Stability analysis of a spinning flexible disk-stationary load system: Application to floppy disk drives

This dissertation presents the theoretical formulation, modeling, and eigenvalue analysis for a spinning flexible disk-stationary load system with a view toward obtaining a fundamental understanding of the head-disk interface instability in computer floppy disk drives. The stationary load system contains such parameters as transverse inertia, stiffness, damping, and their rotary counterparts, as well as a constant friction force between the sliders and disk. A comprehensive parameter study based on a finite element numerical analysis is conducted to show that the instability behavior due to the friction force agrees well with experimental results reported previously for a conventional 5.25-inch floppy disk drive.; In order to explain the dependence of the numerical results on the various parameters, we first established the orthogonality relations and completeness theorem for the eigenfunctions for a freely spinning disk (no stationary load system) in both the sub- and supercritical speed ranges. The analytical expressions for the derivatives of the eigenvalues with respect to various load parameters are then derived to predict the effects of these parameters on the natural frequencies and stability of the system when the eigenvalue of interest is well separated from the others.; In the case when two eigenvalues are closely separated, strong modal interactions occur when the load parameters are introduced. In order to understand the mathematical structure of the modal interactions, we use the eigenfunction expansion method to reduce the partial differential equation to a system of simple algebraic equations. By comparing the results obtained with the finite element numerical solutions, we find that a simple two-mode approximation displays the general features of the eigenvalue changes with the load parameters. Using this two-mode approximation, we examined analytically the properties of the perturbed eigenvalues as functions of load parameters.; Motivated by experimental results with hard disk drives, the effects of rigid body translation and tilting of the disk clamp on the stability of the spinning flexible disk are studied. It is found that the axial rigid body translation of the clamp eliminates the stationary-type instability induced by the transverse stiffness of the load system, while the clamp rigid body tilting has not such effect.