Abstract
Flutter is a major constraint on modern turbomachines; as the designs move toward more slender, thinner, and loaded blades, they become more prone to experience high cycle fatigue problems. Dry friction, present at the root attachment for cantilever configurations, is one of the main sources of energy dissipation. It saturates the flutter vibration amplitude growth, producing a limit cycle oscillation whose amplitude depends on the balance between the energy injected and dissipated by the system. Both phenomena, flutter and friction, typically produce a small correction of the purely elastic response of the structure. A large number of elastic cycles is required to notice their effect, which appears as a slow modulation of the oscillation amplitude. Furthermore, even longer time scales appear when multiple traveling waves are aerodynamically unstable and exhibit similar growth rates. All these slow scales make the system time integration very stiff and CPU expensive, bringing some doubts about whether the final solutions are properly converged. In order to avoid these uncertainties, a numerical continuation procedure is applied to analyze the solutions that set in, their traveling wave content, their bifurcations and their stability. The system is modeled using an asymptotic reduced order model and the continuation results are validated against direct time integrations. New final states with multiple traveling wave content are found and analyzed. These solutions have not been obtained before for the case of microslip friction at the blade attachment; only solutions consisting of a single traveling wave have been reported in previous works.
Highlights
Flutter onset is currently a very important limitation in modern turbomachinery, where blade designs are getting more slender and closer to their mechanical limit
Multi-Traveling Wave (TW) stable states are found in a simplified model of a bladed-disk with microslip friction at the bladeddisk attachment
The model describes the vibration of a nearly flat modal family with several aerodynamically unstable modes and is derived through the application of a multiple scales method that allows to filter out the fast elastic blade oscillation
Summary
Flutter onset is currently a very important limitation in modern turbomachinery, where blade designs are getting more slender and closer to their mechanical limit. We consider the case of flutter vibrations with microslip contact forces at the blade fir-tree, where the effect of friction does not substantially change the natural vibration modes As it was mentioned above, previous works on this configuration [4,9,10] have only found final vibration states consisting of just one single TW. This procedure eliminates the need for direct time integration of the system, which requires very long integration times and always leaves some uncertainty about whether the final state is fully converged To this end, first, we briefly introduce the asymptotic model used, study the stability of the zero solution (no blade vibration) and compute the single TW solutions that appear when the magnitude of the flutter instability is increased. They have two different frequencies and propagate around the rotor with nonuniform blade to blade amplitude
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