Parametric Representation and Shape Optimization of Flapping Micro Air Vehicle Wings

Abstract

The effects of wing planform on the aerodynamic performance of a rigid wing in forward flapping flight and hovering configurations were investigated in this paper. The planform design space was parameterized using a new, modified Zimmerman method based on low aspect ratio Zimmerman planform designs. The aerodynamic forces on the wing were calculated using Peters' aerodynamics with an assumed inflow coupled with blade element theory. A multiobjective optimization approach was taken to find the best planform designs for three objectives: wing area, peak power input, and an aerodynamic force based on the kinematic configuration -lift for hovering and thrust for forward flight. A gradient-based optimizer and the ε-constraint method were used to find the Pareto front of optimal designs with the aerodynamic force as the primary objective function. The choice of primary and secondary objective functions is important in determining the optimal planform. The Pareto optimal planforms for the case when only area is considered as a secondary objective function drastically differ from the optimal planforms when only power is taken as a secondary objective function. As the secondary objective ε values change over the design space, so do the optimal planform shapes. INTRODUCTIONFLAPPING wing micro air vehicles (MAVs) have been gaining attention in recent years. As MAVs have shrunk in size, the conventional fixed-wing and propeller design is being replaced by flappingwing designs with the intent to more efficiently generate greater aerodynamic forces. Thus, there is an increasing need to parametrically study flapping wings and the effects of planform shape on the performance of the wing.Various studies have been carried out to investigate the effect of wing geometry on the aerodynamic characteristics of micro air vehicles. Moschetta and Thipyopas [1] studied the effect of wing planforms on the performance of fixed, biplane wing MAVs in a wind tunnel. They considered twelve specific planforms and experimentally determined the lift and drag characteristics of each wing shape. During parametric studies, they focused on typical biplane configuration variables such as gap, stagger, decalage angle, etc., but only considered specifically chosen wing shapes. Ansari, et al. [2] studied the effect of planform design on aerodynamic performance for wings in hovering motion, but also only investigated specific wing shapes. The authors used a previously-developed aerodynamic code [3,4] to explore the effects of aspect ratio, wing length, area, wing offset, and pitch-axis location and noted how lift, drag, and torque all change when only one parameter at a time was varied.Day [5] created a bird-like wing and parameterized the length of the "feathers" on the fixed wing. The author then used a genetic algorithm to optimize for the length of the individual feathers to maximize the ratio of lift to drag. The set-up allowed for many variations on the bird wing, but did not effectively capture other biomimetic shapes.More recently, Stanfor...

Aeroelastic Shape Optimization of a Flapping Wing

“…The thrust increases nearly linearly with respect to the power constraint, a trend which is consistent with previous studies [8]. The optimizer tends to high-aspect ratio Figure 15.…”

“…A full description of the parameterization method called modified Zimmerman has been given elsewhere [8], but a brief introduction will be given here. Traditional Zimmerman planforms are created by joining two ellipses at the quarter-chord, while inverse Zimmerman planforms are created by joining the two ellipses at the three-quarter chord [14,15,16] as seen in Fig.…”

“…Stewart, et al [8] optimized the planform of a rigid flapping wing in both the forward flapping flight and hovering kinematic configurations.…”

“…The aeroelastic calculations are performed by tightly coupling Discrete Kirchhoff Triangular (DKT) finite elements with an unsteady vortex lattice aerodynamic model. The wing planforms are parameterized using the modified Zimmerman method [8] while the structural variables are the coefficients of the polynomial thickness distribution. Multiobjective optimization is performed using the -constraint method to find the wing that give the highest average thrust over the flapping cycle while minimizing the peak input power required.…”

Dynamic simulation and optimization of artificial insect-sized flapping wings for a bioinspired kinematics using a two resonant vibration modes combination

“…Of course, more practical numerical tools [27][28][29] are existing but they are devoted to computational intensive studies such as flight mechanisms. Few of them have been used for sizing purposes [21,[30][31][32][33] and even fewer for preliminary design tasks [34,35].…”