For a more precise description of rotor–bearing system, a nonlinear supported model is proposed in this paper, where a linear damping, a nonlinear elastic restoring force and a turbulent lubricant flow model are assumed. The dynamics of the rotor center and bearing center are studied. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, Poincare 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 behaviors of the system include 2T-periodic, quasi-periodic and chaotic motions. The modeling 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 behavior of the rotor and bearing center can be avoided.

Bifurcation and chaos analysis of a flexible rotor supported by turbulent long journal bearings

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, Poincare 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 ph...

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

This work reports a numerical study undertaken to investigate the dynamic response of a rotor supported by two turbulent flow model journal bearings with nonlinear suspension and lubricated with couple stress fluid under quadratic damping. This may be the first time that analysis of rotor-bearing system considered the quadratic damping effect. The dynamic response of the rotor center and bearing center are studied. The analysis methods employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincare maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The modeling results provide some useful insights into the design and development of rotor-bearing system for rotating machinery that operates at highly rotational speed and highly nonlinear regimes.

Tsann-Rong Lin

Papers

The effects of three-dimensional irregularities on the performance characteristics of turbulent journal bearing