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Non-linear Modelling of the Rotating Machine in Technical Diagnostics. The Concept of Adequacy Intervals and Weight Functions in the Identification Procedure

  • Jan KicińskiEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

In this paper we will discuss the problem of mathematical description of two basic sub-systems composing a rotating machine, which are the line of rotors with bearings and the supporting structure. If we want to obtain non-elliptic trajectories, with various types of defects in system’s operation and complicated vibration spectra coded in their shapes—which makes the basis for technical diagnostics—we must turn to the non-linear analysis and solve the equations of motion in another reference system. The subsystems that frequently reveal non-linear characteristics include the line of rotors with constructional and operational imperfections (misalignment, shaft cracks), and, undoubtedly, the slide bearings and labyrinth seals. At the same time the supporting structure can be treated with satisfactory accuracy as a subsystem having the linear characteristics.

In this situation a key question is how to unite in one system the supporting structure, with its linear characteristics, and the line of rotors and bearings, rest-ing on the supporting structure and definitely representing the non-linear characteristics. Here, such an elegant notation in the form of a complex matrix for the entire machine is not possible any longer. From the mathematical point of view the situation is becoming dramatically more complicated.

In this paper we will propose solutions to this problem in the form of so-called adequacy intervals of the supporting structure dynamic characteristics, with relevant transformation of those characteristics, and will present a novel concept how to incorporate those characteristics to the rotor line dynamics, based on a so-called weight functions proportional to the vibration spectrum of the supports. The proposed concept can be of extreme value for defining defect-symptom relations, to be used in a new and rapidly developing discipline of science bearing the name of the model based diagnostics.

Keywords:

Dynamics of Rotors and Slide Bearings Identifying Supporting Structure Transformation of Characteristics 

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References

  1. 1.
    Kiciński, J.: Rotor dynamics. IFFM Publishers, Gdansk (2005).Google Scholar
  2. 2.
    Kiciński, J. (Ed.): Modelling and diagnostics of mechanical, aerodynamic and magnetic interactions in power turbosets, PAS Division IV Technical Sciences, IFFM Publishers, Gdansk 2005 (in Polish).Google Scholar
  3. 3.
    Kiciński, J., Drozdowski, R., Materny, P.: The non-linear analysis of the effect of support construction properties on the dynamic properties of multi-support rotor systems. Journal of Sound & Vibration 206(4), 523–539 (1997).Google Scholar
  4. 4.
    Batko,W., Dąbrowski, Z., Kiciński, J.: Nonlinear Effects in Technical Diagnostics. ITE Publishing and Printing House, (2008).Google Scholar
  5. 5.
    Kiciński, J., Prońska, A.: A comparison study of the application of the weight function method for analysing the dynamic state of a three-support laboratory rotor with crack. IFFM PAS Report, Gdansk 2005 (in Polish).Google Scholar
  6. 6.
    Kiciński, J., Prońska, A.: Analysing adequacy intervals and testing the concept of weighting for a large power machine. IFFM PAS Report, Gdansk 2005 (in Polish).Google Scholar
  7. 7.
    Krodkiewski, J.M., Ding, J., Zhang, N.: Identification of unbalance change using a non-linear mathematical model for multi-bearing rotor systems. Journal of Sound and Vibration 169(5), 685– 698 (1994).CrossRefGoogle Scholar
  8. 8.
    Feng, N.S., Hahn, E. J.: Including foundation effects on the vibration behaviour of rotating machinery. Mechanical Systems and Signal Processing 9(3), 243–256 (1995).CrossRefGoogle Scholar
  9. 9.
    Chan, D.S.H.: Nonlinear analysis of rotor dynamic instabilities in high-speed tur-bomachinery. Transactions of the ASME, Journal of Engineering for Gas Turbines and Power 118(1), 122–129 (1996).CrossRefGoogle Scholar
  10. 10.
    Ding J., Krodkiewski M.: Inclusion of static indetermination in the mathematical model for non-linear dynamic analyses of multi-bearing rotor system. Journal of Sound and Vibration 164, 267– 280 (1993).CrossRefGoogle Scholar
  11. 11.
    Chu C.S., Wood, K.L., Busch-Vishniac, I.J.: A nonlinear dynamic model with confidence bounds for hydrodynamic bearings. Transactions of the ASME, Journal of Tribology 120(7), 595– 604 (1998).CrossRefGoogle Scholar
  12. 12.
    Sage, A.P., Melsa, J.L.: System identification. Academic Press, New York (1971).Google Scholar
  13. 13.
    Gerlach, T.: Vibration exciter WZB-2.1. IFFM Report No. 152/97 (in Polish).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Fluid-Flow Machinery, Polish Academy of Sciences (IMP PAN)GdańskPoland

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