Abstract
In rotor dynamics, one of the most common ways for modelling hydrodynamic forces is through the linear coefficients of stiffness and damping since this approach is much less time-consuming. However, in several situations, the rotating system has highly nonlinear behaviour. In these, methods to calculate the hydrodynamic forces in their true nature, without any further simplifications, are required, such as in the fluid-induced instability regime. Therefore, the present work compares numerical vibration data in the time and frequency domains for a real turbine rotor, using linear and nonlinear models to represent the dynamics of hydrodynamic bearings with different geometries. The main analyses are focused on evaluating the effects of nonlinearities on the system’s instability threshold and proposing a way to monitor this process. As a result of using the proposed method, it was observed at the instability threshold, determined in the nonlinear run-up simulations, the excitation of several frequencies and not only the natural frequency as would be expected. This fact evidences the nonlinear character of the phenomenon and the importance of considering nonlinear models to assess the instability threshold of rotating systems. It is concluded that the proposed analysis can monitor the onset of fluid-induced instability in real-time.
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References
Pršić, N., Fragassa, C., Stojanović, V., Pavlovic, A.: Simulation of hydraulic check valve for forestry equipment. Int. J. Heavy Veh. Syst. 24(3), 260 (2017)
Tao, H., Li, J., Chen, Y., Stojanović, V., Yang, H.: Robust point-to-point iterative learning control with trial-varying initial conditions. IET Control Theory Appl. 14(19), 3344–3350 (2020)
Yu, X., Liang, W., Zhang, L., Jin, H., Qiu, J.: Dual-tree complex wavelet transform and SVD based acoustic noise reduction and its application in leak detection for natural gas pipeline. Mech. Syst. Signal Process. 72–73, 266–285 (2015)
Lund, J.W., Thomsen, K.K.: A Calculation Method and Data for the Dynamic Coefficients of Oil-Lubricated Journal Bearings. Topics in Fluid Bearing and Rotor Bearing System Design and Optimization, pp. 11–28. ASME, New York (1978)
Lund, J.W.: Review of the concept of dynamic coefficients for fluid film journal bearings. ASME J. Tribol. 109, 37–41 (1987)
Hattori, H.: Dynamic analysis of a rotor-journal bearing system with large dynamic loads (stiffness and damping coefficients variation in bearing oil films). JSME Int. J. Ser. C36(2), 251–257 (1993)
Khonsari, M.M., Chang, Y.J.: Stability boundary of nonlinear orbits within clearance circle of journal bearings. J. Vib. Acoust. 115, 303–307 (1993)
Machado, T.H., Alves, D.S., Cavalca, K.L.: Discussion about nonlinear boundaries for hydrodynamic forces in journal bearings. Nonlinear Dyn. (2018). https://doi.org/10.1007/s11071-018-4177-2
Smolík, L., Rendl, J., Dyk, S., Polach, P., Hajzman, M.: Threshold stability curves for a nonlinear rotor-bearing system. J. Sound Vib. 442, 698–713 (2018)
Muszynska, A.: Whirl and whip—rotor bearing stability problems. J. Sound Vib. 110(3), 443–462 (1986)
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)
Mendes, R.U., Cavalca, K.L.: On the instability threshold of journal bearing supported rotors. Int. J. Rotating Mach. Article ID 351261 (2014)
Chatzisavvas, I., Boyaci, A., Koutsovasilis, P.: Influence of hydrodynamic thrust bearings on the nonlinear oscillations of high-speed rotors. J. Sound Vib. 380, 224–241 (2016)
Garoli, G.Y., Castro, H.F.: Analysis of a rotor-bearing nonlinear system model considering fluid-induced instability and uncertainties in bearings. J. Sound Vib. 448, 108–129 (2019)
Huang, Y., Tian, Z., Chen, R., Cao, H.: A simpler method to calculate instability threshold speed of hydrodynamic journal bearings. Mech. Mach. Theory 108, 209–216 (2017)
Das, A.S., Nighil, M.C., Dutt, J.K., Irretier, H.: Vibration control and stability analysis of rotor-shaft system with electromagnetic exciters. Mech. Mach. Theory 43, 1295–1316 (2008)
Das, A.S., Nighil, M.C., Dutt, J.K., Irretier, H.: Fluid-induced instability elimination of rotor-bearing system with an electromagnetic exciter. Int. J. Mech. Sci. 52, 581–589 (2010)
Vakakis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear targeted energy transfer in mechanical and structural systems. In: Solid Mechanics and its Applications, p. 647. Springer (2009). https://doi.org/10.1007/978-1-4020-9130-828
Elnady, M.E., Sinha, J.K., Oyadiji, S.O.: Identification of critical speeds of rotating machines using on-shaft wireless vibration measurement. J. Phys. Conf. Ser. 364, 012142 (2012)
Kruger, A.: Transient Dynamic Finite Element Modelling of Flexible Rotor Systems, Dissertation form, University of Pretoria (2014)
Bucher, I.: Experimental decomposition of vibration, whirl and waves in rotating and non-rotating parts. In: IUTAM Symposium on Emerging Trends in Rotor Dynamics, B-S 25 (2011)
Dekys, V., Kalman, P., Hanak, P., Novak, P., Stankovicova, Z.: Determination of vibration sources by using STFT. Proc. Eng. 177, 496–501 (2017)
Li, Q., Wang, W., Chen, L., Sun, D.: Rotor-system log-decrement identification using short-time Fourier-transform filter. Int. J. Rotating Mach. Article ID 809785 (2015)
Su, Y., Gu, Y., Keogh, P.S., Yu, S., Ren, G.: Nonlinear dynamic simulation and parametric analysis of a rotor-AMB-TDB system experiencing strong base shock excitations. Mech. Mach. Theory 155, 104071 (2021)
Tao, H., Wang, P., Chen, Y., Stojanovic, V., Yang, H.: An unsupervised fault diagnosis method for rolling bearing using STFT and generative neural networks. J. Frankl. Inst. 357, 7286–7307 (2020)
Wang, N., Jiang, D., Behdinan, K.: Vibration response analysis of rubbing faults on a dual-rotor bearing system. Arch. Appl. Mech. 87, 1891–1907 (2017)
Wang, N., Liu, C., Jiang, D., Behdinan, K.: Casing vibration response prediction of dual-rotor-blade-casing system with blade-casing rubbing. Mech. Syst. Signal Process. 118, 61–77 (2019)
Wang, N., Jiang, D.: Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults: theoretical analysis and experimental study. Mach. Theory 125, 207–219 (2018)
Machado, T.H., Cavalca, K.L.: Modeling of hydrodynamic bearing wear in rotor-bearing systems. Mech. Res. Commun. (2015). https://doi.org/10.1016/j.mechrescom.2015.05.008
Acknowledgements
The authors would like to thank Coordination of Superior Level Staff Improvement – CAPES, National Council for Scientific and Technological Development – CNPq, Grant # 424899/2018-3, and Grants # 2017/07454-8 and # 2018/21581-5 from the São Paulo Research Foundation (FAPESP) for the financial support to this research.
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Viana, C.A.A., Alves, D.S. & Machado, T.H. Influence of fluid film bearing nonlinearities on monitoring the fluid-induced instability threshold. Nonlinear Dyn 108, 1987–2006 (2022). https://doi.org/10.1007/s11071-022-07302-z
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DOI: https://doi.org/10.1007/s11071-022-07302-z