On The Vibration of a Cracked Rotating Blade

Abstract

The dynamic behavior of a rotating blade containing a transverse crack was investigated. First, the local flexibility of the cracked blade was obtained by using the method of the released energy. An energy principle, in conjunction with a weighted residual method, was then applied to yield the discrete equations of motion. The equations of motion were further utilized to study the influences of the crack depth and location on the bending natural frequencies under various of rotation speeds. The numerical calculation showed that the crack effects the natural frequencies and the response appreciably only if it is relatively deep and locates near the root of the blade. However, the effects increase exponentially with the depth increases. In addition to the natural frequencies, the displacement responses of the blade with a crack under a constant lateral forces were discussed as well. This was done by calculating the deflections at the tip of the blade for various crack depths and locations. Similar to the rotation speed of the blade frequency, the deflection was offset by the increase of the rotation. However, the centrifugal effects increased significantly such that the crack’s effects became relatively insignificant. Nevertheless, the study showed that the changes on the natural frequency and the tip-deflection of the blade due to a crack may be used as indices for on-line detection of cracks.