A Stability Analysis of Constrained Rotating Disks With Different Boundary Conditions

The vibration behavior of constrained high speed rotating disks is of interest in industries as diverse as: aerospace, computer disk manufacture and saw design and usage. The purpose of this study is to investigate the stability behavior of guided circular disks with different boundary conditions. The equations of motion are developed for circular rotating disks constrained by space fixed linear, mass, spring, damper systems. The resulting equation of motion is a two dimensional fourth order partial differential equation that requires numerical solution. The Galerkin Method is employed using the eigenfunctions of the stationary non-constrained disk as approximation functions. Of interest is the effect on stability of conditions at the inner boundary. In particular the difference in behavior for centrally clamped, and splined disks (those disks that run on a spline arbor) is investigated. Also discussed is the effect of constraints on the flutter and divergence instability boundaries. Preliminary experimental results are presented for constrained splined disks, and these results are compared with the analytical predictions.