Free Vibration of a Rotating Disk/Spindle System With Hydrodynamic Bearings

This paper is to study free vibration of a rotating disk/spindle system with hydrodynamic bearings (HDB). The disk/spindle system consists of multiple circular disks clamped on a rigid spindle, which allows infinitesimal rigid-body translation and rotation (rocking). Also, the spindle is mounted on a stationary, flexible, cantilever shaft through two identical radial HDB and a thrust HDB. Equations of motion were first derived in terms of the rigid-body translation and rocking of the spindle, the shaft bending, and the disk vibration. Then an eigenvalue analysis was performed to obtain natural frequencies, modal damping factors, and mode shapes of the rotating disk/spindle system. For a special case of rigid shaft and decoupled translation/rocking spindle, one pair of transverse modes and two pairs of rocking modes were observed. For the transverse modes, the disk/spindle system whirls transversely as a rigid body at half of the rotational speed (i.e., half-speed whirl). In addition, the backward whirl is heavily damped while the forward whirl is lightly damped. The first pair of rocking modes is similar to those found in disk/spindle systems with ball bearings and is lightly damped. The second pair of rocking modes occurs at low frequency. One of these modes is lightly damped and has natural frequency very close to half of the rotational speed. For the general case of a flexible shaft and coupled translation/rocking motion, eight coupled modes were obtained. Three of them occur at the half-speed frequency. Compared with systems with rigid shaft, the other five modes have significantly lower natural frequencies because of the shaft flexibility.