Random fatigue. A new frequency domain criterion for the damage evaluation of mechanical components

Abstract The evaluation of the fatigue behavior of mechanical systems and components subjected to random loads is increasingly being addressed to the frequency domain environment both in terms of dynamic analysis and in terms of results post-processing. The procedure set out in the paper (bands method) is formulated without assumptions about the shape of the Power Spectral Density (PSD) function to be analyzed, in order to obtain a criterion that can be applied to any typology of the related random process. The basic idea of the proposed approach is that each PSD function can be divided into frequency bands, for each of them a Rayleigh distribution could be associated and that the aforementioned distributions could be opportunely combined to obtain the actual damage. The method is theoretically developed and numerically validated on a particular subset of PSD functions by comparing the results obtained with those carried out by the time domain damage evaluation reference method and a frequency domain direct approach (Dirlik’s method). With regard to the time domain reference criterion the stress time histories are generated by the indirect method (a previously defined authors’ method), the cycles spectra are obtained by Rain Flow Counting, (RFC) and the damage is evaluated by Palmgren–Miner’s rule.