Abstract
In this paper, the steady-state responses and their stability of a dual-rotor system with rub-impact are investigated. The nonlinear equations of motion in eight d.o.f.s are obtained with the consideration of the gyroscopic effect. The multi-harmonic balance combined with the alternating frequency/time domain technique (MHB–AFT) is utilized to calculate the accurate amplitude of each harmonic component. Arc-length continuation is embedded in the MHB–AFT procedure to trace the branch of the periodic solutions, and the Floquet theory is used to discuss the stability of the obtained solutions. Through the numerical calculation, complicated nonlinear phenomena, such as combined harmonic vibrations, hysteresis and resonant peak shifting are obtained when the rub-impact occurs. The result also shows that the control parameters such as mass eccentricity, inter-shaft stiffness and rotational speed ratio make significant but different influences on the dynamic characteristics of the two rotors. Therefore, the contribution of this study is to provide a further understanding of the steady-state response characteristics of the dual-rotor system with rub-impact.
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References
Muszynska, A.: Rotor-to-stationary element rub-related vibration phenomena in rotating machinery. Shock Vib. Dig. 21, 3–11 (1989)
Ahmad, S.: Rotor casing contact phenomenon in rotor dynamics–literature survey. J. Vib. Control 16(9), 1369–1377 (2010)
Jiang, J., Chen, Y.H.: Advances in the research on nonlinear phenomena in rotor/stator rubbing systems. Adv. Mech. 43(1), 132–148 (2013)
Zhou, H.L., Chen, G.: Dynamic response analysis of dual rotor-ball bearing-stator coupling system for aero-engine. J. Aerosp. Power 24(6), 1284–1291 (2009)
Han, Q.K., Luo, H.T., Wen, B.C.: Simulations of a dual-rotor system with local rub-impacts based on rigid-flexible multi-body model. Key Eng. Mater. 413, 677–682 (2009)
Chen, S.T., Wu, Z.Q.: Rubbing vibration analysis for a counter-rotating dual-rotor system. J. Vib. Shock 31(23), 142–147 (2012)
Shan, Y.C., Liu, X.D., He, T., Li, Q.H.: Research on the finite element impact-contact analytical model of dual-rotor system and its diagnosis method. J. Aerosp. Power 20(5), 789–794 (2005)
Wang, S.J., Liao, M.F., Jiang, Y.F., Ding, X.F.: Experimental study on local rub-impact fault of counter-rotoring dual-rotor. J. Propuls. Technol. 34(1), 31–36 (2013)
Chua, L.O., Ushida, A.: Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies. IEEE Trans. Circuits Syst. 28(10), 953–971 (1981)
Kim, Y.B., Noah, S.T.: Quasi-periodic response and stability analysis for a non-linear Jeffcott rotor. J. Sound Vib. 190(2), 239–253 (1996)
Kim, Y.B., Choi, S.K.: A multiple harmonic balance method for the internal resonant vibration of a non-linear Jeffcott rotor. J. Sound Vib. 208(5), 745–761 (1997)
Guskov, M., Sinou, J.J., Thouverez, F.: Multi-dimensional harmonic balance applied to rotor dynamics. Mech. Res. Commun. 35(8), 537–545 (2008)
Zucca, S., Firrone, C.M.: Nonlinear dynamics of mechanical systems with friction contacts: coupled static and dynamic multi-harmonic balance method and multiple solutions. J. Sound Vib. 333(3), 916–926 (2014)
Akgün, D., Cankaya, I.: Frequency response investigations of multi-input multi-output nonlinear systems using automated symbolic harmonic balance method. Nonlinear Dyn. 61(4), 803–818 (2010)
Pušenjak, R.R., Oblak, M.M.: Incremental harmonic balance method with multiple time variables for dynamical systems with cubic nonlinearities. Int. J. Numer. Methods Eng. 59(2), 255–292 (2004)
Hou, L., Chen, Y.S., Cao, Q.J.: Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight. Commun. Nonlinear Sci. 19(1), 286–297 (2014)
Liu, L., Cao, D.Q., Sun, S.P.: Dynamic characteristics of a disk-drum-shaft rotor system with rub-impact. Nonlinear Dyn. 80(1–2), 1017–1038 (2015)
Lam, W.F., Morley, C.T.: Arc-length method for passing limit points in structural calculation. J. Struct. Eng. 118(1), 169–185 (1992)
Peletan, L., Baguet, S., Torkhani, M.: Quasi-periodic harmonic balance method for rubbing self-induced vibrations in rotor-stator dynamics. Nonlinear Dyn. 78(4), 2501–2515 (2014)
Von Groll, G., Ewins, D.J.: The harmonic balance method with arc-length continuation in rotor/stator contact problems. J. Sound Vib. 241(2), 223–233 (2001)
Seydel, R.: Practical Bifurcation and Stability Analysis. Springer, New York (2010)
Huang, X.D., Zeng, Z.G., Ma, Y.N.: The Theory and Methods for Nonlinear Numerical Analysis. Wuhan University Press, Wuhan (2004)
Chen, Y.S.: Nonlinear Vibrations. Higher Education Press, Beijing (2002)
Hsu, C.S.: Impulsive parametric excitation: theory. J. Appl. Mech. 39, 551–558 (1972)
Hsu, C.S., Cheng, W.H.: Applications of the theory of impulsive parametric excitation and new treatments of general parametric excitation problems. J. Appl. Mech. 40, 78–86 (1973)
Zhang, H.B., Chen, Y.S.: Bifurcation analysis on full annular rub of a nonlinear rotor system. Sci. China Technol. Sci. 54(8), 1977–1985 (2011)
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The authors would like to acknowledge the financial supports from the National Basic Research Program (973 Program) of China (Grant No. 2015CB057400) and the China Postdoctoral Science Foundation (Grant No. 2016M590277).
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Sun, C., Chen, Y. & Hou, L. Steady-state response characteristics of a dual-rotor system induced by rub-impact. Nonlinear Dyn 86, 91–105 (2016). https://doi.org/10.1007/s11071-016-2874-2
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DOI: https://doi.org/10.1007/s11071-016-2874-2