A Numerical Approach to the Stability of Rotor-Bearing Systems

Abstract

The stability characteristics of a rotor-bearing system which indicate the threshold of instability are generally obtained by applying the Routh-Hurwitz criterion to the characteristic polynomial. Usually the characteristic polynomial is obtained analytically from the characteristic determinant. In the case of the generalized eigenvalue problems, this is practically impossible. To study the stability characteristics of a floating bush bearing, the characteristic polynomial is constructed from the generalized eigenvalue problem using a recently developed numerical technique. Results obtained through this computer package are compared with those already available in the literature.

A Study on Stability and Response Analysis of a Nonlinear Rotor System With Mass Unbalance and Side Load

“…That yields a set of homogeneous ordinary differential equations with constant coefficients. Thus, the stability problem can be examined by solving the eigenvalues of a constant matrix (Hahn, 1979;Athre et al, 1982;Greenhill and Nelson, 1982;Chen, 1987).…”

“…The stability of the centric circular synchronous motion can be studied by firstly perturbing the equations of motion about the steady state solution and secondly solving the eigenvalues problem of the perturbed system. It has been shown by researchers (Hahn, 1979;Athre et at, 1982;Greenhill and Nelson, 1982;Chen, 1987) that the steady state centric circular motion is unstable if one of the real part of eigenvalues is positive. Another method for studying the stability of steady state circular motion is to search for the convergent passage by direct numerical intergation (Taylor and Kumar, 1980).…”