An Instability Analysis Procedure for Three-Level Multi-Bearing Rotor-Foundation Systems

Abstract

A procedure for the instability analysis of three-level multi-span rotor systems is described. This procedure is based on a distributed mass-elastic representation of the rotor system in several eight-coefficient bearings. Each bearing is supported from an elastic foundation on damped, elastic pedestals. The foundation is represented as a general distributed mass-elastic structure on discrete supports, which may have different stiffnesses and damping properties in the horizontal and vertical directions. This system model is suited to studies of instability threshold conditions for multi-rotor turbomachines on either massive or flexible foundations. The instability condition is found by obtaining the eigenvalues of the system determinant, which is obtained by the transfer matrix method from the three-level system model. The stability determinant is solved for the lowest rotational speed at which the system damping becomes zero in the complex eigenvalue, and for the whirl frequency corresponding to the natural frequency of the unstable mode. An efficient algorithm for achieving this is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. A second example discusses a flexible rotor with four damped-elastic bearings. The third case compares the stability of a six-bearing 300 Mw turbine generator unit, using two different bearing types. These applications validate the computer program and various aspects of the analysis.