Bifurcation and chaos of a flexible rotor supported by turbulent journal bearings with non-linear suspension

Abstract This study presents a dynamic analysis of a rotor supported by two turbulent model journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor-bearing system is investigated under the assumptions of turbulent lubricant flow and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the fourth-order Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor centre and bearing centre, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the dynamic behaviours of the system include 3T-periodic, jump phenomena, and chaotic motions. The modelling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behaviour of the rotor and bearing centre can be avoided.

[1]  G. Adiletta,et al.  Chaotic motions of a rigid rotor in short journal bearings , 1996 .

[2]  Cesare Rossi,et al.  Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings. Part II: Experimental Analysis , 1997 .

[3]  G. G. Hirs.  Closure to “Discussion of ‘A Bulk-Flow Theory for Turbulence in Lubricant Films’” (1973, ASME J. Lubr. Technol., 95, pp. 145–146) , 1973 .

[4]  Tsann-Rong Lin,et al.  The effects of three-dimensional irregularities on the performance characteristics of turbulent journal bearing , 1996 .

[5]  R. D. Brown,et al.  Chaos in the unbalance response of journal bearings , 1994 .

[6]  V. Constantinescu,et al.  Analysis of Bearings Operating in Turbulent Regime , 1962 .

[7]  I. W. Mayes,et al.  The aperiodic behaviour of a rigid shaft in short journal bearings , 1978 .

[8]  Cesare Rossi,et al.  Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings. Part I: Theoretical Analysis , 1997 .

[9]  F. F. Ehrich,et al.  Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics , 1991 .

[10]  Hiromu Hashimoto,et al.  Performance Characteristics of Worn Journal Bearings in Both Laminar and Turbulent Regimes. Part I: Steady-State Characteristics , 1986 .

[11]  D. Nicolas,et al.  An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings , 2000 .

[12]  C. Ng,et al.  A Theory for Turbulent Fluid Films and Its Application to Bearings , 1967 .

[13]  Sapna Mishra,et al.  Stability of a rigid rotor in turbulent hydrodynamic worn journal bearings , 1996 .

[14]  G. Capone,et al.  Dynamic characteristics and stability of a journal bearing in a non-laminar lubrication regime , 1987 .

[15]  S. T. Noah,et al.  Bifurcation analysis for a modified Jeffcott rotor with bearing clearances , 1990 .

[16]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .