Robustness Analysis of Helicopter Ground Resonance with Parametric Uncertainties in Blade Properties

Abstract

This paper presents a stability robustness analysis of the helicopter ground-resonance phenomenon. By using the lifting procedure the uncertain linear-time-periodic model of the helicopter is transformed into an augmented uncertain linear-time-invariant model that allows the application of μ-analysis tools. The lifting procedure involves a periodic switching linear-time-invariant piecewise model computed using oversampling of the system period. The representativeness of the lifted model for various oversampling period values and methods is discussed and compared with a Floquet analysis for several parametric discretization configurations. A μ-analysis is then applied to find the worst-case parametric configuration for a given rotor angular rate. The parametric uncertainties taken into account are the dynamic characteristics (stiffness and damping) of each blade hinge. A significant advantage of the proposed approach is that it enables performing ground-resonance analysis for a rotor with dissimilar blade properties due to aging effects. Considering uncertainties on the four blade hinge stiffnesses and damping factors, the μ-analysis performed on the lifted model leads to the conclusion that the worst case for degraded rotor stability corresponds to the symmetric perturbation of all the blades.