Effect of Elastic Blade Deformation on Trim and Vibratory Loads of a Quadcopter

This study examines the effect of rotor blade elastic deformations on a quadcopter in forward flight conditions. The blade equations are discretized using the Galerkin method and the blade periodic response is calculated using the harmonic balance method. Simulations are conducted on a 2 kg quadcopter with 12 inch diameter two-bladed rotors. The blade root vertical shear, flap bending moment and drag shear showed a strong 1/rev variation due to the azimuthal variation in aerodynamic loads. Elastic blade deformations did not affect the aerodynamic loads but the addition of in-phase 1/rev inertial loads resulted in net increases of 28%, 36% and 48% in the 1/rev blade root vertical shear, flap bending moment, and drag shear, respectively, at a forward flight speed of 10 m/s. The in-plane elastic deformations further introduced a 1/rev blade root radial shear due to the radial Coriolis force. At 10 m/s forward flight speed, accounting for elastic blade deformations resulted in a 7.6% reduction in the steady hub drag force, a 37% increase in steady hub roll moment, and a 15% increase in steady hub pitching moment that requires a 12% higher pitch RPM control input to trim the quadcopter. Increases of 103% in the 2/rev rotor hub in-plane loads (drag and side force), of 12% in the 2/rev hub vertical force, and of 25% in the 2/rev hub pitching and rolling moments were also observed. Since the forward rotor, lateral rotors, and the rear rotor operate at distinct rotational speeds, the aircraft is subject to vibratory loading at three different frequencies resulting in a beating phenomenon. The maximum amplitude of these oscillations equals the sum of the amplitudes of the three constituent vibrations, but reaches its maximum only once every twelve cycles. The 2/rev rotor hub vibratory moments are the dominant contributors to the aircraft pitch and roll vibrations, while the 2/rev rotor hub in-plane forces are the dominant contributors to the aircraft vibratory yaw moments. The blade phasing between the two lateral rotors has an effect on the magnitude of the total roll vibrations on the aircraft.

Reference

Niemiec, R., and Gandhi, F., "Effect of Elastic Blade Deformation on Trim and Vibratory Loads of a Quadcopter ,"

Proceedings of the 73rd American Helicopter Society Annual Forum, Fort Worth, Texas, May 9–11, 2017.