Nonlinear Dynamic Behaviors of a Complex Rotor-Bearing System

This paper deals with the long-term dynamic behaviors of a complex rotor-bearing system with multi-degrees-of-freedom and nonclosed form of the bearing forces. Since nonanalytical bearing forces can be available, to increase the numerical accuracy and decrease the CPU time, a new method is presented to calculate the Jacobians of the bearing forces and bearing forces themselves. The algorithm is concise and the computing efforts spent on the Jacobians are very small compared to spend on the bearing forces themselves. In terms of the feature that the nonlinear bearing forces act on the system individually, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease the computing time for the system analysis. The numerical schemes of this study are applied to a rotor system with multi-rigid disks and two elliptical bearing supports. The numerical results reveal very rich and complex non-linear behavior of the system.

[1]  H. D. Nelson.  A Finite Rotating Shaft Element Using Timoshenko Beam Theory , 1980 .

[2]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[3]  T. Shiau,et al.  Prediction of periodic response of flexible mechanical systems with nonlinear characteristics , 1990 .

[4]  H. D. Nelson,et al.  Periodic Solutions in Rotor Dynamic Systems With Nonlinear Supports: A General Approach , 1989 .

[5]  S. T. Noah,et al.  Response and stability analysis of piecewise-linear oscillators under multi-forcing frequencies , 1992 .

[6]  Tsuneo Someya,et al.  Journal-Bearing Databook , 1989 .

[7]  William B. Day.  Asymptotic expansions in nonlinear rotordynamics , 1987 .

[8]  Cesare Rossi,et al.  Static and dynamic behaviour of a rigid rotor on journal bearings , 1992 .

[9]  H. D. Nelson,et al.  Nonlinear Analysis of Rotor-Bearing Systems Using Component Mode Synthesis , 1983 .

[10]  S. T. Noah,et al.  Mode-Locking and Chaos in a Jeffcott Rotor With Bearing Clearances , 1994 .

[11]  An iterative method for the discrete problems of a class of elliptical variational inequalities , 1995 .

[12]  F. F. Ehrich,et al.  High Order Subharmonic Response of High Speed Rotors in Bearing Clearance , 1988 .

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

[14]  Michele Russo,et al.  Journal Orbits and Their Stability for Rigid Unbalanced Rotors , 1995 .

[15]  Nicholas B. Tufillaro,et al.  Experimental approach to nonlinear dynamics and chaos , 1992, Studies in nonlinearity.

[16]  Dara W. Childs.  Fractional-frequency rotor motion due to nonsymmetric clearance effects , 1982 .

[17]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[18]  J. W. Lund,et al.  Calculation of the Dynamic Coefficients of a Journal Bearing, Using a Variational Approach , 1986 .

[19]  E. J. Hahn,et al.  Unbalance Behavior of Squeeze Film Damped Multi-Mass Flexible Rotor Bearing Systems , 1983 .

[20]  M. J. Braun,et al.  Nonlinear Effects in a Plain Journal Bearing: Part 1—Analytical Study , 1991 .

[21]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[22]  Gregory L. Baker,et al.  Chaotic Dynamics: An Introduction , 1990 .