The Vibrations of Radial Ball Bearings

This paper presents a theoretical analysis of the vibration response of a rotating rigid shaft supported by two radial deep-groove lubricated ball bearings. The bearings and their oil films are approximated to a set of non-linear elastic springs and dampers rotating relative to the shaft when it is subjected to a rotating unbalance or inner race surface waviness. Under gravity load, the shaft's initial vibration is damped down to a limit cycle operating at a quasi-simple harmonic frequency of small amplitude. Rotating unbalance and surface features introduce further significant frequencies which influence the output response.