Dynamic Stability of Elastic Rotor-Bearing Systems via Liapunov’s Direct Method

A general method of analysis based on Liapunov’s direct method is presented for studying the dynamic stability of elastic rotor-bearing systems. A model comprised of a continuous elastic shaft mounted on two 8-coefficient bearings is used to develop closed-form (series) stability criteria involving system stiffness and damping parameters. It is quantitatively shown by means of graphs how the instability regions are reduced by (a) increasing the shaft dimensionless stiffness parameters, (b) increasing the bearing direct stiffness and damping parameters, and (c) decreasing the bearing cross-coupling stiffness and damping parameters.