can only qualitatively analyze the dynamic characteristics of HTS maglev, this paper employs the flux flow and creep model to deduce a 2D H formulation of the HTS maglev system to make up for this deficiency. Moreover, related experiments were also carried out to validate the accuracy of this simulation model and comparisons with other previous models have been achieved. The results prove that the simulation model can reduce the calculation time still with a good convergence. Then, an electromagnetic-thermal-force multiphysics coupling model was established to analyze the dynamic characteristics, especially the levitation height drift of an HTS bulk above the permanent magnet guideway. Results indicate that when the superconductor has an initial velocity that causes disturbance at the working position, vibration and drift phenomena will occur, and the vertical levitation drift also grows as the velocity increases. The simulation results also show that resonance will occur if the excitation frequency is close to the HTS maglev system’s resonance frequency, and a strong “beat” phenomenon will occur if the excitation frequency is close to twice the main vibration frequency of the system. Additionally, the HTS maglev system shows good anti-vibration ability on the relatively low-frequency region as well as the high-frequency region, which proves that it can be well applied to the rail transportation field. All results could be supported as references for the design of HTS maglev systems and its future application.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Hull, J.R.: Superconducting bearings [review]. Supercond Sci Technol. 13(2), 1–15 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  2. Werfel, F.N., et al.: Superconductor bearings, flywheels and transportation. Supercond Sci Technol. 25(1), Art. no. 014007 (2012)

    Article  ADS  Google Scholar 

  3. Moon, F.C., Yanoviak, M.M., Ware, R.: Hysteretic levitation forces in superconducting ceramics. Appl Phys Lett. 52(18), 1534–1536 (1988)

    Article  ADS  Google Scholar 

  4. Hull, J.R., Cansiz, A.: Vertical and lateral forces between a permanent magnet and a high-temperature superconductor. J Appl Phys. 86(11), 6396–6404 (1999)

    Article  ADS  Google Scholar 

  5. Hikihara, T., Moon, F.C.: Chaotic levitated motion of a magnet supported by superconductor. Phys Lett A. 191(3), 279–284 (1994)

    Article  ADS  Google Scholar 

  6. Hikihara, T., Fujinami, T., Moon, F.C.: Bifurcation and multifractal vibration in dynamics of a high-Tc superconducting levitation system. Phys Lett A. 231(3), 217–223 (1997)

    Article  ADS  Google Scholar 

  7. Moon, F.C.: Chaotic vibrations of a magnet near a superconductor. Phys Lett A. 132(5), 249–252 (1998)

    Article  ADS  Google Scholar 

  8. Li, J., Zheng, J., Huang, H., Li, Y., Li, H., Deng, Z.: Motion stability of the magnetic levitation and suspension with YBa2Cu3O7-x High-Tc superconducting bulks and NdFeB magnets. J Appl Phys. 122(15), Art. no. 153902 (2017)

    Article  ADS  Google Scholar 

  9. Wang, H., Deng, Z., Ma, S., Sun, R., Li, H., Li, J.: Dynamic Simulation of the HTS Maglev Vehicle-Bridge Coupled System Based on Levitation Force Experiment. IEEE Trans Appl Supercond. 29(5), Art. no. 3601606 (2019)

    Article  Google Scholar 

  10. Deng, Z., Li, J., Wang, H., Li, Y., Zheng, J.: Dynamic simulation of the vehicle/bridge coupled system in high-temperature superconducting maglev. Comput Sci Eng. 21(3), 60–71 (2019)

    Article  Google Scholar 

  11. Li, J., Deng, Z., Xia, C., Gou, Y., Wang, C., Zheng, J.: Subharmonic resonance in magnetic levitation of the high-temperature superconducting bulks YBa2Cu3O7-x under harmonic excitation. IEEE Trans Appl Supercond. 29(4), Art. no. 3600908 (2019)

    Article  Google Scholar 

  12. Morandi, A.: 2D electromagnetic modelling of superconductors. Supercond Sci Technol. 25(10), Art. no. 104003 (2012)

    Article  ADS  Google Scholar 

  13. Lahtinen, V., Lyly, M., Stenvall, A., Tarhasaari, T.: Comparison of three eddy current formulations for superconductor hysteresis loss modelling. Supercond Sci Technol. 25(11), Art. no. 115001 (2012)

    Article  ADS  Google Scholar 

  14. Brambilla, R., Grilli, F., Martini, L.: Development of an edge-element model for AC loss computation of high-temperature superconductors. Supercond Sci Technol. 20(1), 16–24 (2007)

    Article  ADS  Google Scholar 

  15. Hong, Z., Coombs, T.A.: Numerical modelling of AC loss in coated conductors by finite element software using H formulation. J Supercond Nov Magn. 23(8), 1551–1562 (2010)

    Article  Google Scholar 

  16. Zhou, Y.-H., Zhao, X.-F.: Dynamical analysis to the levitated systems of high temperature superconductors with hysteresis. Physica C. 442(1), 55–62 (2006)

    Article  ADS  Google Scholar 

  17. Perini, E., Giunchi, G., Geri, M., Morandi, A.: Experimental and numerical investigation of the levitation force between bulk permanent magnet and MgB2Disk. IEEE Trans Appl Supercond. 19(3), 2124–2128 (2009)

    Article  ADS  Google Scholar 

  18. Morandi, A., Perini, E., Giunchi, G., Fabbri, M.: Numerical analysis and experimental measurements of magnetic bearings based on MgB2 hollow cylinders. IEEE Trans Appl Supercond. 21(3), 1460–1463 (2011)

    Article  ADS  Google Scholar 

  19. Navau, C., Del-Valle, N., Sanchez, A.: Macroscopic modeling of magnetization and levitation of hard type-II superconductors: the critical-state model. IEEE Trans Appl Supercond. 23(1), Art. no. 8201023 (2013)

    Article  ADS  Google Scholar 

  20. Wu, X.-D., Xu, K.-X., Cao, Y., Hu, S.-b., Zuo, P.-x., Li, G.-d.: Modeling of hysteretic behavior of the levitation force between superconductor and permanent magnet. Physica C. 486, 17–22 (2013)

    Article  ADS  Google Scholar 

  21. Azzouza, A., Allag, H., Yonnet, J.P., Tixador, P.: 3-D New Calculation Principle of Levitation Force Between Permanent Magnet and Hard Type-II Superconductor Using Integral Approach. IEEE Trans Magn. 53(11), Art. no. 8109705 (2017)

    Article  Google Scholar 

  22. Bernstein, P., Colson, L., Dupont, L., Noudem, J.: Investigation of the levitation force of field-cooled YBCO and MgB2disks as functions of temperature. Supercond Sci Technol. 30(6), Art. no. 105327 (2017)

    Article  Google Scholar 

  23. Patel, A., Hahn, S., Voccio, J., Baskys, A., Hopkins, S.C., Glowacki, B.A.: Magnetic levitation using a stack of high temperature superconducting tape annuli. Supercond Sci Technol. 30(2), Art. no. 024007 (2017)

    Article  ADS  Google Scholar 

  24. Sass, F., Sotelo, G.G., Junior, R.d.A., Sirois, F.: H-formulation for simulating levitation forces acting on HTS bulks and stacks of 2G coated conductors. Supercond Sci Technol. 28(12), Art. no. 125012 (2015)

    Article  ADS  Google Scholar 

  25. Sass, F., Dias, D.H.N., Sotelo, G.G., de Andrade Junior, R.: Superconducting magnetic bearings with bulks and 2G HTS stacks: comparison between simulations using H and A-V formulations with measurements. Supercond Sci Technol. 31(2), Art. no. 025006 (2018)

    Article  ADS  Google Scholar 

  26. Gou, X.-F., Zheng, X.-J., Zhou, Y.-H.: Drift of levitated/suspended body in high-Tc superconducting levitation systems under vibration—part I: a criterion based on magnetic force-gap relation for gap varying with time. IEEE Trans Appl Supercond. 17(3), 3795–3802 (2007)

    Article  ADS  Google Scholar 

  27. Gou, X.-F., Zheng, X.-J., Zhou, Y.-H.: Drift of levitated/suspended body in high-Tc superconducting levitation systems under vibration—part II: drift velocity for gap varying with time. IEEE Trans Appl Supercond. 17(3), 3803–3808 (2007)

    Article  ADS  Google Scholar 

  28. Wang, L., Deng, Z., Li, Y., Li, H.: Vertical–Lateral Coupling Force Relation of the High-Temperature Superconducting Magnetic Levitation System. IEEE Trans Appl Supercond. 31(1), Art. no. 3600106 (2021)

    Article  Google Scholar 

  29. Quéval, L., Liu, K., Yang, W., Zermeño, V.M.R., Ma, G.: Superconducting magnetic bearings simulation using an H-formulation finite element model. Supercond Sci Technol. 31(8), Art. no. 084001 (2018)

    Article  ADS  Google Scholar 

  30. Quéval, L., et al.: Optimization of the superconducting linear magnetic bearing of a maglev vehicle. IEEE Trans Appl Supercond. 26(3), Art. no. 3601905 (2016)

    Article  Google Scholar 

  31. Yan, Z., et al.: Numerical prediction of levitation properties of HTS bulk in high magnetic fields. IEEE Trans Appl Supercond. 29(5), Art. no. 3602805 (2019)

    Article  Google Scholar 

  32. Yang, W., Queval, L., Ma, G., Ye, C., Li, G., Gong, T.: A 3-D strong-coupled electromagnetic-thermal model for HTS bulk and its uses to study the dynamic characteristics of a linear HTS maglev bearing. IEEE Trans Appl Supercond. 30(6), Art. no. 3602814 (2020)

    Article  Google Scholar 

  33. Ainslie, M., et al.: A new benchmark problem for electromagnetic modelling of superconductors: the high-T c superconducting dynamo. Supercond Sci Technol. 33(10), Art. no. 105009 (2020)

    Article  ADS  Google Scholar 

  34. Ma, S., et al.: Levitation height drifts of HTS bulks under a long-term external disturbance. J Supercond Nov Magn. 32(12), 3803–3810 (2019)

    Article  Google Scholar 

  35. Huang, H., Zheng, J., Liao, H., Hong, Y., Li, H., Deng, Z.: Effect Laws of different factors on levitation characteristics of high-Tc superconducting maglev system with numerical solutions. J Supercond Nov Magn. 32(8), 2351–2358 (2019)

    Article  Google Scholar 

  36. Ma, G.-T., Liu, H.-F., Wang, J.-S., Wang, S.-Y., Li, X.-C.: 3D modeling permanent magnet guideway for high temperature superconducting maglev vehicle application. J Supercond Nov Magn. 22(8), 841–847 (2009)

    Article  Google Scholar 

  37. Ma, G.T., Liu, H., Li, X.T., Zhang, H., Xu, Y.Y.: Numerical simulations of the mutual effect among the superconducting constituents in a levitation system with translational symmetry. J Appl Phys. 115(8), Art. no. 083908 (2014)

    Article  ADS  Google Scholar 

  38. Wang, S., et al.: An update high-temperature superconducting maglev measurement system. IEEE Trans Appl Supercond. 17(2), 2067–2070 (2007)

    Article  ADS  Google Scholar 

  39. Konishi, H., Isono, M., Nasu, H., Hirose, M.: Suppression of rotor fall for radial-type high-temperature superconducting magnetic bearing. Physica C. 392-396, 713–718 (2003)

    Article  ADS  Google Scholar 

  40. Koshizuka, N., et al.: Progress of superconducting bearing technologies for flywheel energy storage systems. Physica C. 386, 444–450 (2003)

    Article  ADS  Google Scholar 

  41. Bræck, S., Shantsev, D.V., Johansen, T.H., Galperin, Y.M.: Superconducting trapped-field magnets: temperature and field distributions during pulsed-field activation. J Appl Phys. 92(10), 6235–6240 (2002)

    Article  ADS  Google Scholar 

  42. Grilli, F., Morandi, A., Silvestri, F.D., Brambilla, R.: Dynamic modeling of levitation of a superconducting bulk by coupled H-magnetic field and arbitrary Lagrangian–Eulerian formulations. Supercond Sci Technol. 31(12), Art. no. 125003 (2018)

    Article  ADS  Google Scholar 

  43. Li, J., Li, H., Zheng, J., Zheng, B., Huang, H., Deng, Z.: Nonlinear vibration behaviors of high-Tc superconducting bulks in an applied permanent magnetic array field. J Appl Phys. 121(24), Art. no. 243901 (2017)

    Article  ADS  Google Scholar 

  44. Wang, B., Zheng, J., Che, T., Zheng, B.T., Si, S.S., Deng, Z.G.: Dynamic response characteristics of high temperature superconducting maglev systems: comparison between Halbach-type and normal permanent magnet guideways. Physica C. 519, 147–152 (2015)

    Article  ADS  Google Scholar 

  45. Huang, C.-G., Xu, B., Zhou, Y.-H.: Dynamic simulations of actual superconducting maglev systems considering thermal and rotational effects. Supercond Sci Technol. 32(4), Art. no. 045002 (2019)

    Article  ADS  Google Scholar 

  46. Deng, Z., et al.: Free vibration of the high temperature superconducting maglev vehicle model. IEEE Trans Appl Supercond. 17(2), 2071–2074 (2007)

    Article  ADS  Google Scholar 

Download references

Funding

This work was partially supported by the National Natural Science Foundation of China (U19A20102), the Science and Technology Partner-ship Program, Ministry of Science and Technology of China (KY201701001), the Sichuan Science and Technology Program (2019YJ0229), the Chengdu International S&T Cooperation Program (2019-GH03-00002-HZ), and the State Key Laboratory of Traction Power at Southwest Jiaotong University (2019TPL-07).

Author information

Authors and Affiliations

  1. State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Ling Chen, Zigang Deng & Jun Zheng

  2. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Ling Chen & Bin Deng

  3. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, Chengdu, 610031, People’s Republic of China

    Zigang Deng

Authors
  1. Ling Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zigang Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jun Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zigang Deng.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, L., Deng, Z., Deng, B. et al. Numerical Simulations on the Vertical Dynamic Characteristics of High-Temperature Superconducting Bulk. J Supercond Nov Magn 34, 683–694 (2021). https://doi.org/10.1007/s10948-020-05780-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-020-05780-z

Keywords

Search

Navigation