Proceedings of the 5th Asian Conference on Multibody Dynamics 2010, 2, 995–998p. (2010)

Application of the recurrence plots algorithm to analysis of chaotic vibrations of rotor systems with hydrostatodynamic bearings

S. Leonid, M. Andrey, M. Sergey

This paper represents a novel algorithm of nonlinear analysis of vibrations of rotor systems with fluid-film bearings (particularly with hydrostatodynamic bearings with feed chambers). This algorithm is based on Recurrence Plots methodology and is intended for identification of chaotic vibrations [1]. The main idea of this approach consists in the one-to-one mapping of m-dimensional phase state trajectory X-(t) onto the two-dimensional square binary matrix with a size of N × N. In this binary matrix "1" (black point) corresponds to the repetition of the phase state (observed in any point of time i) in any other point of time j. Both coordinate axes are time axis. This presentation of nonlinear dynamic process was named as Recurrence Plots. In addition to the qualitative (visual) analysis this approach allows to get some quantitative characteristics of different trajectories of rotor's motion in fluid-film bearings [2]. To get these characteristics we use some quantitative indicators and functions like a recurrence rate, a divergence, an entropy and a trend. These indicators allow analyzing quantitative criterions of a kind of non-linear motion. This approach has some advantages in comparison with the traditional methods in the analysis non-linear and, especially, chaotic vibrations. In particular this approach can increase efficiency of non-analysis of non-stationary and noisy vibration signals. This paper represents a model of non-symmetrical rotor which is installed on the two hydrostatodynamic bearings with feed chambers. These bearings are lubricated by the liquid hydrogen. Pressure field in clearance between the rotor and the bearing is defined on the base of numerical finite element solution of Reynolds' equation. Rotordynamics' equations were solved by means Adams' numerical scheme with adaptive steps [3]. So the phase portraits of rotor's nonlinear motions were gotten and then these chaotic vibrations were analyzed on the base of developed of Recurrence Plots methodology. This approach allowed fulfilling bifurcation analysis and detecting fields of chaotic vibrations in the rotor system's parameter space.

back


Creative Commons License © 2017 SOME RIGHTS RESERVED
The content of this web site is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.0 Germany License.

Please note: The abstracts of the bibliography database may underly other copyrights.

Ihr Browser versucht gerade eine Seite aus dem sogenannten Internet auszudrucken. Das Internet ist ein weltweites Netzwerk von Computern, das den Menschen ganz neue Möglichkeiten der Kommunikation bietet.

Da Politiker im Regelfall von neuen Dingen nichts verstehen, halten wir es für notwendig, sie davor zu schützen. Dies ist im beidseitigen Interesse, da unnötige Angstzustände bei Ihnen verhindert werden, ebenso wie es uns vor profilierungs- und machtsüchtigen Politikern schützt.

Sollten Sie der Meinung sein, dass Sie diese Internetseite dennoch sehen sollten, so können Sie jederzeit durch normalen Gebrauch eines Internetbrowsers darauf zugreifen. Dazu sind aber minimale Computerkenntnisse erforderlich. Sollten Sie diese nicht haben, vergessen Sie einfach dieses Internet und lassen uns in Ruhe.

Die Umgehung dieser Ausdrucksperre ist nach §95a UrhG verboten.

Mehr Informationen unter www.politiker-stopp.de.