Skip to main content
SpringerLink
Log in

Effects of Rub-Impact on Vibration Response of a Dual-Rotor System-Theoretical and Experimental Investigation

  • Research paper
  • Published:
Experimental Techniques Aims and scope Submit manuscript

Abstract

In order to understand the mechanism of fixed-point rub-impact in aero-engine, a dual-rotor system with inter-shaft bearing able to describe the mechanical vibration caused by unbalance and fixed-point rub-impact is developed in this paper. Firstly, a finite element (FE) model of the dual-rotor based on Timoshenko beam element and disk element is proposed, in which the effects of gyroscopic moments, rotary inertias, bending and shear deformations are taken into account. A rub-impact model is developed to derive the rubbing force between the rotor and fixed limiter, in which the softening characteristics of coating painted in casing is fully taken into account. Moreover, the Coulomb model is applied to describe the frictional behaviors. Secondly, the governing equations to describe the motion of the dual-rotor system with rub-impact are solved numerically by the Runge-Kutta method, and the dynamic characteristics are investigated by 3D water-fall plots and frequency spectrum. Combined harmonic frequency, whirling frequency and rotational frequency components of dual rotors are observed. Finally, the experiments of fixed-point rub-impact are performed on a dual-rotor test bench. Good agreement between the theoretical and experimental results shows the accuracy of the dual-rotor FE model and rub-impact model. The results indicate that (1) first backward whirling and forward whirling are excited under the influence of unbalance force; (2) several combination frequency components and second backward whirling and forward whirling frequency components are presented under fixed-point rubbing condition.

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

Similar content being viewed by others

References

  1. Varney P, Green I (2015) Nonlinear phenomena, bifurcations, and routes to chaos in an asymmetrically supported rotor–stator contact system. J Sound Vib 336(336):207–226

    Google Scholar 

  2. Muszynska A (1989) Rotor-to-Stationary Element Rubbing-Related Vibration Phenomena in Rotating Machinery-Literature Survey. Shock & Vibration Digest 21(3):3–11

    Google Scholar 

  3. Isaksson J, Frid A (1999) Analysis of dynamical behaviour of a rotor with deflection limiters. Acta Mech 133(1–4):1–11

    Google Scholar 

  4. Shaw SW (1985) The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 1: Subharmonic Motions and Local Bifurcations. J Appl Mech 52(2):453–458

    Google Scholar 

  5. Shaw SW (1985) The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 2: Chaotic Motions and Global Bifurcations. J Appl Mech 52(2):453–464

    Google Scholar 

  6. Chu F, Zhang Z (1998) Bifurcation and chaos in a rub-impact Jeffcott rotor system. J Sound Vib 210(1):1–18

    Google Scholar 

  7. Choi YS (2002) Investigation on the whirling motion of full annular rotor rub. J Sound Vib 258(1):191–198

    Google Scholar 

  8. Han Q, Zhang Z, Wen B (2008) Periodic motions of a dual-disc rotor system with rub-impact at fixed limiter. AR-CHIVE Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 1989-1996 222(10):1935–1946

    Google Scholar 

  9. Ma H, Shi C, Han Q et al (2013) Fixed-point rubbing fault characteristic analysis of a rotor system based on contact theory. Mech Syst Signal Process 38(1):137–153

    Google Scholar 

  10. Ma H, Wu Z, Tai X et al (2014) Dynamic characteristics analysis of a rotor system with two types of limiters. Int J Mech Sci 88:192–201

    Google Scholar 

  11. Behzad M, Alvandi M, Mba D et al (2013) A finite element-based algorithm for rubbing induced vibration prediction in rotors. J Sound Vib 332(21):5523–5542

    Google Scholar 

  12. Ma H, Zhao Q, Zhao X et al (2015) Dynamic characteristics analysis of a rotor–stator system under different rubbing forms. Appl Math Model 39(8):2392–2408

    Google Scholar 

  13. Shen X, Jia J, Zhao M (2007) Numerical Analysis of a Rub-impact Rotor-bearing System with Mass Unbalance. J Vib Control 13(12):1819–1834

    Google Scholar 

  14. Hu L, Liu Y, Zhao L et al (2016) Nonlinear dynamic response of a rub-impact rod fastening rotor considering nonlinear contact characteristic. Arch Appl Mech 86(11):1869–1886

    Google Scholar 

  15. Chang-Jian CW, Chen CK (2009) Chaos of rub–impact rotor supported by bearings with nonlinear suspension. Tribol Int 42(3):426–439

    Google Scholar 

  16. Wang N, Jiang D, Yang Y et al (2016) Study on the diagnosis of rub-impact fault based on finite element method and envelope demodulation. Journal of Vibroengineering 18(7):4500–4512

    Google Scholar 

  17. Wang NF, Jiang DX, Han T (2016) Dynamic characteristics of rotor system and rub-impact fault feature research based on casing acceleration. Journal of Vibroengineering 18(3):1525–1539

    Google Scholar 

  18. Tai X, Ma H, Liu F et al (2015) Stability and steady-state response analysis of a single rub-impact rotor system. Arch Appl Mech 85(1):133–148

    Google Scholar 

  19. Yuan Z, Chu F, Wang S et al (2007) Influence of rotor’s radial rub-impact on imbalance responses. Mechanism & Machine Theory 42(12):1663–1667

    Google Scholar 

  20. Popprath S, Ecker H (2007) Nonlinear dynamics of a rotor contacting an elastically suspended stator. J Sound Vib 308(3–5):767–784

    Google Scholar 

  21. Zhao Q, Yao H, Xu Q et al (2015) Prediction method for steady-state response of local rubbing blade-rotor systems. J Mech Sci Technol 29(4):1537–1545

    Google Scholar 

  22. Qin Z, Han Q, Chu F (2016) Bolt loosening at rotating joint interface and its influence on rotor dynamics. Eng Fail Anal 59:456–466

    Google Scholar 

  23. Qin ZY, Han QK, Chu FL (2014) Analytical model of bolted disk–drum joints and its application to dynamic analysis of jointed rotor. Proc Inst Mech Eng C J Mech Eng Sci 228(4):646–663

    Google Scholar 

  24. Roques S, Legrand M, Cartraud P et al (2010) Modelling of a rotor speed transient response with radial rubbing. J Sound Vib 329(5):527–546

    Google Scholar 

  25. Guskov M, Sinou JJ, Thouverez F et al (2014) Experimental and Numerical Investigations of a Dual-Shaft Test Rig with Intershaft Bearing. International Journal of Rotating Machinery 2007(2):308–321

    Google Scholar 

  26. Ferraris G, Maisonneuve V, Lalanne M (1996) Prediction of the dynamic behavior of non-symmetrical coaxial co- or counter-rotating rotors. J Sound Vib 195(4):649–666

    Google Scholar 

  27. Childs DW (1976) A Modal Transient Rotordynamic Model for Dual-Rotor Jet Engine Systems. J Manuf Sci Eng 98(3):876–882

    Google Scholar 

  28. Wang N, Jiang D, Hongzhi X Dynamic characteristics analysis of a dual-rotor system with inter-shaft bearing. Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering. https://doi.org/10.1177/0954410017748969

    Google Scholar 

  29. Han QK, Luo HT, Wen BC (2009) Simulations of a Dual-Rotor System with Local Rub-Impacts Based on Rigid-Flexible Multi-Body Model. Key Eng Mater 413-414:677–682

    Google Scholar 

  30. Sun C, Chen Y, Hou L (2016) Steady-state response characteristics of a dual-rotor system induced by rub-impact. Nonlinear Dynamics 86(1):1–15

    Google Scholar 

  31. Jiang D, Wang N (2018) Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults: Theoretical analysis and experimental study. Mechanism & Machine Theory 125:207–219

    Google Scholar 

  32. Wang N, Xu H, Jiang D (2016) Dynamic Model and Fault Feature Research of Dual-Rotor System with Bearing Pedestal Looseness. Math Probl Eng 2016(2):1–18

    Google Scholar 

  33. Yang J, He SZ, Wang LQ (2004) Dynamic Balancing of a Centrifuge: Application to a Dual-Rotor System with Very Little Speed Difference. J Vib Control 10(10):1029–1040

    Google Scholar 

  34. Wang N, Jiang D, Behdinan K (2017) Vibration response analysis of rubbing faults on a dual-rotor bearing system. Arch Appl Mech:1–17

  35. Chiang HWD, Hsu CN, Tu SH (2004) Rotor-Bearing Analysis for Turbomachinery Single- and Dual-Rotor System. J Propuls Power 20(6):1096–1104

    Google Scholar 

Download references

Acknowledgments

The project is supported by the National Natural Science Foundations of China (No. 11572167). We would like to thank China Scholarship Council for support.

Author information

Authors and Affiliations

  1. Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China

    N. Wang, D. Jiang & H. Xu

  2. State Key Laboratory of Control and Simulation of Power System and Generation Equipment, Tsinghua University, Beijing, 100084, China

    N. Wang, D. Jiang & H. Xu

Authors
  1. N. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Wang.

Ethics declarations

Conflict of Interest

There is no conflict of interests in regard to publish of the paper.

Additional information

Publisher’s Note

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

Appendix

Appendix

The stiffness matrix of the Timoshenko beam element:

$$ {K}_T^{es}=\frac{EI}{l^3\left(1+{\Phi}_s\right)}\left[\begin{array}{ccc}12& & \kern1.00em \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\\ {}0& 12& \begin{array}{ccc}& & \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\end{array}\\ {}\begin{array}{c}0\\ {}6l\\ {}\begin{array}{c}-12\\ {}0\\ {}\begin{array}{c}0\\ {}6l\end{array}\end{array}\end{array}& \begin{array}{c}-6l\\ {}0\\ {}\begin{array}{c}0\\ {}-12\\ {}\begin{array}{c}-6l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}\left(4+\Phi \right){l}^2\\ {}0\\ {}\begin{array}{c}0\\ {}6l\\ {}\begin{array}{c}2{l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}\left(4+\Phi \right){l}^2\\ {}\begin{array}{c}-6l\\ {}0\\ {}\begin{array}{c}0\\ {}\left(2-\Phi \right){l}^2\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}12\\ {}0\\ {}\begin{array}{c}0\\ {}-6l\end{array}\end{array}\end{array}& \begin{array}{c} symm\\ {}\\ {}\begin{array}{c}\\ {}12\\ {}\begin{array}{c}6l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\left(4+\Phi \right){l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\left(4+\Phi \right){l}^2\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right] $$
$$ {\Phi}_s=12 EI/{GA}_s{l}^2. $$

The translational inertial matrix of the Timoshenko beam element:

$$ {M}_T^{es}=\frac{\uprho {A}_sl}{820{\left(1+{\Phi}_s\right)}^2}\left[\begin{array}{ccc}{M}_{T1}& & \kern1.00em \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\\ {}0& {M}_{T1}& \begin{array}{ccc}& & \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\end{array}\\ {}\begin{array}{c}0\\ {}{M}_{T2}l\\ {}\begin{array}{c}{M}_{T3}\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{T4}l\end{array}\end{array}\end{array}& \begin{array}{c}-{M}_{T2}l\\ {}0\\ {}\begin{array}{c}0\\ {}{M}_{T3}\\ {}\begin{array}{c}{M}_{T4}l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}{M}_{T5}{l}^2\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{T4}l\\ {}\begin{array}{c}-{M}_{T6}{l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}{M}_{T5}{l}^2\\ {}\begin{array}{c}{M}_{T4}l\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{T6}{l}^2\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}{M}_{T1}\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{T2}l\end{array}\end{array}\end{array}& \begin{array}{c} symm\\ {}\\ {}\begin{array}{c}\\ {}{M}_{T1}\\ {}\begin{array}{c}{M}_{T2}l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}{M}_{T5}{l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}{M}_{T5}{l}^2\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right] $$
$$ {\displaystyle \begin{array}{l}{M}_{T1}=312+588{\Phi}_s+280{\Phi}_s^2,{M}_{T4}=26+63{\Phi}_s+35{\Phi}_s^2\\ {}{M}_{T2}=44+77{\Phi}_s+35{\Phi}_s^2,{M}_{T5}=8+14{\Phi}_s+7{\Phi}_s^2\\ {}{M}_{T3}=108+252{\Phi}_s+140{\Phi}_s^2,{M}_{T56}=6+14{\Phi}_s+7{\Phi}_s^2\end{array}}\kern0.5em {A}_s=\frac{A}{\frac{10}{9}\left(1+\frac{1.6 Dd}{D^2+{d}^2}\right)} $$

The rotational inertial matrix of the Timoshenko beam element:

$$ {M}_R^{es}=\frac{\uprho I}{30{\left(1+{\Phi}_s\right)}^2}\left[\begin{array}{ccc}{M}_{R1}& & \kern1.00em \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\\ {}0& {M}_{R1}& \begin{array}{ccc}& & \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\end{array}\\ {}\begin{array}{c}0\\ {}{M}_{R2}l\\ {}\begin{array}{c}-{M}_{R1}\\ {}0\\ {}\begin{array}{c}0\\ {}{M}_{R2}l\end{array}\end{array}\end{array}& \begin{array}{c}-{M}_{R2}l\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R1}\\ {}\begin{array}{c}-{M}_{R2}l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}{M}_{R5}{l}^2\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R2}l\\ {}\begin{array}{c}-{M}_{R4}{l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}{M}_{R3}{l}^2\\ {}\begin{array}{c}-{M}_{R2}l\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R4}{l}^2\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}{M}_{R1}\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R2}l\end{array}\end{array}\end{array}& \begin{array}{c} symm\\ {}\\ {}\begin{array}{c}\\ {}{M}_{R1}\\ {}\begin{array}{c}{M}_{R2}l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}{M}_{R3}{l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}{M}_{R3}{l}^2\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right] $$
$$ {\displaystyle \begin{array}{l}{M}_{R1}=36,{M}_{R2}=3-15{\Phi}_s,{M}_{R3}=4+5{\Phi}_s+10{\Phi}_s^2\\ {}{M}_{R4}=1+5{\Phi}_s-5{\Phi}_s^2,I=\frac{\uppi}{64}\left({D}^4-{d}^4\right)\end{array}} $$

The gyroscopic matrix of the Timoshenko beam element:

$$ {G}^{es}=\frac{\uprho I}{15l{\left(1+{\Phi}_s\right)}^2}\left[\begin{array}{ccc}0& & \kern1.00em \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\\ {}{M}_{R1}& 0& \begin{array}{ccc}& & \begin{array}{ccc}& & \begin{array}{cc}& \end{array}\end{array}\end{array}\\ {}\begin{array}{c}-{M}_{R2}l\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R1}\\ {}\begin{array}{c}-{M}_{R2}l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c}0\\ {}-{M}_{R2}l\\ {}\begin{array}{c}{M}_{R1}\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R2}l\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}0\\ {}{M}_{R3}{l}^2\\ {}\begin{array}{c}-{M}_{R2}l\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R4}{l}^2\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}0\\ {}\begin{array}{c}0\\ {}-{M}_{R2}l\\ {}\begin{array}{c}{M}_{R4}{l}^2\\ {}0\end{array}\end{array}\end{array}& \begin{array}{ccc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}0\\ {}{M}_{R1}\\ {}\begin{array}{c}{M}_{R2}l\\ {}0\end{array}\end{array}\end{array}& \begin{array}{c} antisymm\\ {}\\ {}\begin{array}{c}\\ {}0\\ {}\begin{array}{c}0\\ {}{M}_{R2}l\end{array}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}0\\ {}{M}_{R3}{l}^2\end{array}\end{array}\end{array}& \begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}\\ {}\begin{array}{c}\\ {}0\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right] $$

where As is effective shear area, A is the cross-sectional area, E is elastic modulus, I is the second moment of area of the cross section about the neutral plane, G is shear modulus, l is the length of beam element, D and d are outer diameter and inner diameter, respectively.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, N., Jiang, D. & Xu, H. Effects of Rub-Impact on Vibration Response of a Dual-Rotor System-Theoretical and Experimental Investigation. Exp Tech 44, 299–311 (2020). https://doi.org/10.1007/s40799-019-00352-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40799-019-00352-w

Keywords

Search

Navigation