“Instability Threshold and Stability Boundaries of Rotor-Bearing Systems,”
W. J. Chen, 1994.


A direct numerical method for the determination of instability threshold and stability boundaries of flexible rotorbearing systems is presented. The stability boundary of an operating parameter is established by examining the variation in the real part of eigenvalue as a function of the operating parameter. This procedure can also be used to improve the system stability by considering the design variables as operating parameters. The finite element method is utilized in the formulation of system equations of motion. The numerical algorithm is based on the nonlinear optimization techniques. Two examples are presented to illustrate the feasibility, desirability and the ability of the proposed algorithm. A simple journal bearing system is used for the parametric study. An industrial high speed compressor is employed to demonstrate the ability of this algorithm to deal with the practical applications. The stability boundaries calculated from this algorithm are in agreement with the experimental results.