Analytical model of squeeze film air damping of perforated plates in the free molecular regime

  • Cunhao Lu
  • Pu LiEmail author
  • Yuming Fang
Technical Paper


In this paper, an analytical model of squeeze film damping (SQFD) of perforated plates in the free molecular regime is developed, which is based on: (1) the modification of the perforated energy transfer model (P-ETM) (Li and Hu, J Micromech Microeng 21:025006, 2011) by giving the probability of molecules entering the gap through holes; (2) the application of Sumali’s formula (J Micromech Microeng 17:2231–2240, 2007) to relate to the Monte Carlo model (MC) (Hutcherson and Ye, J Micromech Microeng 14:1726–1733, 2004) quantitatively. The analytical model can model the perforation effect on SQFD of plates of various hole sizes. Compared with experiment data and numerical models, the analytical model is proved to be accurate, easy to operate. The effect of gap distance on SQFD of perforated plate in the free molecular regime is discussed. Due to perforation effect, as gap distance increases, the damping constant of non-perforated plate decreases faster than that of perforated plate of the same size.



This work is supported by the National Natural Science Foundation of China (Grant No. 51375091).


  1. Bao M, Yang H, Yin H, Sun Y (2002) Energy transfer model for squeeze-film air damping in low vacuum. J Micromech Microeng 12:341–346CrossRefGoogle Scholar
  2. Bao M, Yang H, Sun Y, Wang Y (2003a) Modified Reynolds’ equation and analysis of squeeze-film air damping of perforated structures. J Micromech Microeng 13:795–800CrossRefGoogle Scholar
  3. Bao M, Yang H, Sun Y, Wang Y (2003b) Squeeze-film air damping of thick hole-plate. Sens Actuators A 108:212–217CrossRefGoogle Scholar
  4. Burgdorfer A (1959) The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. J Basic Eng 81:94–99Google Scholar
  5. Hutcherson S, Ye W (2004) On the squeeze-film damping of micro-resonators in the free-molecule regime. J Micromech Microeng 14:1726–1733CrossRefGoogle Scholar
  6. Ishfaque A, Kim B (2016) Analytical modeling of squeeze air film damping of biomimetic MEMS directional microphone. J Sound Vib 375:422–435CrossRefGoogle Scholar
  7. Ishfaque A, Kim B (2017) Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function. Nonlinear Dyn 87:1603–1616CrossRefGoogle Scholar
  8. Kwok P, Weinberg M, Breuer K (2005) Fluid effect in vibrating micromachined structures. J Microelectromech Syst 14:770–781CrossRefGoogle Scholar
  9. Li P, Hu R (2011) A model for squeeze-film damping of perforated MEMS devices in the free molecular regime. J Micromech Microeng 21:025006CrossRefGoogle Scholar
  10. Li P, Fang Y, Wu H (2014a) A numerical molecular dynamics approach for squeeze-film damping of perforated MEMS structures in the free molecular regime. Microfluid Nanofluid 17(4):759–772CrossRefGoogle Scholar
  11. Li P, Fang Y, Xu F (2014b) Analytical modeling of squeeze-film damping for perforated circular microplates. J Sound Vib 333:2688–2700CrossRefGoogle Scholar
  12. Lu C, Li P (2017) An improved model for air damping of perforated structures. In: 4th Int Conf on Mechanics and Mechatronics Research (IOP), vol 224Google Scholar
  13. Lu C, Li P, Bao M, Fang Y (2018) A generalized energy transfer model for squeeze-film air damping in the free molecular regime. J Micromech Microeng 28:085003CrossRefGoogle Scholar
  14. Mohite S, Kesari H, Sonti V, Pratap R (2005) Analytical solutions for the stiffness and damping coefficients of squeeze films in MEMS devices with perforated back plates. J Micromech Microeng 15:2083–2092CrossRefGoogle Scholar
  15. Pandey A, Pratap R (2008) A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry. J Micromech Microeng 18:105003CrossRefGoogle Scholar
  16. Pandy A, Pratap R (2008) A comparative study of analytical squeeze film damping models in rigid rectangular perforated MEMS structures with experimental results. Microfluid Nanofluid 4:205–218CrossRefGoogle Scholar
  17. Pandy A, Pratap R, Chau F (2007) Analytical solution of the modified Reynolds equations for squeeze film damping in perforated MEMS structures. Sens Actuators A 135:839–848CrossRefGoogle Scholar
  18. Pantano M, Pagnotta L, Nigro S (2014) On the effective viscosity expression for modeling squeeze-film damping at low pressure. J Tribol 136:031702CrossRefGoogle Scholar
  19. Sumali H (2007) Squeeze-film damping in the free molecular regime: model validation and measurement on a MEMS. J Micromech Microeng 17:2231–2240CrossRefGoogle Scholar
  20. Veijola T (2006) Analytic damping model for an MEM perforation cell. Microfluid Nanofluid 2:249–260CrossRefGoogle Scholar
  21. Veijola T, Kuisma H, Lahdenpera J, Ryhanen T (1995) Equivalent-circuit model for the squeezed gas film in a silicon accelerometer. Sens Actuators A 48:239–248CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSoutheast UniversityNanjingChina
  2. 2.College of Electronic Science and EngineeringNanjing University of Posts and TelecommunicationsNanjingChina

Personalised recommendations