Impact of damper seal coefficients uncertainties in rotor dynamics

  • Raphael Timbó
  • Thiago G. RittoEmail author
Technical Paper


Damper seals might have a great impact on rotordynamics, but the values of their coefficients are difficult to be determined and have a significant uncertainty. In the present paper, a probabilistic model is proposed to model damper seal coefficients, which are frequency dependent. A stochastic process (frequency indexed) is constructed such that modeling errors are taken into account. The impact of these uncertainties on the rotordynamic behavior of a compressor is analyzed. The deterministic seal coefficients are determined considering a bulk-flow model, and values are calculated by a compressor manufacturer based on experimental data. The results obtained show that uncertainties in these coefficients have a considerable impact on the compressor Campbell diagram, stability, and unbalance response.


Rotor stochastic dynamics Damper seal coefficients uncertainties Stochastic Campbell diagram Model uncertainties 



The authors are grateful for the financial support of the Brazilian agencies CAPES, CNPq, and FAPERJ. This research was partially funded by FAPERJ (Grant Number E-26/201.572/2014) and CNPQ (Grant Number 400933/2016-0).


  1. 1.
    API 617, A..: Api 617, 2014. Axial and centrifugal compressors and expander-compressors, 8th edn. American Petroleum Institute, Washington, DC (2014)Google Scholar
  2. 2.
    Baldassarre L, Bernocchi A, Failli L, Fontana M, Mitaritonna N, Rizzo E (2014) Honeycomb seal effect on rotor response to unbalance. In: Proceedings of the forty-third turbomachinery symposium, Houston, TXGoogle Scholar
  3. 3.
    Baldassarre L, Fontana M, Bernocchi A, Moretti M et al (2016) Effect of relative journal bearing and honeycomb seal direct stiffness on radial synchronous vibrations of high-pressure centrifugal compressors. In: Proceedings of the 45th turbomachinery symposium. Texas A&M University. Turbomachinery LaboratoriesGoogle Scholar
  4. 4.
    Cavalini A, Silva A, Lara-Molina F, Steffen V (2017) Dynamic analysis of a flexible rotor supported by hydrodynamic bearings with uncertain parameters. Meccanica 1(9):1–12MathSciNetGoogle Scholar
  5. 5.
    Childs D, Elrod D, Hale K (1989) Annular honeycomb seals: test results for leakage and rotordynamic coefficients; comparisons to labyrinth and smooth configurations. J Tribol 111(2):293–300CrossRefGoogle Scholar
  6. 6.
    Childs DW, Wade J (2004) Rotordynamic-coefficient and leakage characteristics for hole-pattern-stator annular gas seals—measurements versus predictions. J Tribol 126(2):326–333CrossRefGoogle Scholar
  7. 7.
    Friswell MI (2010) Dynamics of rotating machines. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  8. 8.
    Gelin A, Pugnet JM, Bolusset D, Friez P (1997) Experience in full-load testing of natural gas centrifugal compressors for rotordynamics improvements. J Eng Gas Turbines Power 119(4):934–941CrossRefGoogle Scholar
  9. 9.
    He M (2004) Thermoelastohydrodynamic analysis of fluid film journal bearings, Ph.D. thesis, University of Virginia, 2003Google Scholar
  10. 10.
    Hirs G (1973) A bulk-flow theory for turbulence in lubricant films. J Lubr Technol 95(2):137–145CrossRefGoogle Scholar
  11. 11.
    Holt CG, Childs DW (2002) Theory versus experiment for the rotordynamic impedances of two hole-pattern-stator gas annular seals. J Tribol 124(1):137–143CrossRefGoogle Scholar
  12. 12.
    Hunter JD (2007) Matplotlib: a 2d graphics environment. Comput Sci Eng 9(3):90–95CrossRefGoogle Scholar
  13. 13.
    Jaynes ET (2003) Probability Theory: The Logic of Science. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  14. 14.
    Jones E, Oliphant T, Peterson P (2001) \(\{\text{SciPy}\}\): open source scientific tools for \(\{\text{ Python }\}\).
  15. 15.
    Kleynhans GF (1996) A two-control-volume bulk-flow rotordynamic analysis for smooth-rotor/honeycomb-stator gas annular seals. Ph.D. thesis, Texas A&M UniversityGoogle Scholar
  16. 16.
    Kleynhans GF, Childs DW (1996) The acoustic influence of cell depth on the rotordynamic characteristics of smooth-rotor/honeycomb-stator annular gas seals. In: ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, pp V005T14A017–V005T14A017Google Scholar
  17. 17.
    Lüdtke KH (2013) Process centrifugal compressors: basics, function, operation, design, application. Springer Science & Business Media, BerlinGoogle Scholar
  18. 18.
    Migliorini PJ, Untaroiu A, Wood HG (2015) A numerical study on the influence of hole depth on the static and dynamic performance of hole-pattern seals. J Tribol 137(1):011702CrossRefGoogle Scholar
  19. 19.
    Migliorini PJ, Untaroiu A, Wood HG, Allaire PE (2012) A computational fluid dynamics/bulk-flow hybrid method for determining rotordynamic coefficients of annular gas seals. J Tribol 134(2):022202CrossRefGoogle Scholar
  20. 20.
    Murthy R, Mignolet M, El-Shafei A (2010) Nonparametric stochastic modeling of uncertainty in rotordynamics—part 1: formulation. J Eng Gas Turbines Power 132(9):092501CrossRefGoogle Scholar
  21. 21.
    Nelson C (1984) Analysis for leakage and rotordynamic coefficients of surface-roughened tapered annular gas seals. ASME J Eng Gas Turbines Power 106(4):927–934CrossRefGoogle Scholar
  22. 22.
    Noronha RF, Cavalca KL, Miranda MA, Memmott EA, Ramesh K (2014) Stability testing of CO2 compressors. In: Proceedings of the forty-third turbomachinery symposium, Houston, TXGoogle Scholar
  23. 23.
    Noronha RFd, Ujihara DY, Rezende-Tapajoz Ld, Grosso G, Moreira RPM et al (2015) Applying CFD to solve a vibration problem of a compressor. In: Proceedings of the 44th turbomachinery symposium. Turbomachinery Laboratories, Texas A&M Engineering Experiment StationGoogle Scholar
  24. 24.
    Ritto T, Lopez R, Sampaio R, Souza De Cursi J (2011) Robust optimization of a flexible rotor-bearing system using the Campbell diagram. Eng Optim 43(1):77–96MathSciNetCrossRefGoogle Scholar
  25. 25.
    Sorokes JM, Kuzdzal MJ, Sandberg MR, Colby GM et al (1994) Recent experiences in full load full pressure shop testing of a high pressure gas injection centrifugal compressor. In: Proceedings of the 23rd turbomachinery symposium. Texas A&M University. Turbomachinery LaboratoriesGoogle Scholar
  26. 26.
    Tyminski N, Tuckmantel F, Cavalca K, de Castro H (2017) Bayesian inference applied to journal bearing parameter identification. J Braz Soc Mech Sci Eng 29(8):2983–3004CrossRefGoogle Scholar
  27. 27.
    Vannarsdall M, Childs DW (2014) Static and rotordynamic characteristics for a new hole-pattern annular gas seal design incorporating larger diameter holes. J Eng Gas Turbines Power 136(2):022507CrossRefGoogle Scholar
  28. 28.
    Vannarsdall ML (2011) Measured results for a new hole-pattern annular gas seal incorporating larger diameter holes, comparisons to results for a traditional hole-pattern seal, and predictions. Master’s thesis, Texas A&M UniversityGoogle Scholar
  29. 29.
    Vannini G, Cioncolini S, Calicchio V, Tedone F (2011) Development of a high pressure rotordynamic test rig for centrifugal compressors internal seals characterization. In: Proceedings of the fortieth turbomachinery symposium, Houston, TX, Sept, pp 12–15Google Scholar
  30. 30.
    Van der Walt S, Colbert SC, Varoquaux G (2011) The Numpy array: a structure for efficient numerical computation. Comput Sci Eng 13(2):22–30CrossRefGoogle Scholar
  31. 31.
    Zeidan FY, Perez RX, Stephenson EM et al (1993) The use of honeycomb seals in stabilizing two centrifugal compressors. In: Proceedings of the 22nd turbomachinery symposium. Texas A&M University. Turbomachinery LaboratoriesGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Cenpes, PetrobrasRio de JaneiroBrazil
  2. 2.Mechanical Engineering DepartmentUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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