Diagnostics of the presence of a fatigue crack in the compressor blade using the spectrum of vibration amplitudes at the superharmonic resonance

In this study, the solution of the forced vibration response of a structural element with a fatigue crack was carried out using the finite element method to determine the influence of its presence on the flexural forced vibration behaviour of the compressor blade airfoil at the superharmonic resonance of the order 1/2. The blade airfoil with a low twisted angle was used as an object of investigation to perform the computational analysis. Its vibrations in the plane of minimum stiffness were excited by the kinematic displacement of root edge elements. The fatigue crack was modelled as a mathematical cut. Two locations of the crack were investigated – on the leading edge and convex side of the blade airfoil. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, was taken into account by solving the contact problem. To quantify this kind of nonlinear dynamic behaviour, the vibration diagnostic parameter was defined as the displacement amplitude ratio of the dominant harmonics at the superharmonic resonance of the order 1/2. Based on the results of the calculations it has been found that regardless of the crack location, the ratio nature is the same for all vibration axes. However, with vibrations in the plane of minimum stiffness, the crack on the convex side of the airfoil has an opening mode propagation, which makes it possible to fix its location due to a sharp change in the ratio of the amplitudes of the dominant harmonics along the corresponding axis.