FREE VIBRATION ANALYSIS OF A SPINNING FLEXIBLE DISK–SPINDLE SYSTEM SUPPORTED BY BALL BEARING AND FLEXIBLE SHAFT USING THE FINITE ELEMENT METHOD AND SUBSTRUCTURE SYNTHESIS

Free vibration of a spinning flexible disk–spindle system supported by ball bearing and flexible shaft is analyzed by using Hamiltonʹs principle, FEM and substructure synthesis. The spinning disk is described by using the Kirchhoff plate theory and von Karman non-linear strain. The rotating spindle and stationary shaft are modelled by Rayleigh beam and Euler beam respectively. Using Hamiltonʹs principle and including the rigid body translation and tilting motion, partial differential equations of motion of the spinning flexible disk and spindle are derived consistently to satisfy the geometric compatibility in the internal boundary between substructures. FEM is used to discretize the derived governing equations, and substructure synthesis is introduced to assemble each component of the disk–spindle–bearing–shaft system. The developed method is applied to the spindle system of a computer hard disk drive with three disks, and modal testing is performed to verify the simulation results. The simulation result agrees very well with the experimental one. This research investigates critical design parameters in an HDD spindle system, i.e., the non-linearity of a spinning disk and the flexibility and boundary condition of a stationary shaft, to predict the free vibration characteristics accurately. The proposed method may be effectively applied to predict the vibration characteristics of a spinning flexible disk–spindle system supported by ball bearing and flexible shaft in the various forms of computer storage device, i.e., FDD, CD, HDD and DVD.