ON DYNAMIC RESPONSE OF DISK-SHAFT-BEARING SYSTEMS

The equations of motion of a disk-shaft-bearing system with an elastic attachment of disk to shaft are derived in the form of a set of seven coupled nonlinear second order differential equations. The coupling between system translational and rotational equations have been eliminated by linearizing them for the purpose of seeking their solution. The solution is presented in the form of a sum of forward and backward whirling vectors. The natural frequencies of the translational modes of whirling motion have been obtained in terms of bearing parameters and system mass, whereas those of the rotational modes of whirling motion have been shown to depend on the equivalent rotational stiffness coefficients of the elastic attachment and the system mass moments of inertia. Stability criterion for both the translational and rotational modes of motion has been established based on the solution of system eigen value problem. System stability boundaries are determined and stability regions are illustrated graphically in terms of system parameters

Stability analysis of rotor-bearing systems via Routh-Hurwitz criterion

A method of analysis is developed for studying the whirl stability of rotor-bearing systems without the need to solve the governing differential-equations of motion of such systems. A mathematical model, comprised of an axially-symmetric appendage at the mid-span of a spinning shaft mounted on two dissimilar eight-coefficient bearings, is used to illustrate the method. Sufficient conditions for asymptotic stability of both the translational and rotational modes of motion of the system have been derived. The system's stability boundaries, presented graphically in terms of the various system non-dimensionalized parameters, afford a comprehensive demonstration of the effects of such parameters on the system's stability of motion.