The Effects of Longitudinal and Circumferential Cracks on the Torsional Dynamic Response of Shafts

Abstract

Turbo generator shafts are manufactured through the extrusion process. This results in formation of weak planes along the extrusion direction. Under service loading (e.g. cyclic torsion due to electrical line faults), large longitudinal cracks often form in these shafts before the appearance of any circumferential cracks. The presence of these cracks could severely compromise the shaft resonance frequencies. Here, we investigated the dynamic response of solid turbo generator shafts with longitudinal and circumferential cracks. The longitudinal cracked section of the shaft section was modeled as a shaft with reduced effective torsional rigidity. The effective torsional rigidity was found to be a function of ratio of crack depth to the shaft radius only. The circumferential cracked section was modeled as a torsional spring, with the torsional spring constant determined using fracture mechanics principles. It was found that the resonance frequency of the shaft may be little affected by the presence of a longitudinal crack. The resonance frequencies of the shaft with the circumferential crack depend on the crack length and its location. The effects of crack surface interactions for both longitudinal and circumferential cracks were also investigated. For circumferential cracked shafts, the sever crack surface interaction results in the peak response frequency approaches to that of un-cracked shafts. However the frequency where the peak response occurs for a longitudinally-cracked shaft generally exceeds that of un-cracked shaft first resonance frequency.