Bond graph modeling of a typical flapping wing micro-air-vehicle with the elastic articulated wings

In the present research, a new comprehensive model of a flexible articulated flapping wing robot using the bond graph approach is presented. The flapping kinematics of a two-section wing is introduced via the bond graph based approach on a hybrid mechanism providing amplitude and phase characteristics. The aerodynamic quasi-steady approach equipped with stall correlation is utilized according to the reduced flapping frequency and the angle of attack ranges. The local flow velocity and the wing position are calculated in both wing and body coordinates taking into account rotation and translation of the wing different parts. Estimation of the effective angle of attack is performed by calculating the instantaneous torque distribution on both wing sections. Aeroelastic modeling is employed in which the wing structure is assumed as an elastic Euler–Bernoulli beam at the leading edge with three linear torsional modes. In this novel integrated bond graph model, computation of the performance indices including the average lift and thrust, consumed and produced powers by flapping and mechanical efficiency are presented. Due to existence of the numerous geometric and kinematic parameters in articulated flexible flapping wing, such a model is essential for design and optimization. Consequently, an example of a typical parametric study and the results validation are carried out. It is indicated that the sensitivity of the bird performance to relative change in design variables would increase for out of phase flapping, second part stiffness, flapping amplitude, frequency and velocity respectively. It is interesting that by employing the reverse-phase flapping which is possible only via articulated wings, the maximum efficiency could be achieved. In addition, it is shown that adjusting the wing torsional stiffness is a crucial item in design of passive flapping robots. The key advantage of the two-section flapping wing is depicted as the controlling capability of the angle of attack in the outer part of the wing. Finally, the improved version of the bird is being addressed by approximately 15% progress in propulsive efficiency.