The motion of a rotor carried by a flexible shaft in flexible bearings

Abstract

1.1.— Scope of Investigation .—This paper discusses the transverse motion of a rotor carried by a flexible shaft rotating in flexibly-supported bearings. The rotor is assumed to consist of one or more rigid bodied mounted on a shaft which is weightless and torsionally rigid. The rotor and shaft are in rotation; in the first place, it is taken that the speed of rotation is maintained constant, driving torques being applied if necessary about the shaft axis. Unsymmetrical flexibility of the bearing supports and unsymmetrical transverse flexibility of the shaft of the flexible members of the system is also considered. The work is mainly analytical, but reference is also made to experiments which have been carried out. 1.2. Definitions . —The flexible members (shaft and bearing supports) are described collectively as the mounting. An unstable speed is a speed of rotation at which a rotor, after receiving a small initial displacement from its equilibrium state of motion, tends to increase its amplitude of vibration beyond all bounds; while a critical speed is a speed at which out-of-balance alone tends to set up vibrations of very great amplitude.