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Research on nonlinear stiffness and damping of bellows-type fluid viscous damper

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Abstract

Micro-vibrations in satellites mainly originate from the control moment gyroscope because of its mass imbalance, which seriously affect the image accuracy of high-resolution optical payload, so it must be isolated. Bellows-type fluid viscous damper (FVD) can be used to isolate micro-vibrations. In this paper, a simplified model of the damping element in bellows-type FVD under medium- and high-frequency excitation is proposed according to the concept of bellows effective area. Based on this theoretical model, nonlinear stiffness and damping at different design parameters are extracted by nonlinear fitting method. Then, the main cause of nonlinear stiffness and damping is analyzed by the velocity distribution in the cross section of damping orifice. The factors that affect the intensity of nonlinear stiffness and damping are discussed by using the flow resistance. The results show that the velocity term in the corrected hydraulic resistance is the cause of nonlinear damping and stiffness. Damping orifice diameter, length and silicone oil viscosity will affect the intensity of nonlinear characteristics of this damper. At low viscosity, the nonlinear damping is more obvious. The larger the diameter, the more obvious the nonlinear damping. In the frequency domain between 1 and 200 Hz, the velocity index is not a constant, but changes with frequency. Hydraulic stiffness can be divided by linear stiffness and nonlinear stiffness; both of them can affect the elastic force.

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References

  1. Lin, L., et al.: The influence of flywheel micro vibration on space camera and vibration suppression. Mech. Syst. Signal Process. 100, 360–370 (2018)

    Article  Google Scholar 

  2. Hur, G.: Isolation of micro-vibrations due to reaction wheel assembly using a source-path-receiver approach for quantitative requirements. J. Vib. Control 25, 1424–1435 (2019)

    Article  Google Scholar 

  3. Stabile, A., et al.: A 2-collinear-DoF strut with embedded negative-resistance electromagnetic shunt dampers for spacecraft micro-vibration. Smart Mater. Struct. 26(4), 045031 (2017)

    Article  Google Scholar 

  4. Kwon, S.C., et al.: Viscoelastic multilayered blade-type passive vibration isolation system for a spaceborne cryogenic cooler. Cryogenics 105, 102982 (2020)

    Article  Google Scholar 

  5. Kawak, B.J.: Development of a low-cost, low micro-vibration CMG for small agile satellite applications. Acta Astronaut. 131, 113–122 (2017)

    Article  Google Scholar 

  6. Kawak, B.J., Cabon, B.H., Aglietti, G.S.: Innovative viscoelastic material selection strategy based on dma and mini-shaker tests for spacecraft applications. Acta Astronaut. 131, 18–27 (2017)

    Article  Google Scholar 

  7. Shi, W.K., et al.: Modeling and dynamic properties of a four-parameter zener model vibration isolator. Shock Vib. (2016)

  8. Ma, G., et al.: Active suspension method and active vibration control of a hoop truss structure. AIAA J. 56, 1689–1695 (2018)

    Article  Google Scholar 

  9. Asadi, E., et al.: A new adaptive hybrid electromagnetic damper: modelling, optimization, and experiment. Smart Mater. Struct. 24(7), 075003 (2015)

    Article  Google Scholar 

  10. Oh, H.: Experimental demonstration of an improved magneto-rheological fluid damper for suppression of vibration of a space flexible structure. Smart Mater. Struct. 13(5), 1238–1244 (2004)

    Article  Google Scholar 

  11. Davis, P., Cunningham, D., Harrell, J.: Advanced 1.5 Hz passive viscous isolation system. In: 35th Structures, Structural Dynamics, and Materials Conference (1994)

  12. Tosovsky, J., Janulik, V., Ruebsamen, D.T.: Adaptive three parameter isolator assemblies including external magneto-rheological valves

  13. Martinez, D., Pagan, J., Goold, R.: Isolators including damper assemblies having variable annuli and spacecraft isolation systems employing the same (2017)

  14. Likun, L., Gangtie, Z., Wenhu, H.: Study of liquid viscosity dampers in octo-strut platform for whole-spacecraft vibration isolation. Acta Astronaut. 58(10), 515–522 (2006)

    Article  Google Scholar 

  15. Wang, J., et al.: A test method of dynamic damping coefficient of micro-vibration isolators. Hangkong Xuebao/acta Aeronautica Et Astronautica Sinica 35(2), 454–460 (2014)

    Google Scholar 

  16. Jing, X.J., Lang, Z.Q.: Frequency domain analysis of a dimensionless cubic nonlinear damping system subject to harmonic input. Nonlinear Dyn. 58(3), 469–485 (2009)

    Article  MathSciNet  Google Scholar 

  17. Xing, W., Hongxiang, Y., Gangtie, Z.: Enhancing the isolation performance by a nonlinear secondary spring in the Zener model. Nonlinear Dyn. 87(4), 1–13 (2016)

    Google Scholar 

  18. Laalej, H., et al.: MR damper based implementation of nonlinear damping for a pitch plane suspension system. Smart Mater. Struct. 21(4), 045006 (2012)

    Article  Google Scholar 

  19. Narkhede, D.I., Sinha, R.: Behavior of nonlinear FVDs for control of shock vibrations. J. Sound Vib. 333(1), 80–98 (2014)

    Article  Google Scholar 

  20. Jie, W., Shougen, Z., Dafang, W.: A numerical study on the performance of nonlinear models of a microvibration isolator. Shock Vib. 2014, 1–23 (2014)

    Google Scholar 

  21. Jiao, X, Zhao, Y., Ma, W.: Nonlinear dynamic characteristics of a micro-vibration FVD. Nonlinear Dyn. (2018)

  22. Tabar, A.M.: Linearization of seismic response of structures equipped with nonlinear viscous dampers using perturbation technique. Eng. Struct. 184, 459–468 (2019)

    Article  Google Scholar 

  23. Yin, Y., et al.: Hydraulic damping nonlinearity of a compact hydro-pneumatic suspension considering gas-oil emulsion. Vibroeng. Proc. 30, 68–71 (2020)

    Article  Google Scholar 

  24. Jith, J., Sarkar, S.: A model order reduction technique for systems with nonlinear frequency dependent damping. Appl. Math. Model. 77, 1662–1678 (2020)

    Article  MathSciNet  Google Scholar 

  25. Zhu, R., Guo, T., Mwangilwa, F.: Development and test of a self-centering fluidic viscous damper. Adv. Struct. Eng. 1369433220920464 (2020)

  26. Kizilay, H.S., Cigeroglu, E.: Frequency Domain Nonlinear Modeling and Analysis of Liquid-Filled Column Dampers. Nonlinear Dynamics and Control, pp. 43–57. Springer, Cham (2020)

    MATH  Google Scholar 

  27. Dion, C., et al.: Real-time dynamic substructuring testing of viscous seismic protective devices for bridge structures. Eng. Struct. 33(12), 3351–3363 (2011)

    Article  Google Scholar 

  28. Takeda, S.: Elastomechanical researches on the metallic bellows (beam-theoretical and disc theoretical considerations). Report Techn. Coll. Hosei Univ, Vol. 16 No. 1 (1963)

  29. Langhaar, H.L.: Steady flow in the transition length of straight tube. Trans. ASME 64 (1942)

  30. He, L., Zheng, G.T.: Effect of viscous heating in fluid damper on the vibration isolation performance. Mech. Syst. Signal Process. 21(8), 3060–3071 (2007)

    Article  Google Scholar 

  31. Wang, X., Wu, H., Yang, B.: Micro-vibration suppressing using electromagnetic absorber and magnetostrictive isolator combined platform. Mech. Syst. Signal Process. 139, 1066061–10660620 (2020)

    Google Scholar 

  32. Lee, D.O., Park, G., Han, J.H.: Hybrid isolation of micro vibrations induced by reaction wheels. J. Sound Vib. 363, 1–17 (2016)

    Article  Google Scholar 

  33. Singiresu, S.R.: Mechanical Vibrations. Addison Wesley, Boston, MA (1995)

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the China Postdoctoral Science Foundation (No. 2019M63244) and National Basic Research Program of China (No. 11803034).

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Authors and Affiliations

  1. TianQin Research Center for Gravitational Physics, School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai, 519000, China

    Xiaolei Jiao, Yong Yan & Hongchao Zhao

  2. School of Aeronautics and Astronautics, Sun Yat-Sen University, Guangzhou, 510006, China

    Jinxiu Zhang

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  1. Xiaolei Jiao
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  2. Jinxiu Zhang
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  4. Hongchao Zhao
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Correspondence to Xiaolei Jiao.

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Jiao, X., Zhang, J., Yan, Y. et al. Research on nonlinear stiffness and damping of bellows-type fluid viscous damper. Nonlinear Dyn 103, 215–237 (2021). https://doi.org/10.1007/s11071-020-06146-9

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