Skip to main content
SpringerLink
Log in

Oil-film instability simulation in an overhung rotor system with flexible coupling misalignment

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Aiming at the oil-film instability of the sliding bearings at high speeds, this paper systematically investigates oil-film instability laws of an overhung rotor system with parallel and angular misalignments in the run-up and run-down processes. A finite element (FE) model of the overhung rotor system considering the gyroscopic effect is established, and the sliding bearings are simulated by a nonlinear oil-film force model based on the assumption of short-length bearings. Moreover, the effectiveness of the FE model is also verified by comparing our simulation results with the experimental results in the published literature. In the run-up and run-down processes with constant angular acceleration, the effects of parallel misalignment (PM) and angular misalignment (AM) on oil-film instability laws are simulated. The results show that under the perfectly aligned condition, the onsets of the first and second vibration mode instability in the run-down process are less than those in the run-up process due to the hysteresis effect. Under the misalignment conditions, the misalignment of the coupling can delay the onset of the first vibration mode instability and decrease its vibration amplitude. In comparison with the PM, the amplitudes of multiple frequency components are more obvious under the given AM conditions. Moreover, in the run-up and run-down processes with different misalignment conditions, the variation of the dominant vibration energy was observed according to the rotating frequency \(f_{\mathrm{r}}\), the first-mode whirl/whip frequency \(f_{\mathrm{n}1}\), the second-mode whirl/whip frequency \(f_{\mathrm{n}2}\), or the their combinations, such as \(f_{\mathrm{r}}\)–\(2f_{\mathrm{n}2}\).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Abbreviations

C :

Damping matrix of the global system (Rayleigh damping matrix).

\(c\) :

Mean radial clearance of the sliding bearing

\(D\) :

Journal diameter

\(E\) :

Young’s modulus

\({\varvec{F}}_{bi}\) :

Oil-film force vector of the bearing

\(F_{bxi}, F_{byi}\) :

Oil-film forces in \(x\) and \(y\) directions

\({\varvec{F}}_\mathrm{g}\) :

Static gravitational force vector

\(F_{x2},F_{y2}\) :

Coupling misalignment forces in \(x\) and \(y\) direction

\(f_{bx,} f_{by}\) :

Dimensionless oil-film forces in \(x\) and \(y\) directions

\(f_{\mathrm{r}}\) :

Rotating frequency (Hz)

\(f_{\mathrm{n}1}, f_{\mathrm{n}2}\) :

The first- and second-mode whirl/whip frequencies

G :

Gyroscopic matrix

\(g\) :

Acceleration of gravity

\(I\) :

Area moment of inertia

\(I_{dd}, I_{pd}, I_{dc}, I_{pc}\) :

Diametric and polar moments of inertia of the disk and the coupling

K :

Stiffness matrix of the global system

\(K_\mathrm{b}\) :

Bending spring rate per degree per diskpack

\(L\) :

Bearing length

M :

General mass matrix of the global system

\(M_{xi}, M_{yi}\) (\(i=1,2)\) :

Bending moments in \(x \)and \(y\) directions

me:

unbalance moment

Q :

The excitation forces/moments caused by coupling misalignment

q :

Displacement vector

\({\tilde{\varvec{q}}}\) :

Dimensionless displacement vector

\(T_{q}\) :

Rated torque

\(t\) :

Time (s)

\(x_{i,} y_{i}\) (\(i=1, 2,\ldots ,14\)) :

Displacements in \(x\) and \(y\) directions

\(\tilde{x}_i , \tilde{y}_i \) (\(i=1, 2,\ldots ,14\)) :

Dimensionless displacements in \(x\) and \(y\) directions

\(\Delta X_{i,} \Delta Y_{i}\) (\(i=1, 2)\) :

Misalignment displacements in \(x\) and \(y\) directions

\(Z_{3}\) :

Centre of articulation

\(\alpha \) :

Angular acceleration of the rotor system

\(\eta \) :

Lubricant viscosity

\(\theta _{xi}, \theta _{yi}\) :

Angular displacements in rotation directions

\(\theta _{1}, \theta _{2}, \varphi _{1}, \varphi _{2}, \theta _{3}\) :

Misalignment angles

\(\xi _{1}, \xi _{2}\) :

The first and second modal damping ratios

\(\rho \) :

Density

\(\upsilon \) :

Poisson’s ratio

\(\omega \) :

Rotating speed of rotor (rev/min)

\(\omega _{0}\) :

Initial angular velocity

\(\omega _{\mathrm{n}1}, \omega _{\mathrm{n}2}\) :

The first and second natural frequencies (rev/min)

References

  1. Muszynska, A.: Rotordynamics. CRC Taylor & Francis Group, New York (2005)

    Book  MATH  Google Scholar 

  2. Ding, Q., Cooper, J.E., Leung, A.Y.T.: Hopf bifurcation analysis of a rotor/seal system. J. Sound Vib. 252, 817–833 (2002)

    Article  Google Scholar 

  3. Capone, G.: Orbital motions of rigid symmetric rotor supported on journal bearings. La Meccanica Italiana 199, 37–46 (1986)

    Google Scholar 

  4. Capone, G.: Analytical description of fluid-dynamic force field in cylindrical journal bearing. L’Energia Elettrica 3, 105–110 (1991). (in Italian)

    Google Scholar 

  5. Adiletta, G., Guido, A.R., Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in journal bearings. Part I: theoretical analysis. Nonlinear Dyn. 14, 57–87 (1997)

    Article  MATH  Google Scholar 

  6. Jing, J., Meng, G., Sun, Y., et al.: On the non-linear dynamic behavior of a rotor-bearing system. J. Sound Vib. 274, 1031–1044 (2004)

    Article  Google Scholar 

  7. Jing, J., Meng, G., Sun, Y., et al.: On the oil-whipping of a rotor-bearing system by a continuum model. Appl. Math. Model. 29, 461–475 (2005)

    Article  MATH  Google Scholar 

  8. 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, 273–293 (2008)

    Article  Google Scholar 

  9. Ding, Q., Leung, A.Y.T.: Numerical and experimental investigations on flexible multi-bearing rotor dynamics. J. Vib. Acoust. 127, 408–415 (2005)

    Article  Google Scholar 

  10. Cheng, M., Meng, G., Jing, J.P.: Numerical study of a rotor-bearing-seal system. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 221, 779–788 (2007)

    Article  Google Scholar 

  11. Ma, H., Li, H., Zhao, X.Y., et al.: Effects of eccentric phase difference between two discs on oil-film instability in a rotor-bearing system. Mech. Syst. Signal Process. 41, 526–545 (2013)

    Article  Google Scholar 

  12. Liu, Z.S., Qian, D.S., Sun, L.Q., et al.: Stability analyses of inclined rotor bearing system based on non-linear oil film force models. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 226, 439–453 (2012)

    Article  Google Scholar 

  13. Zhang, W., Xu, X.F.: Modeling of nonlinear oil-film force acting on a journal with unsteady motion and nonlinear instability analysis under the model. Int. J. Nonlinear Sci. Numer. Simul. 1, 179–186 (2000)

    MATH  Google Scholar 

  14. Xie, W.H., Tang, Y.G., Chen, Y.S.: Analysis of motion stability of the flexible rotor-bearing system with two unbalanced disks. J. Sound Vib. 310, 381–393 (2008)

    Article  Google Scholar 

  15. Ding, Q., Leung, A.Y.T.: Non-stationary processes of rotor/bearing system in bifurcations. J. Sound Vib. 268, 33–48 (2003)

    Article  Google Scholar 

  16. Ding, Q., Zhang, K.P.: Order reduction and nonlinear behaviors of a continuous rotor system. Nonlinear Dyn. 67, 251–262 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  17. Friswell, M.I., Penny, J.E.T., Garvey, S.D., et al.: Dynamics of Rotating Machines. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

  19. Schweizer, B., Sievert, M.: Nonlinear oscillations of automotive turbocharger turbines. J. Sound Vib. 321, 955–975 (2009)

    Article  Google Scholar 

  20. Schweizer, B.: Oil whirl, oil whip and whirl/whip synchronization occurring in rotor systems with full-floating ring bearings. Nonlinear Dyn. 57, 509–532 (2009)

    Article  MATH  Google Scholar 

  21. Tian, L., Wang, W.J., Peng, Z.J.: Effects of bearing outer clearance on the dynamic behaviours of the full floating ring bearing supported turbocharger rotor. Mech. Syst. Signal Process. 31, 155–175 (2012)

    Article  Google Scholar 

  22. Tian, L., Wang, W.J., Peng, Z.J.: Nonlinear effects of unbalance in the rotor-floating ring bearing system of turbochargers. Mech. Syst. Signal Process. 34, 298–320 (2013)

    Article  Google Scholar 

  23. El-Shafei, A., Tawfick, S.H., Raafat, M.S., et al.: Some experiments on oil whirl and oil whip. J. Eng. Gas Turbines Power 129, 144–153 (2007)

    Article  Google Scholar 

  24. Wan, Z., Jing, J.P., Meng, G., et al.: Theoretical and experimental study on the dynamic response of multi-disk rotor system with flexible coupling misalignment. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 226, 2874–2886 (2012)

    Article  Google Scholar 

  25. Cao, H.R., Niu, L.K., He, Z.J., et al.: Dynamic modeling and vibration response simulation for high speed rolling ball bearings with localized surface defects in raceways. J. Manuf. Sci. Eng. 136, 041015-1–041015-16 (2014)

    Article  Google Scholar 

  26. Han, Q.K., Chu, F.L.: Dynamic instability and steady-state response of an elliptical cracked shaft. Arch. Appl. Mech. 82, 709–722 (2012)

    Article  MATH  Google Scholar 

  27. Zhang, W.M., Meng, G., Chen, D., et al.: Nonlinear dynamics of a rub-impact micro-rotor system with scale-dependent friction model. J. Sound Vib. 309, 756–777 (2008)

    Article  Google Scholar 

  28. Cao, D.Q., Wang, L.G., Chen, Y.S., et al.: Bifurcation and Chaos of the bladed overhang rotor system with squeeze film dampers. Sci. China Ser. E Technol. Sci. 52, 709–720 (2009)

    Article  MATH  Google Scholar 

  29. Ma, H., Li, H., Niu, H.Q., et al.: Numerical and experimental analysis of the first and second-mode instability in a rotor-bearing system. Arch. Appl. Mech. 84, 519–541 (2014)

    Article  MATH  Google Scholar 

  30. Ma, H., Yang, J., Song, R.Z., et al.: Effects of tip relief on vibration responses of a geared rotor system. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 228, 1132–1154 (2014)

    Article  Google Scholar 

  31. Sekhar, A.S., Prabhu, B.S.: Effects of coupling misalignment on vibrations of rotating machinery. J. Sound Vib. 185, 655–671 (1995)

    Article  MATH  Google Scholar 

  32. Prabhakar, S., Sekhar, A.S., Mohanty, A.R.: Vibration analysis of a misaligned rotor-coupling-bearing system passing through the critical speed. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 215, 1417–1428 (2001)

    Article  Google Scholar 

  33. Bathe, K.J., Wilson, E.L.: Numerical Methods in Finite Element Analysis. Prentice-Hall Inc., New Jersey (1976)

    MATH  Google Scholar 

Download references

Acknowledgments

This project is supported by the Program for New Century Excellent Talents in University (Grant No. NCET-11-0078), the Fundamental Research Funds for the Central Universities (Grant Nos. N130403006 and N140301001) and the Joint Funds of the National Natural Science Foundation and the Civil Aviation Administration of China (Grant No. U1433109) for providing financial support for this work. We also thank the anonymous reviewers for their valuable comments and Dr. Emad Elsamahy for revising the final version of the paper for English style and grammar, and for offering suggestions for improvement.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, Liaoning, People’s Republic of China

    Hui Ma, Xueling Wang, Heqiang Niu & Bangchun Wen

Authors
  1. Hui Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xueling Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heqiang Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bangchun Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hui Ma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, H., Wang, X., Niu, H. et al. Oil-film instability simulation in an overhung rotor system with flexible coupling misalignment. Arch Appl Mech 85, 893–907 (2015). https://doi.org/10.1007/s00419-015-0998-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-0998-3

Keywords

Search

Navigation