A novel three degree-of-freedoms oscillation system of insect flapping wings
We propose an oscillation system to replicate the dynamic behavior of flapping wings, inspired by insect flight muscles. In particular, we study the flight of the fruit fly Drosophila virilis. We model the wing as a rigid body with three degree-of-freedom, described by three Euler angles: the stroke angle, the rotation angle and the deviation angle. Insect flight muscles are separated into two types: power muscles and control muscles. One actuator and one torsional spring at the stroke angle act as the power muscles. Two torsional springs at the rotation angle and the deviation angle mimic the control muscles. A dynamic model, using a blade-element model and a quasi-steady model to calculate aerodynamic forces and moments, is set up for analysis of the system's performance. Using non-dimensional analysis, we are able to identify the dynamic behavior of the system through four coefficients: stroke stiffness coefficient, rotation stiffness coefficient, deviation stiffness coefficient and input torque coefficient. We use the dynamic model to explore a large coefficients space of the oscillation system. We find that tuning deviation stiffness coefficient and rotation stiffness coefficient generates four different types of wing trajectories. Among them, the one with a high deviation stiffness coefficient and a mediate rotation stiffness coefficient produces high lift and high power loading. Its wing trajectory is quite similar to the wing trajectory in actual insects. Furthermore, a hybrid optimization algorithm (a genetic algorithm and a Nelder-Mead simplex algorithm) is implemented to find the optimal stiffness coefficients. Through these coefficients, the system minimizes power loading while still providing enough lift to maintain a time-averaged constant altitude over one stroke cycle. The results of this optimization indicate that the flapping wing with nonzero deviation achieves a better aerodynamic performance than the wing with zero deviation. The oscillatory property of this system does not only explain how insects use flight muscles to tune wing kinematics, but it also allows for design simplifications of the wing driving mechanism of flapping micro air vehicles.
Deng, Purdue University.
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