Critical speeds of a spinning thin disk with an external ring

Abstract

In this work, the dynamics of a spinning thin axisymmetric annular disk with an external ring have been studied and the effect of the ring on the critical speeds of the disk has been investigated. The disk with a ring is modelled using the von Karman plate theory and assuming clamped inner-boundary and free outer boundary. The self-adjoint eigenvalue problem for the linear stiffness operator is solved approximately using the Galerkin method to obtain the linear mode shapes and eigenvalues. These are then used to solve the eigenfrequencies of vibration of the disk. The spin speed corresponding to zero eigenfrequency of a particular mode is the critical speed for that mode. It has been shown that the critical speeds of the disk can be increased substantially by appropriate design of the external ring. A ring of uniform thickness is observed to reduce rather than increase the critical speeds. On the other hand, a tapered ring with increasing thickness is the outward radial direction can greatly improve the critical speeds. These observations have important implications for design of disks for high-speed applications as in computer hard-disk drives.