Time-Frequency Analysis of Experimental and Analytical Hub Loads of a Rotor Undergoing a Rotor Speed Change

A two-part analytical study was conducted examining a small-scale, two-bladed rotor undergoing a change in rotor speed. First, a parametric study was conducted to understand how rotor transient response, determined using a time-marching solution, is affected by the choice of rotor wake model, blade elasticity, and inclusion of an elastic support structure model. The second part of the study compared results from an analytical model of the NASA Multirotor Test Bed (MTB) undergoing a rotor speed change to wind tunnel data. Since the analytical and experimental time histories were nonstationary signals, a Stockwell transform was employed to analyze the data in lieu of traditional Fourier transform-based methods. The analysis included extraction of time-varying frequency content of the rotor thrust and hub motion, damping ratios, instantaneous rotor speed, and instantaneous phase difference between thrust and hub motion. Use of a free wake model was found to be necessary to predict higher-harmonic thrust, however, it underpredicted the amplitude of the unsteady loads. Modeling the elasticity of the stiff rotor blades installed on the MTB resulted in minimal impact on the computed vibratory loads compared to a rigid blade model. The current analytical model of the MTB, including an elastic support structure, properly predicted the measured trends in the frequency content of the thrust.