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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 7/2019

07-02-2019 | Original

Nonlinear vibration and dynamic stability analysis of rotor-blade system with nonlinear supports

Authors: Bingqiang Li, Hui Ma, Xi Yu, Jin Zeng, Xumin Guo, Bangchun Wen

Published in: Archive of Applied Mechanics | Issue 7/2019

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Abstract

A dynamic model of a rotor-blade system is established considering the effect of nonlinear supports at both ends. In the proposed model, the shaft is modeled as a rotating beam where the gyroscopic effect is considered, while the shear deformation is ignored. The blades are modeled as Euler–Bernoulli beams where the centrifugal stiffening effect is considered. The equations of motion of the system are derived by Hamilton principle, and then, Coleman and complex transformations are adopted to obtain the reduced-order system. The nonlinear vibration and stability of the system are studied by multiple scales method. The influences of the normal rubbing force, friction coefficient, damping and support stiffness on the response of the rotor-blade system are investigated. The results show that the original hardening type of nonlinearity may be enhanced or transformed into softening type due to the positive or negative nonlinear stiffness terms of the bearing. Compared with the system with higher support stiffness, the damping of the bearing has a more powerful effect on the system stability under lower support stiffness. With the increase in rubbing force and support stiffness, the jump-down frequency, resonant peak and the frequency range in which the system has unstable responses increase.
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Appendix
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Literature
1.
Khadem, S.E., Shahgholi, M., Hosseini, S.A.A.: Primary resonances of a nonlinear in-extensional rotating shaft. Mech. Mach. Theory 45(8), 1067–1081 (2010)CrossRefMATH
2.
Khadem, S.E., Shahgholi, M., Hosseini, S.A.A.: Two-mode combination resonances of an in-extensional rotating shaft with large amplitude. Nonlinear Dyn. 65(3), 217–233 (2011)MathSciNetCrossRefMATH
3.
Shahgholi, M., Khadem, S.: Resonances of an in-extensional asymmetrical spinning shaft with speed fluctuations. Meccanica 48(1), 103–120 (2013)MathSciNetCrossRefMATH
4.
Chiu, Y.Z., Chen, D.Z.: The coupled vibration in a rotating multi-disk rotor system. Int. J. Mech. Sci. 53(1), 1–10 (2011)CrossRef
5.
Chiu, Y.Z., Huang, S.C.: The influence on coupling vibration of a rotor system due to a mistuned blade length. Int. J. Mech. Sci. 49(4), 522–532 (2007)CrossRef
6.
Ma, H., Lu, Y., Wu, Z.Y., et al.: A new dynamic model of rotor-blade systems. J. Sound Vib. 357, 168–194 (2015)CrossRef
7.
Genta, G., Feng, C., Tonoli, A.: Dynamics behavior of rotating bladed discs: a finite element formulation for the study of second and higher order harmonics. J. Sound Vib. 329(25), 5289–5306 (2010)CrossRef
8.
Diken, H., Alnefaie, K.: Effect of unbalanced rotor whirl on blade vibrations. J. Sound Vib. 330(14), 3498–3506 (2011)CrossRef
9.
Wang, L., Cao, D.Q., Huang, W.: Nonlinear coupled dynamics of flexible blade-rotor-bearing systems. Tribol. Int. 43(4), 759–778 (2010)CrossRef
10.
Santos, I.F., et al.: Contribution to experimental validation of linear and non-linear dynamic models for representing rotor-blade parametric coupled vibrations. J. Sound Vib. 271(3–5), 883–904 (2004)CrossRef
11.
Najafi, A., Ghazavi, M.R., Jafari, A.A.: Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor. Nonlinear Dyn. 78(2), 1049–1064 (2014)MathSciNetCrossRefMATH
12.
Najafi, A., Ghazavi, M.R., Jafari, A.A.: Application of Krein’s theorem and bifurcation theory for stability analysis of a bladed rotor. Meccanica 49(6), 1507–1526 (2014)MathSciNetCrossRefMATH
13.
Ghazavi, M.R., Najafi, A., Jafari, A.A.: Bifurcation and nonlinear analysis of nonconservative interaction between rotor and blade row. Mech. Mach. Theory 65, 29–45 (2013)CrossRef
14.
Sanches, L., et al.: Instability zones for isotropic and anisotropic multibladed rotor configurations. Mech. Mach. Theory 46(8), 1054–1065 (2011)CrossRefMATH
15.
Parent, M.O., Thouverez, F.: Phenomenological model for stability analysis of bladed rotor-to-stator contacts. Int. Symp. Transp. Phenom. Dyn. Rotating Mach. 10–15, 1–13 (2016)
16.
Hou, L., Chen, Y.S., Fu, Y.Q., Li, Z.G.: Nonlinear response and bifurcation analysis of a Duffing type rotor model under sine maneuver load. Int. J. Non-linear Mech. 78, 133–141 (2016)CrossRef
17.
Hou, L., Chen, Y.S., Cao, Q.J.: Nonlinear vibration phenomenon of an air-craft rub-impact rotor system due to hovering flight. Commun. Nonlinear Sci. Numer. Simulat. 19, 286–297 (2014)CrossRefMATH
18.
Bolotin, V.V.: Nonconservative Problems of the Theory of Elastic Stability. Pergamon Press, New York (1963)MATH
19.
Kleim, W., Pommer, C., Stoustrup, J.: Stability of rotor systems: a complex modeling approach. ZAMP 49, 644–655 (1998)MATH
20.
21.
Bucciarelli, L.L.: On the instability of rotating shafts due to internal damping. J. Appl. Mech. 49(2), 425–428 (1982)CrossRefMATH
22.
Sorge, F., Cammalleri, M.: On the beneficial effect of rotor suspension anisotropy on viscous-dry hysteretic instability. Meccanica 47(7), 1705–1722 (2012)CrossRefMATH
23.
Samantaray, A.K., Mukherjee, A., Bhattacharyya, R.: Some studies on rotors with polynomial type non-linear external and internal damping. Int. J. Non-linear Mech. 41(9), 1007–1015 (2006)CrossRefMATH
24.
Genta, G.: On the stability of rotating blade arrays. J. Sound Vib. 273(4–5), 805–836 (2004)CrossRef
25.
Bab, S., Khadem, S.E., Abbsi, A., Shahgholi, M.: Dynamic stability and nonlinear vibration analysis of a rotor system with flexible/rigid blades. Mech. Mach. Theory 105, 633–653 (2016)CrossRef
26.
Petrov, E.: Multiharmonic analysis of nonlinear whole engine dynamics with bladed disc-casing rubbing contacts. In: ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers
27.
Petrov, E.: Analysis of bifurcations in multiharmonic analysis of nonlinear forced vibrations of gas-turbine engine structures with friction and gaps. In: ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers
28.
Sinha, S.K.: Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end. Int. J. Nonlinear Mech. 40, 113–149 (2015)CrossRefMATH
29.
Sinha, S.K.: Combined torsional-bending-axial dynamics of a twisted rotating cantilever Timoshenko beam with contact-impact loads at the free end. J. Appl. Mech. 74, 505–522 (2007)CrossRefMATH
30.
Turner, K., Adams, M., Dunn, M.: Simulation of engine blade tip-rub induced vibration. In: ASME Turbo Expo: Power for Land, Sea and Air, pp. 391–396 (2005)
31.
Turner, K., Dunn, M., Padova, C.: Airfoil deflection characteristics during rub events. J. Turbomach. 134, 112–121 (2012)CrossRef
32.
Kou, H.J., Yuan, H.Q.: Rub-induced non-linear vibrations of a rotating large deflection plate. Int. J. Nonlinear Mech. 58, 283–294 (2014)CrossRef
33.
Ma, H., Wang, D., Tai, X.Y., Wen, B.C.: Vibration response analysis of blade-disk dovetail structure under blade tip rubbing condition. J. Vib. Control 23, 252–271 (2017)CrossRef
34.
Wang, C., Zhang, D.Y., Ma, Y.H., Liang, Z.C., Hong, J.: Dynamic behavior of aero-engine rotor with fusing design suffering blade off. Chin. J. Aeronaut. 30, 918–931 (2017)CrossRef
35.
Wang, C., Zhang, D.Y., Ma, Y.H., Liang, Z.C., Hong, J.: Theoretical and experimental investigation on the sudden unbalance and rub-impact in rotor system caused by blade off. Mech. Syst. Signal Process. 76–77, 111–135 (2016)CrossRef
36.
Yu, P.C., Zhang, D.Y., Ma, Y.H., Hong, J.: Dynamic modeling and vibration characteristics analysis of the aero-engine dual-rotor system with fan blade out. Mech. Syst. Signal Process. 106, 158–175 (2018)CrossRef
37.
Ma, H., Yin, F.L., Wu, Z.Y., Tai, L.X.Y.: Nonlinear vibration response analysis of a rotor-blade system with blade-tip rubbing. Nonlinear Dyn. 84, 1225–1258 (2016)MathSciNetCrossRef
38.
Ma, H., Tai, X.Y., Han, Q.K., Wu, Z.Y., Wang, D., Wen, B.C.: A revised model for rubbing between rotating blade and elastic casing. J. Sound Vib. 337, 301–320 (2015)CrossRef
39.
Yuan, H.Q.: Analysis Method of Rotor Dynamics. Metallurgical Industry Press, Beijing (2017)
Metadata
Title
Nonlinear vibration and dynamic stability analysis of rotor-blade system with nonlinear supports
Authors
Bingqiang Li
Hui Ma
Xi Yu
Jin Zeng
Xumin Guo
Bangchun Wen
Publication date
07-02-2019
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 7/2019
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-019-01509-0

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