power into consideration and explored various multi-objective formulations [13]. Our future pursuit is a more expansive multi-objective optimization, utilizing both thrust and power consumption and a more generalized design space. A study by Combes and Daniel identified scaling laws between geometric dimensions on the wing, such as span, and the flexural stiffness for a variety of insect forewings [14]. This suggests that stiffness is important for both efficiency and thrust production. This work can be effective in identifying whether scaling laws exist in a synthetic platform where there is only one active degree of freedom, and the materials differ from those used in nature. This paper explores the effect of synthetic wing stiffness on the thrust production and power consumption. The objective is to use the stiffness ratio between span-wise and chord-wise measurements as a simple indicator of efficiency. We study the effect of the stiffness ratio on the thrust, power and an efficiency indicator (thrust/power). The final step is to use a surrogate (or response surface or metamodels) for approximating the stiffness ratios of a wing and then use the surrogate in a multiobjective optimization as an extra constraint, deterring sampling in the region that is inefficient. This can save time and prevent waste of resources. In this paper, we explore this idea of identifying efficient wing designs through stiffness ratio measurements. The simplicity of these measurements make it easy to model, and can provide alternative optimization opportunities. 28.2 Wing Construction The components of the wing include a plastic frame, a unidirectional carbon fiber rod, and a nylon membrane. The plastic used for the frame was Acetal resin (DuPont™Delrin ® ) and was chosen for is machinability and stiffness. The 250mmthick plastic sheets were CNC machined using a four-fluted square endmill (1 mm diameter), using a 3-axis Haas TM-1 milling machine. A channel was milled into the leading edge along the whole span that assisted in locating a 0.5 mm diameter carbon fiber rod (Avia Sport Graphlite ® ). A cyanoacrylate adhesive was then utilized to bond the carbon rod to the frame. The assembly is completed by applying a Capran ® nylon film (Honeywell) to the bottom of the skeleton, using an adhesive transfer film (Scotch ® 3 M 9471LE) Fig. 28.1. 28.3 Thrust and Current Testing Procedure A custom flapping mechanism is used to test the wing pairs. This single active degree of freedom device is fixed to a six axis force-torque sensor (ATI Nano 17), allowing for thrust and lift forces to be measured. A Maxon EC16 brushless motor drives a slider crank mechanism that oscillates the wing clamps Fig. 28.2. They allow for a stroke angle of 96 and are fixed in the other two rotational axis; therefore, the passive rotation of the wing is due to twisting of the wing structure. The wings are tested at 20, 25, and 30 Hz flapping frequencies, and data is collected for 10 s for each frequency. To account for any offset in the load measurement, a tare is taken for 6 s before the flapping begins. The average force in the 10 s window is used to represent the thrust at that frequency. A second order Butterworth low pass filter is used to reduce high frequency noise in the measurement. A 16-bit National Instruments USB-6251 data acquisition device was utilized, while a LabVIEW virtual (Stiffness %) x ½ Span Θ Batten Angle ½ Span Chord Capran® Membrane Root Batten Radial Batten A-A A A Fig. 28.1 The components and terminology used in this optimization are presented in the illustration. The 0.5 mm diameter commercial off the shelf carbon fiber rod is placed in a channel and extends a portion of the span described by the stiffness percentage design variable 250 K. Chang et al.
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