Definition and computation of a flutter safety margin for quadcopters by chained 2-DOF aeroelastic models

Abstract

When thin, flexible structures, such as the rotors of a quadcopter, are subjected to airflow, aeroelastic phenomena (e.g. flutter) may occur due to the interaction of elastic, inertial, and aerodynamic forces. We examine rotor blade flutter during forward flight. In this regime, the relative wind experienced by the rotor blades changes periodically, which may result in parametric excitation and a corresponding reduced critical velocity. To capture the variation of relative wind along the rotor radius, we construct a three-dimensional reduced-order model by chaining multiple two-degree-of-freedom aeroelastic models. The aerodynamic forces are computed using a quasi-steady approach. Wind tunnel measurements on the quadcopter are used to obtain the rotor angular velocities corresponding to different forward flight speeds. We then compute the stability chart for the quadcopter by numerically solving the equations of motion of the reduced-order model. From this chart we can determine -for a given rotor speed and forward flight velocity- the minimal speed increase (the flutter safety margin) required for the rotors to lose their stability.