Study of the Influence of the Presence of Local Edge Damage on the Spectrum of Natural Frequencies of Torsional Vibrations of Cantilever Rods

The results of computational experiments to determine the influence of the width and location of a groove as a model of open edge crack on the formation of the spectrum of natural frequencies of torsional vibrations of cantilever rods are presented. The modal characteristics of rods with geometrical parameters corresponding to a wide slenderness range of turbomachine rotor blades are considered. A modal analysis of rods with local material discontinuity in the form of a groove was carried out by means of three-dimensional finite element modeling. Based on the results of computational studies, the dependence of the change in the natural frequency of the 1st–4th torsional vibration modes on the location and depth of a 1 mm wide groove was determined. It is shown that under torsional vibrations at a certain location of the damage, the natural frequency of the rod is equal to the frequency without it. It was established that this relative location, called the transition point, is inherent in all modes of torsional vibrations of the objects under study. A characteristic feature is that the transition point depends on the depth of damage and the radius of inertia of the rod cross-section and does not depend on the rod length. It is shown that, in addition to the presence of a transition point, the obtained plots for the 2nd–4th modes of torsional vibrations are characterized by the presence of ranges of the relative location of the groove, at which there is exceeding the value of the vibration frequency of the undamaged rod which is caused by the ratio of its elastic and inertial properties. A comparative analysis of the laws governing the formation of the spectra of natural frequencies of torsional and bending vibrations of the rods under study in the fundamental mode and higher modes was carried out. These plots can be used to select a method for the vibration diagnostics of highly stressed parts of modern machines, in particular, turbomachine blades.