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Research nonlinear vibrations of a dual-rotor system with nonlinear restoring forces

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

A dual-rotor system is a core component of an aero-engine, and it is very important to study the nonlinear vibrational characteristics for the aero-engine’s development. Based on analyzing structural characteristics of aero-engine’s rotors, a novel and more practical dual-rotor dynamic coupling model with nonlinear restoring forces of high-pressure and low-pressure rotors is first proposed. In the linear dynamic coupling model, the coupling critical speed, natural frequencies and vibration responses of the low-pressure rotor are analyzed systematically. In the nonlinear dynamic coupling model, the vibrational characteristics of the dual-rotor system with different nonlinear parameters are simulated numerically based on the nonlinear dynamic theory. The improved shooting method combined the harmonic balance method, and the genetic algorithm is proposed to calculate theoretical solutions of the nonlinear dynamic coupling model. The stability of theoretical solutions is investigated by the Floquet theory. The research results show that the dual-rotor system appears very complicated nonlinear vibrations such as nonlinear multitudinal solutions, double period motions, almost periodic motions and chaotic motions. The transition between nonlinear vibrations occurs suddenly.

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Abbreviations

xi, yi :

Displacement in x and y directions

r i :

Radial deflection of the rotor

θx, θy :

Inclination of the low-pressure rotor in x and y directions

θ, θ1 :

Inclination angle of the shaft at the position of the disk, Euler angle representing an inclination of the Z1-axis

m i :

Mass of the dual rotor

ei, τ :

Eccentricity of the dual rotor, skew angle of the low-pressure rotor

I, Ip :

Moment of inertia of the low-pressure shaft, polar moment of inertia of the low-pressure disk

c11, c12, c21, c22, c :

Damping coefficients of the dual rotor

α, γ, δ, k :

Stiffness coefficients of the dual rotor

β τ :

Inclination initial value of the low-pressure rotor

ωi, ωLj, ωH, ω :

Rotating speed of the dual rotor, major critical speed of the low-pressure rotor, major critical speed of the high-pressure rotor, excitation rotational speed

PLx, PLy, PL, Pθ, PH :

Amplitudes of the low-pressure rotor in x and y directions, amplitudes of deflection and amplitude of inclination of the low pressure, amplitude of the high-pressure rotor

M-XYZ, M-X1Y1Z1, M-X0Y0Z0,:

Translating coordinate system and rotating coordinate systems [when i = 1 (2), it is parameters of the low (high) pressure rotor]

References

  1. Yamamoto T (1955) On the vibrations of a shaft supported by bearings having radial clearances. Trans Jpn Soc Mech Eng 21(103):186–192. https://doi.org/10.1299/kikai1938.21.186

    Article  Google Scholar 

  2. Ishida Y, Inoue T, Liu J et al (2008) Vibrations of an asymmetrical shaft with gravity and nonlinear spring characteristics (isolated resonances and internal resonances). J Vib Acoust Trans ASME 130(4):178–187. https://doi.org/10.1115/1.2889475

    Article  Google Scholar 

  3. Ishida Y, Inoue T (1997) Internal resonance of the Jeffcott rotor (critical speed of twice the major critical speed). Trans Jpn Soc Mech Eng 63(606):321–327 (in Japanese)

    Article  Google Scholar 

  4. Ehrich FF (1988) High order subharmonic response of high speed rotors in bearing clearance. J Vib Acoust-Trans ASME 110(1):9–16. https://doi.org/10.1115/1.3269488

    Article  Google Scholar 

  5. Ehrich FF (1991) Some observations of chaotic vibration phenomena in high-speed rotordynamics. J Vib Acoust-Trans ASME 113(1):50–57. https://doi.org/10.1115/1.2930154

    Article  Google Scholar 

  6. Sinou JJ, Lees AW (2007) A non-linear study of a cracked rotor. Eur J Mech A-Solids 26(1):152–170. https://doi.org/10.1016/j.euromechsol.2006.04.002

    Article  MATH  Google Scholar 

  7. Sinou JJ, Lees AW (2005) The influence of cracks in rotating shafts. J Sound Vibr 285(4–5):1015–1037. https://doi.org/10.1016/j.jsv.2004.09.008

    Article  Google Scholar 

  8. Liu J, Liu WL, Chen JN (2019) Research of vibration characteristics based on a crystal format model of rotor. J Sound and Vibr 460:114864. https://doi.org/10.1016/j.jsv.2019.114864

    Article  Google Scholar 

  9. Jiang J, Ulbrich H (2001) Stability analysis of slidingwhirl in a nonlinear Jeffcott rotor with cross-coupling stiffness coefficients. Nonlinear Dyn 24(3):269–283. https://doi.org/10.1023/A:1008376412944

    Article  MATH  Google Scholar 

  10. Jiang J, Ulbrich H, Chavez A (2003) Improvement of rotor performance under rubbing conditions through active auxiliary bearings. Int J Non-Linear Mech 41(8):949–957. https://doi.org/10.1016/j.ijnonlinmec.2006.08.004

    Article  Google Scholar 

  11. Chu F, Zhang Z (1998) Bifurcation and chaos in a rub-impact Jeffcott rotor system. J Sound Vibr 210(1):1–18. https://doi.org/10.1006/jsvi.1997.1283

    Article  Google Scholar 

  12. Chu F, Zhang Z (1997) Periodic, quasi-periodic and chaotic vibrations of a rub-impact rotor system supported on oil film bearings. Int J Eng Sci 35(10–11):963–973. https://doi.org/10.1016/S0020-7225(97)89393-7

    Article  MATH  Google Scholar 

  13. Zhang Z, Wan K, Li J et al (2018) Synchronization identification method for unbalance of dual-rotor system. J Braz Soc Mech Sci Eng. https://doi.org/10.1007/s40430-018-1133-5

    Article  Google Scholar 

  14. Hu Q, DengA comparison study on S et al (2011) A 5-DOF model for aeroengine spindle dual-rotor system analysis. Chin J Aeronaut 24(2):224–234. https://doi.org/10.1016/S1000-9361(11)60027-7

    Article  Google Scholar 

  15. Deng S, He F, Yang H et al (2010) Analysis on dynamic characteristics of a dual rotor-rolling bearing coupling system for aero-engine. J Aerosp Power 25(10):2386–2395

    Google Scholar 

  16. Yang X, Luo G, Tang Z et al (2014) Modeling method and dynamic characteristics of high-dimensional counter-rotating dual rotor system. J Aerosp Power 29(3):585–595

    Google Scholar 

  17. Wang F, Luo G, Yan S et al (2017) A comparison study on co- and counterrotating dual-rotor system with squeeze film dampers and intermediate bearing. Shock Vibr 4:1–25. https://doi.org/10.1155/2017/5493763

    Article  Google Scholar 

  18. Jin Y, Lu K, Huang C et al (2019) Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method. Appl Math Model 75(2019):553–571. https://doi.org/10.1016/j.apm.2019.05.045

    Article  MathSciNet  MATH  Google Scholar 

  19. Lu Z, Wang X, Hou L et al (2019) Nonlinear response analysis for an aero engine dual-rotor system coupled by the inter-shaft bearing. Arch Appl Mech 89:1275–1288. https://doi.org/10.1007/s00419-018-01501-0

    Article  Google Scholar 

  20. Sun C, Chen Y, Hou L (2016) Steady-state response characteristics of a dual-rotor system induced by rub-impact. Nonlinear Dyn 86(1):1–15. https://doi.org/10.1007/s11071-016-2874-2

    Article  Google Scholar 

  21. Sun C, Chen Y, Hou L (2018) Nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact. Arch Appl Mech 88(8):1305–1324. https://doi.org/10.1007/s00419-018-1373-y

    Article  Google Scholar 

  22. Xu H, Wang N, Jiang D et al (2016) Dynamic characteristics and experimental research of dual-rotor system with rub-impact fault. Shock Vibr 3:1–11. https://doi.org/10.1155/2016/6239281

    Article  Google Scholar 

  23. Yang Y, Ouyang H, Yang Y et al (2020) Vibration analysis of a dual-rotor-bearing-double casing system with pedestal looseness and multi-stage turbine blade-casing rub. Mech Syst Signal Process 143:106845. https://doi.org/10.1016/j.ymssp.2020.106845

    Article  Google Scholar 

  24. Wang N, Jiang D (2018) Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults: Theoretical analysis and experimental study. Mech Mach Theory 125:207–219. https://doi.org/10.1016/j.mechmachtheory.2018.03.009

    Article  Google Scholar 

  25. Gao P, Hou L, Yang R et al (2019) Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system. Appl Math Model 68:29–47. https://doi.org/10.1016/j.apm.2018.11.014

    Article  MathSciNet  MATH  Google Scholar 

  26. Yamamoto T, Ishida Y, Kawasumi J (2008) Oscillations of a rotating shaft with symmetrical nonlinear spring characteristics. Bull JSME 41(341):133–142. https://doi.org/10.1299/kikai1938.41.133

    Article  Google Scholar 

  27. Yamamoto T, Ishida Y (2012) Linear and nonlinear rotordynamics: a modern treatment with applications, 2nd edn. Wiley, New York

    Google Scholar 

  28. Yamamoto T, Ishida Y (1997) Theoretical discussions on vibrations of a rotating shaft with nonlinear spring characteristics. Ingenieur-Archiv 46(2):125–135. https://doi.org/10.1007/BF00538746

    Article  MATH  Google Scholar 

  29. Wolf A, Swift JB, Swinney HL et al (1985) Determining Lyapunov exponents from a time series. Phys D 16(3):285–317. https://doi.org/10.1016/0167-2789(85)90011-9

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFB1303304) and the Tianjin Natural Science Foundation of China (Grant No.17JCZDJC38500).

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Authors and Affiliations

  1. Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechanical System, National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China

    Jun Liu & Chang Wang

  2. Department of Computational Science Graduate School of System Informatics, KOBE University, 657-8501, Kobe, Japan

    Zhiwei Luo

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  1. Jun Liu
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Correspondence to Jun Liu.

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Technical Editor: Thiago Ritto.

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Liu, J., Wang, C. & Luo, Z. Research nonlinear vibrations of a dual-rotor system with nonlinear restoring forces. J Braz. Soc. Mech. Sci. Eng. 42, 461 (2020). https://doi.org/10.1007/s40430-020-02541-w

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