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Numerical investigation of rotor-bearing systems with fractional derivative material damping models

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Języki publikacji
EN
Abstrakty
EN
The increasing demand for high-speed rotor-bearing systems results in the application of complex materials, which allow for a better control of the vibrational characteristics. This paper presents a model of a rotor including viscoelastic materials and valid up to high spin speeds. Regarding the destabilization of rotor-bearing systems, two main effects have to be investigated, which are strongly related to the associated internal and external damping of the rotor. For this reason, the internal material damping is modeled using fractional time derivatives, which can represent a large class of viscoelastic materials over a wide frequency range. In this paper, the Numerical Assembly Technique (NAT) is extended for the rotating viscoelastic Timoshenko beam with fractional derivative damping. An efficient and accurate simulation of the proposed rotor-bearing model is achieved. Several numerical examples are presented and the influence of internal damping on the rotor-bearing system is investigated and compared to classical damping models.
Rocznik
Strony
art. no. e148610
Opis fizyczny
Bibliogr. 30 poz., rys., tab.
Twórcy
  • Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria
autor
  • Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria
  • Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria
  • Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria
Bibliografia
  • [1] M. Klanner, M. Prem, and K. Ellermann, “Quasi-analytical solutions for the whirling motion of multi-stepped rotors with arbitrarily distributed mass unbalance running in anisotropic linear bearings,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 69, no. 6, p. e138999, Dec 2021, doi: 10.24425/bpasts.2021.138999.
  • [2] P. Nutting, “A new general law of deformation,” J. Frankl. Inst., vol. 191, no. 5, pp. 679–685, May 1921, doi: 10.1016/s0016-0032(21)90171-6.
  • [3] T. Pritz, “Analysis of four-parameter fractional derivative model of real solid materials,” J. Sound Vibr., vol. 195, no. 1, pp. 103–115, Aug 1996, doi: 10.1006/jsvi.1996.0406.
  • [4] A. Labuschagne, N. van Rensburg, and A. van der Merwe, “Comparison of linear beam theories,” Math. Comput. Model., vol. 49, no. 1-2, pp. 20–30, Jan 2009, doi: 10.1016/j.mcm.2008.06.006.
  • [5] P. Ruge and C. Birk, “A comparison of infinite Timoshenko and Euler–Bernoulli beam models on winkler foundation in the frequency- and time-domain,” J. Sound Vibr., vol. 304, no. 3-5, pp. 932–947, Jul 2007, doi: 10.1016/j.jsv.2007.04.001.
  • [6] R. Tamrakar and N. Mittal, “Modal behaviour of rotor considering rotary inertia and shear effects,” Persp. Sci., vol. 8, pp. 87–89, Sep 2016, doi: 10.1016/j.pisc.2016.04.003.
  • [7] E. S. Zorzi and H. D. Nelson, “Finite element simulation of rotor-bearing systems with internal damping,” J. Eng. Power, vol. 99, pp. 71–76, 1977.
  • [8] G. Genta, “On a persistent misunderstanding of the role of hysteretic damping in rotordynamics,” J. Vib. Acoust., vol. 126, no. 3, pp. 459–461, Jul 2004, doi: 10.1115/1.1759694.
  • [9] K. Baumann, E. Bopple, R. Markert, and W. Schwarz, “Einfluss der inneren Dämpfung auf das dynamische Verhalten von elastischen Rotoren,” VDI Berichte, no. 2003, pp. 55–69, 2007.
  • [10] H.D. Nelson, “A finite rotating shaft element using timoshenko beam theory,” J. Mech. Des., vol. 102, no. 4, pp. 793–803, Oct 1980, doi: 10.1115/1.3254824.
  • [11] H. N. Özgüven and Z. Özkan, “Whirl speeds and unbalance response of multibearing rotors using finite elements,” J. Vib. Acoust.-Trans. ASME, vol. 106, pp. 72–79, 1984.
  • [12] M.A. Prohl, “A general method for calculating critical speeds of flexible rotors,” J. Appl. Mech., vol. 12, no. 3, pp. A142–A148, Sep 1945, doi: 10.1115/1.4009455.
  • [13] A.-C. Lee, Y.-P. Shih, and Y. Kang, “Analysis of linear rotor-bearing systems. A general transfer matrix method,” J. Vib. Acoust.-Trans. ASME, vol. 115, no. 4, pp. 490–497, Oct 1993.
  • [14] Y.-P. Shih and A.-C. Lee, “Identification of the unbalance distribution in flexible rotors,” Int. J. Mech. Sci., vol. 39, pp. 841–857, 1997.
  • [15] O. Özşahin, H. Özgüven, and E. Budak, “Analytical modeling of asymmetric multi-segment rotor – bearing systems with timoshenko beam model including gyroscopic moments,” Comput. Struct., vol. 144, pp. 119–126, Nov 2014, doi: 10.1016/j.compstruc.2014.08.001.
  • [16] J.-S. Wu and H.-M. Chou, “A new approach for determining the natural frequencies and mode shapes of a uniform beam carrying any number of sprung masses,” J. Sound Vibr., vol. 220, no. 3, pp. 451–468, Feb 1999, doi: 10.1006/jsvi.1998.1958.
  • [17] M. Klanner, M. Prem, and K. Ellermann, “Steady-state harmonic vibrations of a linear rotor-bearing system with a discontinuous shaft and arbitrarily distributed mass unbalance,” in Proceedings of ISMA 2020 International Conference on Noise and Vibration Engineering and USD2020 International Conference on Uncertainty in Structural Dynamics, Oct 2020, pp. 1257–1272.
  • [18] G. Quinz, M. Prem, M. Klanner, and K. Ellermann, “Balancing of a linear elastic rotor-bearing system with arbitrarily distributed unbalance using the numerical assembly technique,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 69, no. 6, p. e138237, Dec 2021, doi: 10.24425/bpasts.2021.138237.
  • [19] G. Quinz, M. Klanner, and K. Ellermann, “Balancing of flexible rotors supported on fluid film bearings by means of influence coefficients calculated by the numerical assembly technique,” Energies, vol. 15, no. 6, pp. 1–18, Mar 2022, doi: 10.3390/en15062009.
  • [20] G. Quinz, M. Klanner, and K. Ellermann, “Balancing of rotor-bearing systems without trial runs using the numerical assembly technique – an experimental investigation,” in Proceedings of ISMA 2022 International Conference on Noise and Vibration Engineering and USD2022 International Conference on Uncertainty in Structural Dynamics, Sep 2022, pp. 1542–1553.
  • [21] G. Quinz, G. Überwimmer, M. Klanner, and K. Ellermann, “Field balancing of flexible rotors without trial runs using the numerical assembly technique,” in Proceedings of the SIRM2023: 15th European Conference on Rotordynamics, Feb 2023.
  • [22] R.L. Bagley and P.J. Torvik, “A theoretical basis for the application of fractional calculus to viscoelasticity,” J. Rheol., vol. 27, no. 3, pp. 201–210, Jun 1983, doi: 10.1122/1.549724.
  • [23] M. Caputo and F. Mainardi, “A new dissipation model based on memory mechanism,” Pure Appl. Geophys. PAGEOPH, vol. 91, no. 1, pp. 134–147, 1971, doi: 10.1007/bf00879562.
  • [24] M. Caputo, “Linear models of dissipation whose q is almost frequency independent – II,” Geophys. J. Int., vol. 13, no. 5, pp. 529–539, Nov 1967, doi: 10.1111/j.1365-246x.1967.tb02303.x.
  • [25] K. Singh, R. Saxena, and S. Kumar, “Caputo-based fractional derivative in fractional fourier transform domain,” IEEE J. Emerg. Sel. Top. Circuits Syst., vol. 3, no. 3, pp. 330–337, Sep 2013, doi: 10.1109/jetcas.2013.2272837.
  • [26] G. Genta, Dynamics of Rotating Systems. Springer-Verlag, 2005, doi: 10.1007/0-387-28687-x.
  • [27] O.A. Bauchau and J.I. Craig, Structural Analysis. Springer-Verlag GmbH, Aug 2009.
  • [28] P. Hagedorn and A. DasGupta, Vibrations and Waves in Continuous Mechanical Systems. John Wiley & Sons, 2007.
  • [29] M.I. Friswell, J.E.T. Penny, S.D. Garvey, and A.W. Lees, Dynamics of Rotating Machines. Cambridge University Press, Mar 2010, doi: 10.1017/cbo9780511780509.
  • [30] M. Caputo and F. Mainardi, “Linear models of dissipation in anelastic solids,” La Rivista del Nuovo Cimento, vol. 1, no. 2, pp. 161–198, Apr 1971, doi: 10.1007/bf02820620.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-487da6ba-f4aa-4b2d-a133-81f918c47bf9
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