PSI - Issue 19

Giovanni M. Teixeira et al. / Procedia Structural Integrity 19 (2019) 175–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

192 18

Table 1 below provides detailed diagnostics for the two referred critical nodes on Welds 1 and 2.

Table 1. Diagnostics for the worst nodes on Welds 1 and 2. An example of a column heading Weld1

Weld2 1458 123.3 3639.1 140315

Node Number

2423 260.2

0th spectral moment 1st spectral moment 2nd spectral moment 4th spectral moment

8855.3 391251

1.062e+09

3.111e+08

Peaks per second

52.1 38.8 0.74

47.09 33.73

Upward mean crossings per second

Irregularity factor Central frequency

0.72

0.65 Hz

0.63 Hz

Fatigue Life (Frequency Domain)

51.5k repeats

195k repeats

6. Final Remarks The paper approaches two of the most important subjects in the fatigue field for the automotive industry: random vibration and welded joints. The two fields have been significantly developed over the last two decades as a result of the high demand for accurate and consistent results that could be safely used in the early stages of design. Although both fields (frequency domain fatigue and fatigue of welds) received substantial attention from a number of researchers around the world, a considerable gap existed between the two, thereby motivating the research presented here. Battelle Equivalent Structural Stress Method (Verity®) itself has been largely scrutinized and validated in the time domain. Therefore it is sufficient to show it works in the frequency domain as well as in the time domain (verification). The results presented show very small differences in the predicted fatigue results (4.5% and 10.1%) for the particular case study (brake chamber). Many other scenarios and structures have been tested by the authors and the differences (in the fatigue lives) found were smaller than 20%. These additional tests could not be disclosed in this paper for confidentiality reasons. The discussion about the most appropriate frequency domain fatigue method to be used with Verity® is beyond the scope of this paper, but it is the author’s opinion that Dirlik and Tovo&Benasciutti are among the best. Both time and frequency domain approaches were based on the same assumptions of linearity, Gaussianity, ergodicity and stationarity. The time domain inputs were realized from the PSDs, making possible to enforce Gaussianity in the process. The same damping, finite element model and modal superposition strategy was adopted in both approaches. In addition to the assumptions aforementioned the slope of the Master SN Curve (h=3.13) largely contributes to minimize the differences in the fatigue results. It is also worth noting that the “Belgian blocks track” is only a small fraction of the whole durability program and for this reason further investigations are suggested in order to understand how close the results can be when multiple blocks of loading are combined and a variety of narrow and broad band scenarios are mixed together. The proposed approach will allow designers to use the Verity® method before the loads are measured, as they can’t be measured before a physical prototype is built. At the early stages of design only loading envelopes (usually in the PSD form) are available and therefore the analysis in the frequency domain is the most straightforward. The frequency domain also elegantly provides a way to identify the vibration modes that contribute the most to fatigue damage, which is a valuable information to hold upfront and consequently reduce the time spent on the design cycle.