Free and forced vibrations of a rotating disk nook and spindle motor system with hydrodynamic bearings

This paper is to study free and forced vibrations of a rotating disk-spindl e system supported by hydrodynamic bearings (HDB's). The disk-spindle syste m consists of multiple circular disks clamped to a rigid spindle, which spi ns at constant speed and allows infinitesimal rigid-body translation and ro cking. In addition, the spindle is mounted on a flexible, stationary shaft through radial and thrust HDB's. Furthermore, the disk-spindle system is su bjected to external force and base excitations. Equations of motion are der ived through Lagrange equations and discretized in terms of spindle rocking , spindle translation, disk eigenmodes, and shaft eigenmodes. For free vibr ation, an eigenvalue analysis predicts natural frequencies, modal damping, and mode shapes of the rotating disk-spindle system. For forced vibration, use of Laplace transforms and Green's functions predicts transfer functions and transient responses of the system. Compared with disk-spindle systems with ball bearings, those with HDB's have a fundamental change in rocking v ibration. Specifically, the rocking vibration consists of a pair of heavily damped rocking modes, a pair of half-speed whirls, and two pairs of lightl y damped rocking modes. Also, the flexibility of the shaft significantly re duces the resonance frequencies and modal damping of the lightly damped roc king modes. Finally, a frequency-response function and a transient shock re sponse are predicted numerically and compared with existing experimental me asurements to validate the mathematical model.