Analysis of the Dynamic Behavior of a Cracked Rotating Shaft by Using the Harmonic Balance Approach

There are several SHM techniques proposed in the literature for crack detection in rotating machines. Among them, the ones based on vibration measurements are recognized as useful tools in the industrial context. Although widely used, when applied under non-ideal conditions, such techniques can only detect cracks that eventually have already spread significantly along the cross section of the shaft. Therefore, currently, the researchers' attention is turning to more sophisticated methods capable of identifying incipient cracks, which represent a type of damage that are hardly observable in classical vibration analysis. In a previous contribution, a crack identification methodology based on a nonlinear approach was proposed. The technique uses external applied diagnostic forces at certain frequencies attaining combinational resonances, together with a pseudo-random optimization code, known as Differential Evolution, in order to characterize the signatures of the crack in the spectral responses of flexible rotor. In the present paper, the favorable conditions to apply the proposed methodology are investigated. The analysis procedure is confined to the operating parameters of the system, being characterized by the rotation speed of the rotor and the amplitude and frequency of the diagnostic forces. The harmonic balance approach is used to determine the vibration responses of the cracked rotor system and the open crack behavior is simulated according to the FLEX model. For illustration purposes, a rotor composed by a horizontal flexible shaft, two rigid discs, and two self-aligning ball bearings is used to compose a FE model of the system.