PSI - Issue 35

A. Bovsunovsky et al. / Procedia Structural Integrity 35 (2022) 74–81 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The reliability of gas turbine engines is primarily determined by the operability of working blades due to their significant mechanical (static and dynamic) and thermal loading. According to Nalimov (2014), damage of blades during operation are considered either as malfunctions (handling mark, wear of shroud shelves and blades ends), if they can be removed by refurbishment, or as failures (cracks, corrosion, surface erosion, etc.), if blades are severely damaged or rejected as defective during engine repair. In the aviation industry of Ukraine, there is an industry standard (Branch Standard-1-00304-79), which is designed to determine the mechanical damage that is permissible during operation of gas turbine engines. The standard normalizes the magnitude of damage in engine structural elements that can be removed as a result of repair, as well as those that are not allowed during operation. The application of this standard is possible only in condition that various types of damage are highly likely to be detected during the operation or repair of an engine. Since the damage specified by the standard is relatively small (their depth should not exceed 0.3 mm), there is a need for sensitive methods of damage diagnostics in structural elements of gas turbine engines. At the same time, these methods should be suitable for the flaw detection in numerous structural elements (such as turbine blades) in a limited time. Diagnostics of damages based on changes in vibration parameters corresponds to these conditions to the greatest extent. Vibration damage detection is an integral and non-destructive methodology for diagnostics of structures and structural elements, Bovsunovsky and Surace (2015). The basis of vibration diagnostics is the fact that mechanical damage in the form of local plastic deformation and/or crack changes the rigidity and damping capacity of mechanical system. This change is used as an informative sign of damage. The most studied vibration characteristics of damage are the change in natural frequencies and mode shapes. Attempts have been made to use anti-resonant frequencies, Afolabi (1987), amplitudes of forced vibration, Collins and Plaut (1992), the occurrence of sub- and super-harmonic resonances, Tsyfansky and Beresnevich (2000), and damping, Bovsunovsky (2004), as applied to damage detection. The higher harmonics method and the method based on the change of damping characteristics have recently been considered as the most promising for practical use. These methods under certain conditions are extremely sensitive to the damage of crack type. Their sensitivity can be one to two orders of magnitude higher than the sensitivity of conventional vibration diagnostics based on the change of natural frequencies. The most common type of damage in structures subjected to dynamic loading is a fatigue crack, which arises because of long time accumulation of plastic deformation, Bovsunovsky and Surace (2015). In problems of vibrations, it is considered as a periodically closing crack. The simplest model of structure with a closing crack is shown in Fig. 1, Bovsunovskii (2001). The presence of fatigue crack is modeled by a piecewise linear characteristic of the restoring force ( R ). The break of this function characterizes the moment of structural stiffness change while crack opens or closes.

R

1 C

0

x

0

C o

m

x

Fig. 1. Modelling of a closing crack in structure.

In Fig. 1 C = C 1 + C 0 is the generalized stiffness of structure when the crack is closed; C 0 is the generalized stiffness of the structure when the crack is open. According to Bovsunovskii (2001), the stiffness ratio C 0 / C can be determined experimentally or analytically through the natural frequencies of an undamaged and damaged structure. A characteristic feature of vibrations of a structure with a closing crack is the manifestation of the so-called non linear effects, namely the appearance of super- and sub-harmonic resonances (Fig. 2), Bovsunovskii (2001). The