Research PaperNo Access

Modeling and Dynamics of Magnetically Repulsive Negative Stiffness Permanent Magnetic Array for Precision Air/Magnetic Composite Vibration Isolation

Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, P. R. China

Key Lab of Ultra-Precision Intelligent Instrumentation, (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, P. R. China

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Junning Cui

Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, P. R. China

Key Lab of Ultra-Precision Intelligent Instrumentation, (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, P. R. China

E-mail Address: cuijunning@hit.edu.cn

Corresponding author.

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Limin Zou

Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, P. R. China

Key Lab of Ultra-Precision Intelligent Instrumentation, (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, P. R. China

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, and

Zhongyi Cheng

Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, P. R. China

Key Lab of Ultra-Precision Intelligent Instrumentation, (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, P. R. China

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https://doi.org/10.1142/S0219455422500316Cited by:9 (Source: Crossref)

Abstract

To reduce the natural frequency of air isolators and realize low or ultra-low frequency air/magnetic composite vibration isolation with large payloads, a magnetically repulsive negative stiffness permanent magnetic array (MRNSPMA) is proposed. Specifically, we utilize cuboidal permanent magnets to form a spatial array that is mechanically repulsive in the horizontal direction and structurally parallel in the vertical direction. The superiority of MRNSPMA in achieving high amplitude negative stiffness is verified. Furthermore, the effects of structural parameters on vibration transmissibility under the base and force excitations are investigated with the introduction of MRNSPMA. The displacement transmissibility, the force transmissibility and the frequency corresponding to the peak transmissibility are significantly reduced, validating the promise of MRNSPMA for improving the isolation performance of cutting-edge scientific experimental systems and facilities.

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References

1. Y. H. Shan, W. J. Wu and X. D. Chen , Design of a miniaturized pneumatic vibration isolator with high-static-low-dynamic stiffness, J. Vib. Acoust. 137(4) (2015) 045001. Crossref, Web of Science, Google Scholar
2. Y. M. Zhao, J. N. Cui, J. C. Zhao, X. Y. Bian and L. M. Zou , Improving low frequency isolation performance of optical platforms using electromagnetic active-negative-stiffness method, Appl. Sci-Basel. 10(20) (2020) 7342. Crossref, Web of Science, Google Scholar
3. L. Wang, J. Z. Li, Y. Y. Yang, J. Wang and J. B. Yuan , Active control of low-frequency vibrations in ultra-precision machining with blended infinite and zero stiffness, Int. J. Mach. Tool. Manuf. 139 (2019) 64–74. Crossref, Web of Science, Google Scholar
4. Y. Bai, Y. M. Liu, Y. F. Lu, P. C. Hu, D. W. Wang, Z. K. Li, J. B. Tan and Z. H. Zhang , Stability improvement for coil position locking of joule balance, Metrologia 54(4) (2017) 461–467. Crossref, Web of Science, Google Scholar
5. R. Courtland , Moore’s law’s next step, 10 nanometers, IEEE Spectrum. 54(1) (2017) 52–53. Crossref, Web of Science, Google Scholar
6. Y. S. Zheng, X. N. Zhang, Y. J. Luo, B. Yan and C. C. Ma , Design and experiment of a high-static-low-dynamic stiffness isolator using a negative stiffness magnetic spring, J. Sound Vibr. 360 (2016) 31–52. Crossref, Web of Science, Google Scholar
7. Y. S. Zheng, Q. P. Li, B. Yan, Y. J. Luo and X. N. Zhang , A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs, J. Sound Vibr. 422 (2018) 390–408. Crossref, Web of Science, Google Scholar
8. Z. H. Zhou, S. H. Chen, D. Xia, J. J. He and P. Zhang , The design of negative stiffness spring for precision vibration isolation using axially magnetized permanent magnet rings, J. Vib. Control. 25(19–20) (2019) 2667–2677. Crossref, Web of Science, Google Scholar
9. J. X. Zhou, K. Wang, D. L. Xu, H. J. Ouyang and Y. L. Li , A six degrees-of-freedom vibration isolation platform supported by a hexapod of quasi-zero-stiffness struts, ASME. J. Vib. Acoust. 139(3) (2017) 034502. Crossref, Web of Science, Google Scholar
10. J. X. Zhou, K. Wang, D. L. Xu, H. J. Ouyang and Y. M. Fu , Vibration isolation in neonatal transport by using a quasi-zero-stiffness isolator, J. Vib. Control. 24(15) (2018) 3278–3291. Crossref, Web of Science, Google Scholar
11. Q. Wang, J. X. Zhou, D. L. Xu and H. J. Ouyang , Design and experimental investigation of ultra-low frequency vibration isolation during neonatal transport, Mech. Syst. Signal Proc. 139 (2020) 106633. Crossref, Web of Science, Google Scholar
12. G. J. Nijsse, Linear motion systems, a modular approach for improved straightness performance, Ph.D. thesis, Delft University of Technology, Netherlands (2001). Google Scholar
13. A. Carrella, M. J. Brennan, T. P. Waters and K. Shin , On the design of a high-static-low-dynamic stiffness isolator using linear mechanical springs and magnets, J. Sound Vibr. 315(3) (2008) 712–720. Crossref, Web of Science, Google Scholar
14. K. H. Shin , On the performance of a single degree-of-freedom high-static-low-dynamic stiffness magnetic vibration isolator, Int. J. Precis. Eng. Manuf. 15(3) (2014) 439–445. Crossref, Web of Science, Google Scholar
15. M. Wang, X. D. Chen and X. Q. Li , An ultra-low frequency two DOFs’ vibration isolator using positive and negative stiffness in parallel, Math. Probl. Eng. 2016 (2016) 1–15. Crossref, Web of Science, Google Scholar
16. X. Shi, S. Y. Zhu and B. F. Spencer , Experimental study on passive negative stiffness damper for cable vibration mitigation, J. Eng. Mech. 143(9) (2017) 04017070. Crossref, Web of Science, Google Scholar
17. X. Shi and S. Y. Zhu , Magnetic negative stiffness dampers, Smart Mater. Struct. 24(7) (2015) 072002. Crossref, Web of Science, Google Scholar
18. W. J. Wu, X. D. Chen and Y. H. Shan , Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness, J. Sound Vibr. 333(13) (2014) 2958–2970. Crossref, Web of Science, Google Scholar
19. J. Z. Shan, Z. G. Shi, N. Gong and W. X. Shi , Performance improvement of base isolation systems by incorporating eddy current damping and magnetic spring under earthquakes, Struct. Control. Health Monit. 27(6) (2020) e2524. Crossref, Web of Science, Google Scholar
20. A. O. Oyelade, Z. W. Wang and G. K. Hu , Dynamics of 1D mass-spring system with a negative stiffness spring realized by magnets, Theoretical and experimental study, J. Theor. App. Mech.-Pol. 7(1) (2017) 17–21. Google Scholar
21. A. O. Oyelade, Y. Chen, R. J. Zhang and G. K. Hu , Analytical and experimental investigation on sound transmission of double thin plates with magnetic negative stiffness, Int. J. Appl. Mech. 10(5) (2018) 1850054. Link, Web of Science, Google Scholar
22. A. O. Oyelade , Experiment study on nonlinear oscillator containing magnetic spring with negative stiffness, Int. J. Nonlin. Mech. 120 (2020) 103396. Crossref, Web of Science, Google Scholar
23. H. Allag and J. P. Yonnet , 3D analytical calculation of the forces exerted between two cuboidal magnets, IEEE Trans. Magn. 20(10) (1984) 1962–1964. Google Scholar
24. J. L. G. Janssen, J. J. H. Paulides, E. A. Lomonova, F. Boeloeni, A. Tounzi and F. Piriou , Analytical calculation of interaction force between orthogonally magnetized permanent magnets, Sens. Lett. 7(3) (2009) 442–445. Crossref, Google Scholar
25. J. L. G. Janssen, J. J. H. Paulides and E. A. Lomonova , Analytical force and stiffness calculations for magnetic bearings and vibration isolation, Comput. Field Models Electromagn. Dev. 34 (2010) 502–511. Google Scholar
26. J. Z. Li, Q. Liu, L. Wang, S. T. Wang and J. Wang , Considering operating point variation in 3D analytical charge model used for design of low-stiffness permanent magnet vibration isolator, IEEE Trans. Ind. Electron. 67(8) (2020) 6732–6741. Crossref, Web of Science, Google Scholar
27. F. D. Di, L. Chen and L. M. Sun , Optimal design of dampers for multi-mode cable vibration control based on genetic algorithm, Int. J. Struct. Stab. Dyn. 21(4) (2021) 2150058. Link, Web of Science, Google Scholar
28. R. Alfattani, M. Yunus, T. Alamro and I. Alnaser , Linkage factors optimization of multi-outputs of compliant mechanism using response surface, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 59–74. Web of Science, Google Scholar
29. D. L. Xu, Q. P. Yu, J. X. Zhou and S. R. Bishop , Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic, J. Sound Vibr. 332(14) (2013) 3377–3389. Crossref, Web of Science, Google Scholar
30. B. Yan, H. Y. Ma, B. Jian, K. Wang and C. Y. Wu , Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets, Nonlinear. Dyn. 97(4) (2019) 2499–2519. Crossref, Web of Science, Google Scholar
31. K. G. Zou, S. Nagarajaiah and A. Dick , Asymmetric solutions of SDOF system with wire rope vibration isolator subjected to harmonic excitation, Int. J. Struct. Stab. Dyn. 15(6) (2015) 1450089. Link, Web of Science, Google Scholar
32. K. Wang, J. X. Zhou, Y. P. Chang, H. J. Ouyang, D. L. Xu and Y. Yang , A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism, Nonlinear. Dyn. 101(2) (2020) 755–773. Crossref, Web of Science, Google Scholar
33. K. Wang, H. J. Ouyang, J. X. Zhou, Y. P. Chang, D. L. Xu and H. Zhao , A nonlinear hybrid energy harvester with high ultralow-frequency energy harvesting performance, Meccanica 56(2) (2020) 461–480. Crossref, Web of Science, Google Scholar
34. S. K. Lai, X. Yang, C. Wang and W. J. Liu , An analytical study for nonlinear free and forced vibration of electrostatically actuated MEMS resonators, Int. J. Struct. Stab. Dyn. 19(7) (2019) 1950072. Link, Web of Science, Google Scholar
35. H. P. Liu and P. P. Zhao , Displacement transmissibility of a four-parameter isolator with geometric nonlinearity, Int. J. Struct. Stab. Dyn. 20(8) (2020) 2050092. Link, Web of Science, Google Scholar
36. H. Li, J. C. Li, Y. Yu and Y. C. Li , Modified adaptive negative stiffness device with variable negative stiffness and geometrically nonlinear damping for seismic protection of structures, Int. J. Struct. Stab. Dyn. 21(8) (2021) 2150107. Link, Web of Science, Google Scholar