Forced Vibration of a Disk/Spindle System With Hydrodynamic Bearings

This paper presents forced vibration of a rotating disk/spindle system with hydrodynamic bearings (HDB). The system consists of multiple elastic disks clamped on a rigid spindle, which spins at constant speed and performs infinitesimal rigid-body translation and rocking. The spindle is mounted on a flexible, stationary shaft through radial and thrust HDB’s. In addition, the disk/spindle system is subjected to two types of excitations: concentrated force excitations and base excitations. Moreover, the base excitations consist of an in-plane and an angular component. Equations of motion are derived through Lagrange equations and discretized in terms of spindle rocking, spindle translation, disk eigenmodes, and shaft eigenmodes. Transfer functions and transient response of the system are obtained by using Laplace transform and Green’s functions. As an example, both frequency response functions (FRF) and shock response of a hydro-spindle subject to in-plane and angular base excitations are presented numerically. Typical FRF presents resonances of a half-speed whirl and two pairs of rocking modes. To verify the mathematical model, theoretical predictions of FRF and shock response are compared with experimental measurements. The close agreement of the results validates the mathematical model of the disk/spindle system.