This paper presents the analytic analysis, and proof-of-principle prototyping of a new type of magnetic spring with preload and a linear stroke length. An analytic based magnetic charge modeling approach is utilized to investigate the magnetic spring's energy density, stiffness characteristics and linearity. It is shown that whilst the proposed magnetic spring has a lower mass and energy density than a mechanical spring, the magnetic spring offers several unique characteristics, such as contact-free operation, inherent preload as well as over-force failure protection. In addition, the operating principle of the presented magnetic spring can be extended to realize both positive and negative variable stiffness adjustment characteristics.
1. Hol, S. A. J., Design and optimization of a magnetic gravity compensator, Ph.D. Dissertation, Eindhoven University of Technology, 2004.
2. Patt, P. J., M. Kisco, and F. R. Stolfi, Linear magnetic spring and spring/motor combination, Patent 5,017,819, 1989.
3. Robertson, W., B. Cazzolato, and A. Zander, "A multipole array magnetic spring," IEEE Transactions on Magnetics, Vol. 41, No. 10, 3826-3828, 2005. doi:10.1109/TMAG.2005.854981
4. Robertson, W., Modelling and design of magnetic levitation systems for vibration isolation, Thesis, 2013.
5. Wu, W., X. Chen, and Y. Shan, "Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness," Journal of Sound and Vibration, Vol. 333, No. 13, 2958-2970, Jun. 23, 2014. doi:10.1016/j.jsv.2014.02.009
6. Casteren, D. T. E. H. V., J. J. H. Paulides, J. L. G. Janssen, and E. A. Lomonova, "Analytical force, stiffness, and resonance frequency calculations of a magnetic vibration isolator for a microbalance," IEEE Transactions on Industry Applications, Vol. 51, No. 1, 204-210, 2015. doi:10.1109/TIA.2014.2328780
7. Zhang, H., B. Kou, Y. Jin, and H. Zhang, "Modeling and analysis of a new cylindrical magnetic levitation gravity compensator with low stiffness for the 6-DOF fine stage," IEEE Transactions on Industrial Electronics, Vol. 62, No. 6, 3629-3639, 2015.
8. Olaru, R., A. Arcire, C. Petrescu, M. M. Mihai, and B. Gırtan, "A novel vibration actuator based on active magnetic spring," Sensors and Actuators A: Physical, Vol. 264, 11-17, Sep. 01, 2017.
9. Paden, B. E., C. Chen, and O. J. Fiske, Magnetic spring and actuators with multiple equilibrium position, Patent 7,265,470 B1, 2009.
10. Janssen, J., Extended analytical charge modeling for permanent-magnet based devices: Practical application to the interactions in a vibration isolation system, Ph.D. Dissertation, Eindhoven University of Technology, 2011.
11. Janssen, J. L. G., J. J. H. Paulides, E. A. Lomonova, B. Delinchant, and J. P. Yonnet, "Design study on a magnetic gravity compensator with unequal magnet arrays," Mechatronics, Vol. 23, No. 2, 197-203, Mar. 1, 2013. doi:10.1016/j.mechatronics.2012.08.003
12. Zhou, Y., B. Kou, L. Wang, and F. Xing, "Modeling and analysis of a maglev vibration isolation unit using rectangle Halbach permanent magnet array," 2014 17th International Conference on Electrical Machines and Systems (ICEMS), 1711-1714, Oct. 22–25, 2014.
13. Zhou, Y., B. Kou, P. Liu, H. Zhang, and B. Cazzolato, "Force characteristic analysis of a magnetic gravity compensator with annular magnet array for magnetic levitation positioning system," AIP Advances, Vol. 8, 2018.
14. Janssen, J. L. G., J. J. H. Paulides, and E. A. Lomonova, "Study of magnetic gravity compensator topologies using an abstraction in the analytical interaction equations," Progress In Electromagnetics Research, Vol. 128, 75-90, 2012. doi:10.2528/PIER11101408
15. Zhang, Q., Y. Wang, and E. S. Kim, "Electromagnetic energy harvester with flexible coils and magnetic spring for 1–10 Hz resonance," Journal of Microelectromechanical Systems, Vol. 24, No. 4, 1193-1206, 2015. doi:10.1109/JMEMS.2015.2393911
16. Tan, Y., Y. Dong, and X. Wang, "Review of MEMS electromagnetic vibration energy harvester," Journal of Microelectromechanical Systems, Vol. 26, No. 1, 1-16, 2017. doi:10.1109/JMEMS.2016.2611677
17. Gırtan, N. and R. Olaru, "Improving the performance of a vibration electromagnetic actuator based on active magnetic springs," 2018 International Conference and Exposition on Electrical And Power Engineering (EPE), 284-289, Oct. 18–19, 2018.
18. Woodward, M. A. and M. Sitti, "Universal custom complex magnetic spring design methodology," IEEE Transactions on Magnetics, Vol. 54, No. 1, 1-13, 2018. doi:10.1109/TMAG.2017.2759099
19. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Halbach structures for permanent magnets bearings," Progress In Electromagnetics Research M, Vol. 14, 263-277, 2010. doi:10.2528/PIERM10100401
20. Puccio, F. D., R. Bassani, E. Ciulli, A. Musolino, and R. Rizzo, "Permanent magnet bearings: Analysis of plane and axisymmetric V-shaped element design," Progress In Electromagnetics Research M, Vol. 26, 205-223, 2012. doi:10.2528/PIERM12091406
21. Jungmayr, G., E. Marth, W. Amrhein, H. Berroth, and F. Jeske, "Analytical stiffness calculation for permanent magnetic bearings with soft magnetic materials," IEEE Transactions on Magnetics, Vol. 50, No. 8, 1-8, 2014. doi:10.1109/TMAG.2014.2310437
22. Safaeian, R. and H. Heydari, "Comprehensive comparison of different structures of passive permanent magnet bearings," IET Electric Power Applications, Vol. 12, No. 2, 179-187, 2018. doi:10.1049/iet-epa.2017.0308
23. Furlani, E. P., "Formulas for the force and torque of axial couplings," IEEE Transactions on Magnetics, Vol. 29, No. 5, 2295-2301, 1993. doi:10.1109/20.231636
24. Rakotoarison, H. L., J. Yonnet, and B. Delinchant, "Using coulombian approach for modeling scalar potential and magnetic field of a permanent magnet with radial polarization," IEEE Transactions on Magnetics, Vol. 43, No. 4, 1261-1264, 2007. doi:10.1109/TMAG.2007.892316
25. Jefimenko, O. D., Electricity and Magnetism, Meredith Publishing Co., New York, 1966.
26. Furlani, E. P., Permanent Magnet and Electromechanical Devices Materials, Analysis, and Applications, Academic Press, San Diego, 2001.
27. Rawlings, J. O., S. G. Pantula, and D. A. Dickey, Applied Regression Analysis: A Research Tool, 2nd Ed., Springer, 1998. doi:10.1007/b98890
28. Raymond, round wire compression springs, part # C1351-250-3000-S, https://www.asraymond.com/round-wire-compression-springs/C13512503000S, (accessed Dec. 22, 2020).
29. Raymond, round wire compression springs, part # C1218-105-1000-S, https://www.asraymond.com/round-wire-compression-springs/C12181051000S, (accessed Dec. 20, 2020.