Effect of a Circumferential Arc Crack on the Vibration Characteristics of a Flexible Spinning Disk

Abstract

The vibration characteristics of a circumferentially cracked rotating disk are investigated. The disk is assumed to be axisymmetric, flexible and clamped at the center. The crack increases the local flexibility of the disk at the crack location and is modeled as linear and torsional springs, connecting the two segments of the disk. The spring constants are evaluated by considering crack opening displacements due to bending moment and shear force at the crack location. The equations of motion of two segments of the disk, for disk operating in vacuum as well as subjected to shear fluid flow are developed. Using the Finite Difference Technique, the coupled systems of equations are solved and the natural frequencies and mode shapes are obtained. The mode shapes are seen to be comparatively flattened in the inner region of the disk separated by the crack and heightened towards the periphery of the disk. Shear fluid loading reduces the critical speeds and results in a quicker onset of instability. The degree of instability caused by the crack is a function of crack depth and location. Critical speeds increase with increasing crack distance from the central clamp and decrease with increasing crack depth.