PSI - Issue 24

Filippo Cianetti et al. / Procedia Structural Integrity 24 (2019) 526–540 Author name / Structural Integrity Procedia 00 (2019) 000–000

535

10

For each frequency, the maximum value was therefore taken regardless of the maneuver, obtaining a worst case envelope (Max in Fig. 10 (a) and Fig. 10 (b)), which will be taken as the basis for subsequent assessments. The objective is to synthesize a PSD, similarly to what has been done on a normative basis, which is representative of the accelerations derived from flight. To this end, from the FFT (Fig. 10 (a)) the frequency peaks of the Main Rotor (blue triangles) and of the Tail Rotor (red triangles) have been calculated and appropriately scaled in the synthesized PSD. From the PSD instead (Fig. 10 (b)) the levels of the random were obtained, using the frequencies foreseen by the MIL-STD-810-H, and obtaining the spectrum in green. Applying (17) a synthesis spectrum has been obtained (orange in Fig. 11 (a)) which is believed to be reasonably representative of the aircraft vibration environment. This that can be called operational PSD and was compared with the PSD derived from MIL-STD-810-H, using the suggested formulation in the calculation of accelerated spectra:

m 2

W r W e

t e t r

(18)

=

In the (18), where with the subscripts e and r identify the equivalent and real conditions respectively. The exponent m even if formally similar to (3), is slightly di ff erent in phisical meaning and is suggested by MIL-STD-810-H, which assumes values between 5 and 8. The number obtained is known as Exaggeration Factor (EF), or a multiplier that if greater than one decreases the test time compared to operating conditions, if less it slows it down. Knowing the com pression ratio of the times, the EF imposed by the guideline was calculated for the di ff erent suggested m exponents. Therefore the ”experimental” EF was calculated from the relationship between the two PSDs. The di ff erence gives an idea of how conservative the norm tends to be, having to adapt to the most disparate cases.

Exaggeration Factor

10 2

Max Synt

Experimenal EF Calculated EF

10 -1

10 -2

m 2 s -4 Hz -1

10 -3

m=5

10 -4

Exaggeration Factor

10 1

m=6

10 -5

m=7

m=8

10 -6

10 0

10 1

10 2

10 3

0 50 100 150 200 250 300 350 400 450 500 Hz

Hz

(a) Sine time-history

(b) Equivalent PSD

Fig. 11: Final PSD & Exaggeration Factor

3. Fatigue Life Extimation

In the logical flow described in Fig. 2, the estimation of fatigue life requires three input elements: the properties of the material, or the Wohler curves, Lalanne (2009a) the stress state of the component, coded in terms of time history or PSD, and a criterion of accumulation of the damage Fatemi and Yang (1998). It is known that for large models it is advantageous, in computational terms, to approach the problem in the frequency domain. However, the applicability of the method is subject to two hypotheses Lalanne (2009a); Pitoiset and Preumont (2000):

• the stress has a zero mean, in the impossibility of correcting the alternating stress, according to the average component, as required from the Haigh diagram Budynas and Nisbett (2006); Juvinall and Marshek (2008);