A Simple Stability Analysis for Flexible Rotors in Tilting Pad Bearings

Abstract

A simplified stability analysis for flexible rotors in tilting pad bearings is developed which provides a convenient and practical approach for the consideration of nonsynchronous vibrations during the design phase of rotor bearing systems. It is known that the synchronous unbalance response of a single mass Jeffcott rotor in linear isotropic bearings is identical in form to the response of a simple spring-mass-damper system excited by a rotating unbalance. This paper demonstrates that the free vibrations, and hence the system damping factor, of a distributed mass flexible rotor in tilting pad bearings may be analyzed using a single mass, two tier spring-damper model. The relationship between the system damping factor and rotor stability is discussed. Non-synchronous tilting pad bearing characteristics are incorporated into the expression for the damping factor, and nondimensional curves are presented which establish values of the damping factor as a function of operating speed, critical speed, bearing clearance and Sommerfeld number. The subject curves provide a quick method for establishing stability guidelines during rotor design and for comparing existing rotor bearing systems.