Abstract
This paper represents a novel algorithm of non-linear 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. 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 non-linear 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. 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. So the phase portraits of rotor's non-linear 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.
