volume | PIER Journals

Abstract

This work concerns the study of the reliability of a magnetic levitation system. A numerical calculation method based on the introduction of a random variable on the physical property of the materials constituting the levitation system is proposed. The latter is called intrusive stochastic finite element method (ISFEM), and the randomness of physical properties is taken care of, thus modeling in uncertain medium is feasible. The electromagnetic problem is treated with 2D hypotheses for modeling in an uncertain environment. This method was developed in 1991 and used for sensitivity and reliability analysis in the mechanical field; it is extended to the study of applications in linear elasticity and in electromagnetism. The random variable is of Gaussian type. The assessment of the reliability of the levitation system is discussed. The results obtained are compared with those found by the Latin hyper cube method. The intrusive stochastic finite element model provides very conclusive results in a very short time compared to those obtained by Latin hyper cube modeling.

1. Bancel, F., "Magnetic nodes," Journal of Physics D: Applied Physics, Vol. 32, No. 17, 2155-2161, 1999. Google Scholar

2. Furlani, Edward P., Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications, 1st Ed., Academic Press, New York, 2001.

3. Lemaire, M., "Sensitivity and reliability analysis in an uncertain environment," 5th European Conference on Numerical Methods in Electromagnetism, NUMELEC'06, Lille, 2006.

4. Logesh, K. and Srinivasa Rao Madane, "Improved CLC routing protocol with node classification algorithm for MANET," Applied Mathematics & Information Sciences, Vol. 12, No. 5, 1013-1019, 2018.
doi:10.18576/amis/120514 Google Scholar

5. Al-Qrinawi, Mohammed S., Taher M. El-Agez, Monzir S. Abdel-Latif, and Sofyan A. Taya, "Capacitance-voltage measurements of hetero-layer OLEDs treated by an electric field and thermal annealing," International Journal of Thin Film Science and Technology, Vol. 10, 217-226, 2021. Google Scholar

6. Yonnet, Jean-Paul and Hicham Allag, "Three-dimensional analytical calculation of permanent magnet interactions by magnetic node representation," IEEE Transactions on Magnetics, Vol. 47, No. 8, 2050-2055, 2011.
doi:10.1109/TMAG.2011.2122339 Google Scholar

7. Yonnet, J., "Permanent magnet bearings and couplings," IEEE Transactions on Magnetics, Vol. 17, No. 1, 1169-1173, 1981. Google Scholar

8. Berkache, Azouaou, Jinyi Lee, and Eunho Choe, "Evaluation of cracks on the welding of austenitic stainless steel using experimental and numerical techniques," Applied Sciences, Vol. 11, No. 5, Mar. 2021.
doi:10.3390/app11052182 Google Scholar

9. Berveiller, M., "Stochastic finite element analysis: Intrusive and non-intrusive approaches for reliability analysis," Blaise Pascal-Clermont II University, 2005.

10. Haldar, A. and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design, 1st Ed., Wiley, USA, 1999.

11. Pranesh, Srikara and Debraj Ghosh, "A FETI-DP based parallel hybrid stochastic finite element method for large stochastic systems," Computers and Structures, Vol. 195, 64-73, Jan. 2018.
doi:10.1016/j.compstruc.2017.09.011 Google Scholar

12. Fang, K. T. and C. X. Ma, "Wrap-around L2-discrepancy of random sampling, Latin hypercube and uniform designs," Journal of Complexity, Vol. 17, No. 4, 608-624, Dec. 2001.
doi:10.1006/jcom.2001.0589 Google Scholar

13. Fang, K. T., D. Maringer, Y. Tang, and P. Winker, "Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels," Mathematics of Computation, Vol. 75, No. 254, 859-878, 2006.
doi:10.1090/S0025-5718-05-01806-5 Google Scholar

14. Lyskawinski, Wieslaw, Cezary Jedryczka, Dorota Stachowiak, Piotr Lukaszewicz, and Michel Czarnecki, "Finite element analysis and experimental verification of high reliability synchronous reluctance machine," Eksploatacja i Niezawodnosc-Maintenance and Reliability, Vol. 24, No. 2, 386-393, 2022.
doi:10.17531/ein.2022.2.20 Google Scholar

15. Oudni, Zehor, M. Feliachi, and H. Mohellebi, "Assessment of the probability of failure for EC nondestructive testing based on intrusive spectral stochastic finite element method," Eur. Phys. J. Appl. Phys., Vol. 66, No. 5, 133-137, 2014. Google Scholar

16. Furlani, E. P., "A formula for the levitation force between magnetic disks," IEEE Transactions on Magnetics, Vol. 29, No. 6, 4165-4169, Nov. 1993.
doi:10.1109/20.280867 Google Scholar

17. Furlani, Edward P., Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications, 1st Ed., Academic Press, New York, 2001.

18. Meeker, D. C., "Finite element method magnetics, Version 4.0.1 (03déc2006 Build)," http://femm.foster-miller.net, 2003.

19. Elhadary, Abdelmonsef A., A. El-Zein, M. Talaat, G. El-Aragi, and A. El-Amawy, "Studying the effect of the dielectric barrier discharge non-thermal plasma on colon cancer cell line," International Journal of Thin Film Science and Technology, Vol. 10, 161-168, 2021. Google Scholar

20. Thota, Srinivasarao and Shiv Datt Kumar, "A new reduction algorithm for differential-algebraic systems with power series coefficients," Information Sciences Letters, Vol. 10, No. 1, 59-66, 2021.
doi:10.18576/isl/100108 Google Scholar

21. Marsden, G., "Magnetic levitation kit," http://www.arttec.net/Levitation/Gallery/Levitation_Applications.htm.

22. Kosmas, Konstantinos and Evangelos Hristoforou, "The effect of magnetic anomaly detection technique in eddy current non-destructive testing," International Journal of Applied Electromagnetics and Mechanics, Vol. 25, No. 1-4, 319-324, 2007.
doi:10.3233/JAE-2007-826 Google Scholar

23. Baghli, L., "Magnetic levitation," http://www.baghli.com/dspic_levitation.

24. Baghli, L. and A. Rezzougm, "Magnetic levitation, an object-project approach," Vol. 9, https://doi.org/10.1051/j3ea/2010002, 2010.

25. Baghli, L. and A. Rezzoug, "Actionneurs linéaires, MRVlin et MSlin, un projet pédagogique," CETSIS 2007, Vol. 7, 1638-1963, 2007.

26. Marsden, G., "Levitation flotter objets in servocontrolled magnetic field," Nuts & Volt Magazine, Sep. 2003. Google Scholar

27. Allag, H., J.-P. Yonnet, and M. E. H. Latreche, "Analytical calculation of the torque exerted between two perpendicularly magnetized magnets," Journal of Applied Physics, Vol. 109, No. 7, 07E701-07E701-3, Apr. 2011.
doi:10.1063/1.3535148 Google Scholar

28. Ali, A. Refaie, N. T. M. Eldabe, A. E. H. Abd El Naby, M. Ibrahim, and O. M. Abo-Seida, "EM wave propagation within plasma-filled rectangular waveguide using fractional space and LFD," The European Physical Journal Special Topics, 2023.
doi:10.1140/epjs/s11734-023-00934-1 Google Scholar

29. Abo-Seida, Osama M., Nabil T. M. El-Dabe, A. Refaie Ali, and G. A. Shalaby, "Cherenkov FEL reaction with plasma-filled cylindrical waveguide in fractional D-dimensional space," IEEE Transactions on Plasma Science, Vol. 49, No. 7, 2070-2079, Jul. 2021.
doi:10.1109/TPS.2021.3084904 Google Scholar

30. Da Silva Junior, Claudio Roberto Avila, Andre Teofilo Beck, and Edison da Rosa, "Solution of the stochastic beam bending problem by Galerkin method and the Askey-Wiener scheme," Latin American Journal of Solids and Structures, Vol. 6, No. 1, 51-72, Mar. 2009. Google Scholar

31. Berveiller, Marc, Bruno Sudret, and M. Lemaire, "Comparison of methods for computing the response coefficients in stochastic finite element analysis," Proc. Asranet, Vol. 2, 51-72, 2004. Google Scholar

32. Mahmuda Maya, Mst Umme, Md. Nur Alam, and Ahmed Refaie Ali, "Influence of magnetic field on MHD mixed convection in lid-driven cavity with heated wavy bottom surface," Scientific Reports, Vol. 13, No. 1, 18959, 2023. Google Scholar

33. Carpenter, C. J., "Surface-integral methods of calculating forces on magnetized iron parts," Proceedings of the IEE-Part C: Monographs, Vol. 107, No. 11, 19-28, 1960. Google Scholar

34. Jacques, Ringler, Precis of Probabilities and Statistics for the Use of Reliability, Octares Edition, Toulouse, 1996.

35. Oudni, Zehor, Azouaou Berkache, Hamid Mehaddene, Hassane Mohellebi, and Jinyi Lee, "Comparative study to assess reliability in the presence of two geometric defect shapes for non-destructive testing," Przeglad Elektrotechniczny, Vol. 95, No. 12, 48-52, 2019.
doi:10.15199/48.2019.12.09 Google Scholar

36. Sudret, B., M. Berveiller, and M. Lemaire, Stochastic Finite Elements in Linear Elasticity, Elsevier, 2004.

37. Sudret, B., M. Berveiller, and M. Lemaire, "Stochastic finite elements: New perspectives," 16th French Mechanical Congress, Nice, Sep. 2003.

38. Harisson, A. J., "An optimised 50 Nms momentum wheel utilising magnetic repulsion bearings," Proceedings of ADCS Conference, 389-393, Noordwijk, 1977.

39. Yang, Xiao-Jun, Abdulrahman Ali Alsolami, and Ahmed Refaie Ali, "An even entire function of order one is a special solution for a classical wave equation in one-dimensional space," Thermal Science, Vol. 27, No. 1, 491-495, 2023. Google Scholar

40. Islam, Shariful, Bishnupada Halder, and Ahmed Refaie Ali, "Optical and rogue type soliton solutions of the (2+1) dimensional nonlinear Heisenberg ferromagnetic spin chains equation," Scientific Reports, Vol. 13, No. 1, Jun. 2023.
doi:10.1038/s41598-023-36536-z Google Scholar

41. Kumar, Sachin, Jinde Cao, and Mahmoud Abdel-Aty, "A novel mathematical approach of COVID-19 with non-singular fractional derivative," Chaos Solitons & Fractals, Vol. 139, Elsevier, Oct. 2020.
doi:10.1016/j.chaos.2020.110048 Google Scholar

42. Dutta, Subhrajit and Amir H. Gandomi, "Design of experiments for uncertainty quantification based on polynomial chaos expansion metamodels," Handbook of Probabilistic Models, 2020. Google Scholar

Ms. Zehor Oudni

Dr. Thinhinane Mahmoudi