A study of the dynamics in a rotating flexible disk-spindle system

Current technological advances in hard disks, CD-drives, DVD-drives, turbomachinery, gearboxes, cutting tools, etc. have lowered the limit of allowable vibrations and necessitated a detailed study of the dynamics in such systems. All these are essentially disk-spindle systems, with the geometric scale varying greatly---from large (turbomachinery) to small (miniature disk drives). To gain a physical understanding of the eigensolutions and the coupling mechanisms that govern the dynamics of these systems, it is imperative to have a model that is valid for all geometries and material properties.; Such a model is developed here and allows qualitative predictions regarding the coupling between the various deformations in a disk-spindle system. The corresponding eigensolutions are used to measure the magnitude of this coupling. In addition, the evolution of the modeshapes with changes in geometric and material parameters is studied.; The desired three-dimensional model is developed in steps to facilitate our understanding of the underlying physics. First a model using restricted plate and beam theories to model the disks and spindle respectively is derived. This gives an insight into the dynamical interaction between the zero and one nodal diameter disk modes and the spindle modes. An adequate model for the in-plane motions of a rotating disk was not available, and is developed here using finite elasticity to accommodate the effects of finite rotation speeds.; This restricted model, predicts that disk modes with two or more nodal diameter numbers do not couple to the spindle modes. This is an artifact of the kinematical assumptions used to derive the restricted plate and beam theories, and is overcome by constructing a second model considering the disk-spindle system as an assemblage of elastic three-dimensional cylinders.; Disk modes couple to the spindle modes for all nodal diameter numbers. The spindle coupling with the zero and one nodal diameter disk modes is dominant for long spindle lengths and is particularly pronounced when the frequencies of the individual disk and spindle modes are in close proximity. The spindle coupling with the two and higher nodal diameter disk modes is dominant for short spindles and allows the corresponding disk modes to couple to each other through the spindle.; The existence of these coupling mechanisms opens many paths for energy transfer to and from the various disks in a stack and can be exploited to devise new active/passive control schemes to restrict the amplitude of disk vibration without placing a control unit on it.