Computation of bladed disk response with nonlinear friction forces

Friction effects (at the blade-disk attachment, dampers, shrouds,...) dissipate the energy introduced by the aerodynamic forcing of the rotating wakes of the upstream rows, in the case of forced response, or by the aeroelastic instability, in the flutter case. The balance between the energy pumped into the system and the friction dissipation ultimately determines the final amplitude of the blade limit cycle oscillation that sets in. The accurate computation of the blade vibration amplitude is therefore essential for the correct estimation of the fatigue effects and the blade operative life. The energy method uses the elastic mode shapes to estimate friction dissipation. This assumption seems justified, since the motion at the contact interfaces is typically very small, but it has recently been shown that it severely underestimates the friction effects. The purpose of this paper is to investigate the reason behind the failure of the energy method. A simple FEM model is used to study this problem, first in a purely linear case, and then in a configuration with nonlinear friction effects. It is seen that the linear vibration modes, with the contacts bonded, have to be considered together with the so-called constraint modes, associated with the motion at the contact interface, in order to accurately determine the friction dissipation using the energy method.