Nonlinear dynamics of a flapping rotary wing:Modeling and optimal wing kinematic analysis

The analysis of the passive rotation feature of a micro Flapping Rotary Wing（FRW）applicable for Micro Air Vehicle（MAV） design is presented in this paper. The dynamics of the wing and its influence on aerodynamic performance of FRW is studied at low Reynolds number（~10~3）.The FRW is modeled as a simplified system of three rigid bodies： a rotary base with two flapping wings. The multibody dynamic theory is employed to derive the motion equations for FRW. A quasi-steady aerodynamic model is utilized for the calculation of the aerodynamic forces and moments. The dynamic motion process and the effects of the kinematics of wings on the dynamic rotational equilibrium of FWR and the aerodynamic performances are studied. The results show that the passive rotation motion of the wings is a continuous dynamic process which converges into an equilibrium rotary velocity due to the interaction between aerodynamic thrust, drag force and wing inertia. This causes a unique dynamic time-lag phenomena of lift generation for FRW, unlike the normal flapping wing flight vehicle driven by its own motor to actively rotate its wings. The analysis also shows that in order to acquire a high positive lift generation with high power efficiency and small dynamic time-lag, a relative high mid-up stroke angle within 7–15° and low mid-down stroke angle within -40° to -35° are necessary. The results provide a quantified guidance for design option of FRW together with the optimal kinematics of motion according to flight performance requirement.

Automated Kinematics Measurement and Aerodynamics of a Bioinspired Flapping Rotary Wing

A physical model for a micro air vehicle with Flapping Rotary Wings （FRW） is investigated by measuring the wing kine- matics in trim conditions and computing the corresponding aerodynamic force using computational fluid dynamics. In order to capture the motion image and reconstruct the positions and orientations of the wing, the photogrammetric method is adopted and a method for automated recognition of the marked points is developed. The characteristics of the realistic wing kinematics are presented. The results show that the non-dimensional rotating speed is a linear function of non-dimensional flapping frequency regardless of the initial angles of attack. Moreover, the effects of wing kinematics on aerodynamic force production and the underlying mechanism are analyzed. The results show that the wing passive pitching caused by elastic deformation can sig- nificantly enhance lift production. The Strouhal number of the FRW is much higher than that of general flapping wings, indi- cating the stronger unsteadiness of flows in FRW.

Unsteady Aerodynamic Forces and Power Consumption of a Micro Flapping Rotary Wing in Hovering Flight

The micro Flapping Rotary Wing （FRW） concept inspired by insects was proposed recently. Its aerodynamic performance is highly related to wing pitching and rotational motions. Therefore, the effect of wing pitching kinematics and rotational speed on unsteady aerodynamic forces and power consumption of a FRW in hovering flight is further studied in this paper using computational fluid dy- namics method. Considering a fixed pitching amplitude （i.e., 80°）, the vertical force of FRW increases with the downstroke angle of attack and is enhanced by high wing rotational speed. However, a high downstroke angle of attack is not beneficial for acquiring high rotational speed, in which peak vertical force at balance status （i.e., average rotational moment equals zero.） is only acquired at a comparatively small negative downstroke angle of attack. The releasing constraint of pitching amplitude, high rotational speed and enhanced balanced vertical force can be acquired by selecting small pitching amplitude despite high power consumption. To confirm which wing layout is more power efficient for a certain vertical force requirement, the power consumed by FRW is compared with the Rotary Wing （RW） and the Flapping Wing （FW） while considering two angle of attack strategies without the Reynolds number （Re） constraint. FRW and RW are the most power efficient layouts when the target vertical force is produced at an angle of attack that corresponds to the maximum vertical force coefficient and power efficiency, respectively. However, RW is the most power efficient layout overall despite its insufficient vertical force production capability under a certain Re.