A diagnostic method of determining the position and size of a transverse open crack on a stationary shaft without disengaging it from the machine system is investigated. The crack is modelled as a joint of a local spring. To obtain the dynamic characteristics of a stepped shaft and a multi-disc shaft, the transfer matrix method is employed on the basis of Timoshenko beam theory. It can be combined with beam segments to derive the frequency equation for the assembly, and is then solved for the frequency as well as the corresponding mode shape of the cracked shaft. Verification of this approach by comparison with some already existing published experimental data is presented. The position of the crack can be predicted by comparing the fundamental mode shapes of the shaft with and without a crack. Furthermore the depth of the crack can be obtained by the change of natural frequency of the shaft with and without a crack. (C) 1996 Academic Press Limited
