Determination of the Vibration Diagnostic Parameters Indicating the Presence of a Mode I Crack in a Blade Airfoil at the Main, Super- and Subharmonic Resonances

Abstract

The paper presents the results of numerical calculations to determine the regularities underlying the influence of the characteristics of a mode I breathing fatigue crack on the leading edge of the aircraft gas turbine engine blade airfoil – that is responsible for the nonlinearity of the vibratory system – on its flexural forced vibration behavior. Their comparison with similar data for the rod of a rectangular cross section has shown satisfactory agreement. The calculation of the vibration diagnostic parameters indicating the presence of damage is performed using the developed finite element models of the investigation objects whose forced vibrations were excited by the kinematic displacement of fixed edge elements. The breathing crack is modeled as a mathematical cross section, the non-penetration of its faces is ensured by solving the contact problem of their interaction. The problem of the system forced vibrations is solved using the Newmark method and fast Fourier transformation. The obtained amplitude-frequency characteristics of the undamaged and damaged blade airfoil are indicative of the increase in the energy dissipation in the system in the presence of a breathing crack. The change in the resonant vibration frequency of the cracked object of investigation and the amplitude ratio of the dominant harmonics of displacements and accelerations (the ratio of the former to the latter at the superharmonic resonance and the latter to the former at the main and subharmonic resonances) were chosen as the vibration diagnostic indicators of damage. The amplitude ratio of the dominant harmonics of accelerations at the superharmonic resonance and that of displacements at the subharmonic resonance is found to be the most sensitive indicator of the presence of cracks.