PSI - Issue 35

5

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

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PC

Frame

Voltmeter

Electromagnet

Straine gage Blade

Oscilloscope A/D

Frequencymeter

Amplifier

Fig. 5. Photo and block diagram of the experimental setup KD-1M.

3. Higher harmonics method As shown in the Introduction, the amplitudes of non-linear resonances are very small. Therefore, they are of little use for the purpose of damage diagnostics. At the same time, the non-linearity of vibrations of cracked structure at sub- and super-harmonic resonances, which manifests itself in the appearance of higher harmonics in the spectrum of vibration response, under certain conditions is enormous. One such condition is the relatively low level of damping in the mechanical system. The blades of aircraft gas turbine engines are made of low damping alloys. Their damping ability in terms of logarithmic decrement of vibration does not exceed  <0.003, Pisarenko et al. (1971). It follows from Section 4, that damping characteristic of engine D-36 blades does not exceed  <0.0017. This means that one can expect high sensitivity to damage of both methods under consideration. As a result of numerical studies by Bovsunovskii (1999), it was shown that the non-linear viscous and hysteresis friction (the latter is peculiar to metallic materials) leads to the appearance of odd harmonics in the spectrum of vibration response. At the same time, a break in the characteristic of restoring force (see Fig. 1) causes the appearance of even harmonics, the largest of which, the second, is a reliable sign of closing crack. Experimental procedure was as follows. Initially, the resonant frequency of the intact blade ( f ) was determined. At this frequency, the blade was cyclically loaded with a stress amplitude in the root section  a =250 MPa until the appearance of minimal crack became visible by microscope. After that, the amplitude of vibration was reduced to  a =5 MPa to prevent crack growth during vibration diagnostics, and a search for super-harmonic resonance was carried out in the vicinity of the frequency f с /2 ( f с is the resonant frequency of cracked blade). After finding this resonance, a spectral analysis of vibration response was carried out. The presence of crack was associated with the second harmonic of strain and acceleration vibration response spectrum ( A 2 ). The sizes of crack in the tested blades are given in Table 2, where 2 c is the length of crack on the surface; a is the depth of crack; S с - crack area; S is the cross-sectional area of the blade in the plane of crack. The calculated values of crack depth are shown in brackets. After the length of crack on the surface reached the value 2 c =9.7 and 7.5 mm, respectively, the blades were heated to mark the crack, after which they were destroyed by cyclic deformation. Heating intensifies the process of crack surface oxidation, because of which its color changes. This made it possible to determine actual shape, depth, and area of cracks (Fig. 6).