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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Expensive accelerometers require a power supply and may interact with the flow if mounted on a streamlined surface. Aiming for optimal solution for rotating measurement system Mironov et al. (2019a) proposed to substitute accelerometers by cheap dynamic deformation sensors with negligible thickness and mass. The influence of operation factors (speed, maneuvers, and payload) essentially influence the blade’s modal properties. Such influence was studied for different purposes, for instance Oktay & Sal (2015) researched the variation of constrained controllers under flight condition. The main problem is that modal properties of helicopter blades depend of external factors, including: • centrifugal and bending loads subjected to rotation speed, pitch and payload , • ambient factors like wind, temperature and others, • differences between serial blades caused by technological reasons. To reduce influence of external factors Mironov et al. (2019b) offered the modal passport (MP) approach that allows estimation of modal properties of the operating structure taking into account the ambient and operational factors. The MP concept also includes the technique for quantitative estimation of modal parameters modification to compute the difference between two modal states using modal properties of multiple oscillation modes. Also MP takes into account individual specialties of each particular blade. The typical MP describes common modal properties of all blades of the same type. It considers the idealized blade, whose modal parameters are equal to averaged ones of a set of similar blades. The typical MP of operating blade is based on testing of mean set of blades and includes two parts. The first one is the matrix of typical modal parameters (averaged means and confidence intervals) computed from experimentally measured modal data of non-rotating blades in reference state. The second one are dependence functions (analytical and empirical) describing the relation between typical modal parameters and specific operational factor. For instance, rotation speed, pitch and payload are the samples of such factors affecting modal parameters. The typical MP is valid within the range of determined dependence functions. Therefore, to develop the typical MP for SHM of operating blades the complete range of operational factors have to be used for testing. If the number of operational factors is p , the collected testing data (1) Here the dependence functions , , relate the parameters ( , , , ) of m th mode to i th factor to reference modal parameters ( 0 , 0, , 0 , ) that are modified under influence of operational factor . Being calculated based on sufficient set of typical blades both modal parameters in reference state and dependence functions of operational factors represent common properties of similar (typical) blades. The individual passport reflects modal properties of the particular blade and serves as the tool for its monitoring. Individual MP uses comparable parameters for estimating the difference between two states of the blade. To clean out parameters from operational influence of factor, the individual MP recalculates the modal parameters measured to comparable ones ̂ , ̂ , ̂ using typical dependence functions ( ), ( ), ( ) of typical MP. ̂ = ( ); ⁄ ̂ = ( ) ⁄ ; ̂ = ( ) ⁄ (2) To estimate the change of the blade’s modal shape Mironov et al. (2019b) offered the diagnostic Modal Parameters Variation ( MPV ). MPV computes the difference of comparable modal shapes between j th and reference states in normalized scale. A similar approach may be used for comparable parameters of frequency and damping in two different states. The aggregated MPV (AMPV ) utilizes normalized changes of all modal parameters for diagnosis. This allows forming the multidimensional ( p+2 ) modal parameters matrix. Modal parameters dependence on the operational factor is given by: = ( 0 , ) ; = ( 0, , ) ; = ( 0 , ) 2. Modal passport 2.1. MP structure There are typical and individual components of the blade MP.