A Methodology for the Vibration Amplitude Prediction of Self-Excited Rotors Based on Dimensional Analysis

The dimensional analysis of a simple model that represents the vibration of aerodynamically unstable rotor blades is presented. Based on this analysis a methodology to determine the rotor blade vibration amplitude is outlined. The method assumes that the forcing is due solely to the self-excitation of the airfoil and that the vibration amplitude is small enough to represent the unsteady aerodynamics associated to the airfoil motion using the linearized Navier-Stokes equations. The vibration amplitude is saturated due to the non-linearity of fir-tree dry friction which is modelled using a simplified approach. To compensate for the limitations of the friction model several hypotheses need to be done, among them, the geometric similarity of the different configurations and that the aspect ratio of the rotor blades is high. The application of the method to a low-pressure-turbine bladed-disk is discussed in detail. A comparison of the present method against experimental data is presented.