PSI - Issue 57

Marco Bonato et al. / Procedia Structural Integrity 57 (2024) 799–809 / Structural Integrity Procedia 00 (2019) 000 – 000

801

3

1.1. Simplification of Vibration Signals Previous studies had investigated the problem of the simplification of complex vibration signals only for mechanical components such as heat exchangers (Bonato (2015)). The focus of this work was mainly to find the validity limit of this approach, based on experimental measures of fatigue damage during vibration tests. The approach was based on the implementation of the Fatigue Damage Spectrum and the Fatigue Da mage Equivalent Vibration testing (McNeil (2008), Bonato and Goge (2016)). The FDS is obtained from input accelerations by calculating the displacement seen by the component assuminga Single Degree of Freedom (SDOF) response (Figure 1). Because the natural frequencies of the component are often unknown,the SDOF filter is repeated over a given range of naturalfrequencies to make sure that all eventualities are taken into account. The stress cycles of the output SDOF transfer function response are counted (rainflow cycles counting algorithm), and the related fatigue damage is calculated using the material S- N curve (Basquin’s equation) and Miner’s cumulative law. The typicalDynamic Amplification factorfor the heat exchangers considered is Q = 10. Real world applications are seldom SDOF systems. Nevertheless, in most cases the response is dominated by a single dynamic mode and this, together with the conservatism of the assumption, makes this approach applicable for all practical cases.

Figure 1. 1 Single Degree of Freedom System. Also defined as a mass-spring-damper model.

In the case of a signal given in the frequency domain, the FDS is obtained through a probabilistic approach. The stress peaks distribution is estimated statistically. Rayleigh, Lalanne and Dirlik’s formulations are the peak distribution equations most commonly used (Halfpenny and Kihm (2010)). The FDS can be calculated also from the time series of input accelerations (Halfpenny (2006)). In this case, a numeric integration of the signal is required to extrapolate the displacement cycles after the SDOF filter. In both situations, the counted displacement ranges are converted to stress (in case of linear dynamic response, the displacement and the local stress are proportional) are then used to calculate the cumulative fatigue damage. Once the FDS of the original signal is obtained, its inversion allows to derive fatigue equivalent random or harmonic signals.This direct transformation is possible only in case of stochastic and deterministic signals (random PSD and sine sweep), since the probability density function (amplitude and frequency) of stress cycles is analytically quantified (Lalanne 2002) Indeed,the ability to calculate the FDS from the complex vibration signals to be simplified is the first step of the process. The parameters needed for calculation of the FDS estimates the output displacement and the relative fatigue damage for each SDOF filer frequency. The damping ratio Q is proportional to the damping  of the system: = 2 1 (1) At the very beginning of the product development phase the exact dampingof the system is not known, however its knowledge can be estimated from previous experimental measures. In general, two conservative assumptions are considered in order to comply with the fatigue damage equivalence criteria: if the failure occurs on mechanical parts of the component (aluminum or hard plastic) the damping ratio is