Skip to main content
Log in

Detection and quantification of oil whirl instability in a rotor-journal bearing system using a novel dynamic recurrence index

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper presents a new Dynamic Recurrence Index (DRI) to detect the occurrence and quantify the evolution of oil whirl instability in the rotor-journal bearing system by measuring the dynamical similarity between the normal working condition and unstable operating states of the system. In this method, two signals, one normal operating condition signal as the reference signal and one unstable operating condition signal, are reconstructed into the same phase space before the Cross-Recurrence Plots (CRP) are prepared. Then, the structure of these CRPs is analyzed by applying the Cross-Recurrence Quantification Analysis (CRQA) to estimate the dynamical difference between the normal operating condition and unstable operating states of the rotor-journal bearing system. Finally, those CRQA variables are mapped by Support Vector Data Description (SVDD) into a dynamic recurrence index to monitor the evolution and evaluate the severity degree of the oil whirl instability. The simulation and experimental results show that the CRQA variables and DRI are sensitive to the occurrence of oil whirl instability, and the proposed method is a practical approach to monitoring the oil whirl instability for the rotor-journal bearing system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig.8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Data availability

The simulation and experimental datasets analyzed during the current work are available in the OneDrive repository, [https://1drv.ms/u/s!AtNlnPMcJW38p0W-Kg6v-hnL0tU4?e=siuegP].

References

  1. Xiang, L., Deng, Z., Hu, A., Gao, X.: Multi-fault coupling study of a rotor system in experimental and numerical analyses. Nonlinear Dynam. 97(4), 2607–2625 (2019)

    Article  Google Scholar 

  2. Jalan, A.K., Mohanty, A.R.: Model based fault diagnosis of a rotor–bearing system for misalignment and unbalance under steady-state condition. J. Sound Vib. 327(3–5), 604–622 (2009)

    Article  Google Scholar 

  3. Hu, A., Hou, L., Xiang, L.: Dynamic simulation and experimental study of an asymmetric double-disk rotor-bearing system with rub-impact and oil film instability. Nonlinear Dynam. 84(2), 1–19 (2015)

    Google Scholar 

  4. Liu, X., Lin, B., Luo, H.: Directional cyclic demodulation with application to identification of rotor oil film instability fault coupled with rub–impact. IET Sci. Meas. Technol. 12(4), 567–574 (2018)

    Article  Google Scholar 

  5. Jeffcott, H.H.: XXVII The lateral vibration of loaded shafts in the neighbourhood of a whirling speed—the effect of want of balance. Philos. Mag. 37(219), 304–314 (1919)

    Article  MATH  Google Scholar 

  6. Reynolds, O.: On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments including an experimental determination of the viscosity of olive oil. Phi. Trans. Ro.y Soc. lond 177, 191–203 (1886)

    MATH  Google Scholar 

  7. Lund, J.W.: Spring and damping coefficients for the tilting-pad journal bearing. A S L E Trans. 7(4), 342–352 (1964)

    Article  Google Scholar 

  8. Sabin, S.: Understanding and using dynamic stiffness-a tutorial. Orbit 65, 44–54 (2000)

    Google Scholar 

  9. Gardner, M., Myers, C., Savage, M., Taylor, C.: Analysis of limit-cycle response in fluid-film journal bearings using the method of multiple scales. Q. J. Mech. Appl. Math. 38(1), 27–45 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  10. Muszynska, A.: Whirl and whip—rotor/bearing stability problems. J. Sound Vib. 110(3), 443 (1985)

    Article  Google Scholar 

  11. Muszynska, A.: Stability of whirl and whip in rotor/bearing systems. J. Sound Vib. 127(1), 49–64 (1988)

    Article  MathSciNet  Google Scholar 

  12. Zanarini, A., Cavallini, A.: Experiencing rotor and fluid film bearing dynamics. Proceedings of the Quinta Giornata di Studio Ettore Funaioli, pp. 23–38, Bologna, Italy (2011)

  13. Tiwari, R., Lees, A.W., Friswell, M.I.: Identification of dynamic bearing parameters: a review. Shock Vib. Digest 36, 99 (2004)

    Article  Google Scholar 

  14. Xiang, L., Hu, A., Hou, L., Xiong, Y., Xing, J.: Nonlinear coupled dynamics of an asymmetric double-disc rotor-bearing system under rub-impact and oil film forces. Appl. Math. Model 40(7–8), 4505–4523 (2016)

    Article  Google Scholar 

  15. De Castro, H.F., Cavalca, K.L., Nordmann, R.: Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model. J Sound Vib. 317(1–2), 273–293 (2008)

    Article  Google Scholar 

  16. Xiang, L., Gao, X., Hu, A.: Nonlinear dynamics of an asymmetric rotor-bearing system with coupling faults of crack and rub-impact under oil film forces. Nonlinear Dynam. 86(2), 1057–1067 (2016)

    Article  Google Scholar 

  17. Mobley, R. K.: Plant engineer’s handbook. Elsevier, MA (2001)

    Google Scholar 

  18. Boyce, M. P.: Gas turbine engineering handbook. Elsevier, MA (2011)

    Google Scholar 

  19. Fan, C.C., Pan, M.C.: Active elimination of oil and dry whips in a rotating machine with an electromagnetic actuator. Int. J. Mech. Sci. 53(2), 126–134 (2011)

    Article  Google Scholar 

  20. Safizadeh, M.S., Golmohammadi, A.: Prediction of oil whirl initiation in journal bearings using multi-sensors data fusion. Measurement 151, 107241 (2020)

    Article  Google Scholar 

  21. Ojaghi, M., Yazdandoost, N.: Oil-whirl fault modeling, simulation, and detection in sleeve bearings of squirrel cage induction motors. IEEE T Energy Conver. 30(4), 1537–1545 (2015)

    Article  Google Scholar 

  22. Fan, C.C., Syu, J.W., Pan, M.C., Tsao, W.C.: Study of startup vibration response for oil whirl, oil whip and dry whip. Mech. Syst. Signal Process. 25(8), 3102–3115 (2011)

    Article  Google Scholar 

  23. Eckmann, J.P., Kamphorst, S.O., Ruelle, D.: Recurrence plots of dynamical systems. World Sci. Ser. Nonlinear Sci. Ser. A 16, 441–446 (1995)

    Google Scholar 

  24. Zbilut, J.P., Webber, C.L.: Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171(3–4), 199–203 (1992)

    Article  Google Scholar 

  25. Webber, C.L., Zbilut, J.P.: Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76(2), 965 (1994)

    Article  Google Scholar 

  26. Zbilut, J.P., Giuliani, A., Webber, C.L.: Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification–science direct. phys. Lett. A 246(1–2), 122–128 (1998)

    Article  Google Scholar 

  27. Marwan, N., Thiel, M., Nowaczyk, N.R.: Cross recurrence plot based synchronization of time series. Nonlinear Proc. Geoph. 9(3), 325–331 (2002)

    Article  Google Scholar 

  28. Marwan, N., Kurths, J.: Nonlinear analysis of bivariate data with cross recurrence plots. Phys. Lett. A 302, 299 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  29. Marwan, N., Kurths, J.: Cross recurrence plots and their applications. Math. Phys. Res. Cut. Edge 35, 101–139 (2004)

    MathSciNet  Google Scholar 

  30. Marwan, N., Romano, M.C., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5–6), 237–329 (2007)

    Article  MathSciNet  Google Scholar 

  31. Shockley, K., Butwill, M., Zbilut, J.P., Webber, C.L.: Cross recurrence quantification of coupled oscillators. Phys. Lett. A 305(1–2), 59–69 (2002)

    Article  MATH  Google Scholar 

  32. Elias, J., Namboothiri, V.N.N.: Cross-recurrence plot quantification analysis of input and output signals for the detection of chatter in turning. Nonlinear Dynam. 76(1), 255–261 (2014)

    Article  Google Scholar 

  33. Zarghami, Reza, Mostoufi, Navid, Ziaei-Halimejani, Hooman: Investigation of hydrodynamics of gas-solid fluidized beds using cross recurrence quantification analysis. Adv. Powder Technol. Int. J. Soc. Powder Technol. Japan 28, 1237 (2017)

    Google Scholar 

  34. Tax, D.M.J., Duin, R.P.W.: Support vector data description. Mach. Learn. 54(2), 45–66 (2004)

    Article  MATH  Google Scholar 

  35. Vapnik, V.N.: The nature of statistical learning theory. Springer, NY (1995)

    Book  MATH  Google Scholar 

  36. Takens, F.: Detecting strange attractors in turbulence. Lect. Notes Math. 898, 336 (1981)

    MathSciNet  MATH  Google Scholar 

  37. Cao, L.: Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110, 43 (1997)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the project from the National Natural Science Foundation of China (No. 52175077).

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lin Bo.

Ethics declarations

Conflict of interest

The authors declared that they have no conflicts of interest to this work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, H., Bo, L., Peng, C. et al. Detection and quantification of oil whirl instability in a rotor-journal bearing system using a novel dynamic recurrence index. Nonlinear Dyn 111, 2229–2261 (2023). https://doi.org/10.1007/s11071-022-07932-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-07932-3

Keywords

Navigation