PSI - Issue 37

Aleksey Mironov et al. / Procedia Structural Integrity 37 (2022) 241–249 Aleksey Mironov, Pavel Doronkin / Structural Integrity Procedia 00 (2019) 000 – 000

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Table 1. Changes of modal parameters

Modal frequency change,%

MPV change, %

fault, mm

fault, mm

mode No Hz

20

30

20

30

1 2 3 4 5 6 7 8 9

3,4 3,6 8,6

-0,44 0,008 -0,081 0,005 0,003 0,004 -0,015 0,098 -0,003 -0,001

-0,76 0,008 -0,035 0,009 0,034 0,004 -0,015 0,098 -0,001 -0,001

4,51 0,46 0,02 0,03 0,08 0,06 0,19 1,53 0,03 0,02

7,54 1,41 0,32 0,05 0,15 0,10 0,49 1,53 0,03 0,03

19,3 20,9 35,8 41,1 50,3 52,3 75,3

10

MPVI 2,48 For MPV calculation only those modes are selected, which shapes similarity confirmed by at least 0.95 value of Modal Assurance Criteria (MAC). The Modal Parameter Variation Integrated ( MPVI ) accumulates changes of multiple ( ) modal shapes of the blade. This parameter represents geometric average of normalized difference between eigenvectors of modified and reference states = √∑ 2 ⁄ (6) where – mode number ( … ) , – MPV of mode. Results of modal simulation are presented in Table 1 that illustrates MPV of each mode and MPVI for all modes caused by faults simulation. Equations 4-6 are used for above parameters calculation. Analyzing the data of Table 1 some observations are evident. Fault simulation causes slight change of modal frequencies (exception is 1 st mode only) and may be less than measurement system resolution. MPV is more sensitive to virtual faults than frequency, as it summarizes difference in many DOFs. It makes MPV more informative for monitoring of rotating blade. MPVI grows along scale of simulated fault (1,5%...2,5%), though MPV of some modes may vary nonlinearly. Finally, comparative analysis of modal simulation indicates the scale of modal parameters response to virtual faults and shows the shape of modes is more informative than the frequency. 6. Experimental verification The operating helicopter-demonstrator and SHM system provided experimental verification of modelling results. The seeded faults indicated as d20mm , and d30mm were implemented as the holes in tail foam-filled part of the blade (fig.2a). 1,52