Conceptual Analysis of the Non-Linear Forced Response of Aerodynamically Unstable Bladed-Discs

Abstract

The response of aerodynamically unstable tuned bladed-discs with non-linear friction dissipation at blade-root attachments due to harmonic external excitation is studied. The bladed-disc is modeled using a simple mass-spring system and the effect of friction is modeled using a micro-slip friction model. The response is computed in time domain using a Runge-Kutta scheme. The time domain response is decomposed to obtain the evolution of traveling waves in the bladed-disc. Parametric studies have been conducted to study the non-linear response at different vibration amplitudes at high and low engine orders of excitation. It is seen that the non-linearity due to friction gives rise to a complicated interaction between the synchronous response of the system due to harmonic excitation and the non-synchronous response of the system due to aerodynamic instability. For low excitation levels the system behaves as in the pure flutter regime where a single, or at most a few, aerodynamically unstable modes may be found in the final state when a limit cycle is reached. When the forcing is large enough the aerodynamic instability is suppressed and only the non-linear response of the excited mode may be seen. It is concluded that the superimposition of the flutter and forced response analysis in terms of vibration amplitude is not valid and leads to prediction of vibration amplitudes significantly larger than that obtained when both phenomena are simulated together.