Stability of Rotorcraft Ground Resonance by Estimating Lyapunov Characteristic Exponents From Multibody Dynamics

Abstract

This work discusses the use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from existing multibody solvers. Helicopter ground resonance is analyzed. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.