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Quasi-analytical solutions for the whirling motion of multi-stepped rotors with arbitrarily distributed mass unbalance running in anisotropic linear bearings

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Vibration in rotating machinery leads to a series of undesired effects, e.g. noise, reduced service life or even machine failure. Even though there are many sources of vibrations in a rotating machine, the most common one is mass unbalance. Therefore, a detailed knowledge of the system behavior due to mass unbalance is crucial in the design phase of a rotor-bearing system. The modelling of the rotor and mass unbalance as a lumped system is a widely used approach to calculate the whirling motion of a rotor-bearing system. A more accurate representation of the real system can be found by a continuous model, especially if the mass unbalance is not constant and arbitrarily oriented in space. Therefore, a quasi-analytical method called Numerical Assembly Technique is extended in this paper, which allows for an efficient and accurate simulation of the unbalance response of a rotor-bearing system. The rotor shaft is modelled by the Rayleigh beam theory including rotatory inertia and gyroscopic effects. Rigid discs can be mounted onto the rotor and the bearings are modeled by linear translational/rotational springs/dampers, including cross-coupling effects. The effect of a constant axial force or torque on the system response is also examined in the simulation.
Rocznik
Strony
art. no. e138999
Opis fizyczny
Bibliogr. 21 poz., il., tab., wykr.
Twórcy
  • 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] J.W. Lund and F.K. Orcutt, “Calculations and Experiments on the Unbalance Response of a Flexible Rotor,” J. Eng. Ind., vol. 89, no. 4, pp. 785–796, 1967.
  • [2] A. Vollan and L. Komzsik, Computational Techniques of Rotor Dynamics with the Finite Element Method. Boca Raton: CRC Press, 2012.
  • [3] J. S. Rao, Rotor Dynamics. New Delhi: New Age International, 1996.
  • [4] A.-C. Lee and Y.-P. Shih, “The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method., J. Vib. Acoust., vol. 115, no. 4, pp. 490–497, 1993.
  • [5] T. Yang and C. Lin, “Estimation of Distributed Unbalance of Rotors,” J. Eng. Gas Turbines Power, vol. 124, no. 4, pp. 976‒983, 2002.
  • [6] 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 Vib., vol. 81, no. 3, pp. 1–10, 1999.
  • [7] J.-S. Wu, F.-T. Lin, and H.-J. Shaw, “Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks,” J. Appl. Mech., vol. 220, no. 3, pp. 451–468, 2014.
  • [8] M. Klanner and K. Ellermann, “Steady-state linear harmonic vibrations of multiple-stepped Euler-Bernoulli beams under arbitrarily distributed loads carrying any number of concentrated elements,” Appl. Comput. Mech., vol. 14, no. 1, pp. 31–50, 2020.
  • [9] M. Klanner, M.S. Prem, and K. Ellermann, “Steady-state harmonic vibrations of a linear rotor-bearing system with a discontinuous shaft and arbitrary distributed mass unbalance,” in Proceedings of ISMA2020 International Conference on Noise and Vibration Engineering and USD2020 International Conference on Uncertainty in Structural Dynamics, Leuven, Belgium, Sep. 2020, pp. 1257–1272.
  • [10] H. Ziegler, “Knickung gerader Stäbe unter Torsion,” J. Appl. Math. Phys. (ZAMP), vol. 3, pp. 96–119, 1952.
  • [11] V.V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability. New York: Pergamon Press, 1963.
  • [12] H. Ziegler, Principles of Structural Stability. Basel: Springer Basel AG, 1977.
  • [13] L. Debnath and D. Bhatta, Integral Transforms and Their Applications. CRC Press, 2015.
  • [14] D. Mitrinović and J.D. Kečkić, The Cauchy Method of Residues. D. Reidel Publishing, 1984.
  • [15] S.I. Hayek, Advanced Mathematical Methods in Science and Engineering. CRC Press, 2010.
  • [16] B. Adcock, D. Huybrechs, and J. Martín-Vaquero, “On the Numerical Stability of Fourier Extensions,” Found. Comput. Math., vol. 14, no. 4, pp. 638–687, 2014.
  • [17] R. Matthysen and D. Huybrechs, “Fast Algorithms for the Computation of Fourier Extensions of Arbitrary Length,” SIAM J. Sci. Comput., vol. 38, no. 2, pp. A899–A922, 2016.
  • [18] A.-C. Lee, Y. Kang, and L. Shin-Li, “A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems,” J. Appl. Mech., vol. 58, no. 3, pp. 776–783, 1991.
  • [19] M.I. Friswell, J.E. T. Penny, S.D. Garvey, and A.W. Lees, Dynamics of Rotating Machines. New York: Cambridge University Press, 2010.
  • [20] A. De Felice and S. Sorrentino, “On the dynamic behaviour of rotating shaftsunder combined axial and torsional loads,” Meccanica, vol. 54, no. 7, pp. 1029–1055, 2019.
  • [21] R.L. Eshleman and R.A. Eubanks, “On the Critical Speeds of a Continuous Rotor,” J. Manuf. Sci. Eng., vol. 91, no. 4, pp. 1180‒1188, 1969.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dcc54ec9-306e-41fc-b545-8612c6d34ab6
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