An Improved Method for Stability and Damped Critical Speeds of Rotor-Bearing Systems

Abstract

Many computer programs are available for stability and critical speed analysis of rotor-bearing systems. The iterative search-transfer matrix method is widely used for such programs. However, this method sometimes fails to converge or may miss some critical speeds. The polynomial method, which derives the characteristic polynomial and solves for the critical speeds, can partly overcome these shortcomings. However, the advantage of the polynomial method disappears as the number of elements in the system increases. This is because the computational time required to find a characteristic polynomial increases exponentially with the number of elements. This paper describes an improved technique based on the transfer matrix-polynomial method, which reduces the computational time significantly and completely eliminates the possibility of missing some critical speeds. A new technique is developed for the derivation of the characteristic polynomial. The characteristic polynomial equation is then converted into an eigenvalue problem of its companion matrix, whose eigenvalues are identical with the roots of the polynomial equation. The process, which can find only some dominant eigenvalues, eliminates the possibility of missing some eigenvalues without any penalties in the computational time and accuracy. The results from the method presented here are compared with those from some other methods.