Analysis of the periodic breathing of a transverse annular crack propagated in a real rotating machine

This paper shows the numerical results of a model-based analysis carried out to investigate the experimental dynamic behaviour of the shaft of a real steam turbine in which a deep annular – or circumferential – crack propagated. The shape of this transverse crack was caused by the generation of multiple initiation points, equally spaced over the whole circumferential surface of the shaft cross-section located at the first high pressure stage of the steam turbine. The periodic breathing of the crack caused changes in the area moments of inertia of the damaged cross-section and fault symptoms. Conversely, the shaft heating that affected the turbine during the load rises performed at the end of the runups carried out from a cold state pointed out an abnormal sensitivity of the synchronous vibrations to the machine thermal state. As a result, the fault symptoms caused by this crack were quite different from those induced by common shaft transverse cracks. The breathing of this crack, caused by gravity, has been studied by means of a mathematical model in order to investigate the influence of the crack opening and closure on the harmonic content of the turbine vibration. A new approach is used in this paper, considering a more appropriate 3D FE model that allowed the non-linear distribution of the stresses in the cracked section to be estimated. The method used for the present study has proved that the non-linear distribution of the axial stresses in the area close to the crack tip gives only minor effects on the breathing mechanism. This is an original contribution, which could have not been observed in previous authors' papers that employed simplified models for the periodic breathing. The good accordance between numerical results and experimental data confirms the adequacy of the investigation method used for this study. With reference to diagnostic purposes, this involves that the early on-line detection of annular cracks propagated in the shafts of rotating machinery needs to use more accurate techniques, based on the analysis of vibration data, which can point out fault symptoms, even in the case of very deep transverse cracks.