A Design Procedure for Flapping Wings Comprising Piezoelectric Actuators, Driver Circuit, and a Compliant Mechanism
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Flapping-wing micro air vehicle (MAV) is an emerging micro-robotic technology, which has several challenges toward its practical implementation. Inspired by insect flight, researchers have adopted bio-mimicking approach to accomplish its engineering model. There are several methods to synthesize such an electromechanical system. A piezoelectric actuator driven flapping mechanism, being voltage controlled, monolithic, and of solid state type exhibits greater potential than any conventional motor driven flapping wing mechanism at small scale. However, the demand for large tip deflection with constrained mass introduces several challenges in the design of such piezoelectric actuators for this application. The mass constraint restricts the geometry, but applying high electric field we can increase the tip deflection in a piezoelectric actuator. Here we have investigated performance of rectangular piezo-actuator at high electric field. The performance measuring attributes such as, the tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically calculated for the actuator at high electric field. The analytical results suggest that the performance of such an actuator can be improved by tailoring the geometry while keeping the mass and capacitance constant. Thereby, a tapered piezoelectric bimorph cantilever actuator can provide better electromechanical performance for out-of-plane deflection, compared to a rectangular piezoelectric bimorph of equal mass and capacitance. The constant capacitance provides facility to keep the electronic signal bandwidth unchanged. We have analytically presented improvement in block force and its corresponding output strain energy, energy density and energy effi- ciency with tapered geometry. We have quantitatively and comparatively shown the per- formance improvement. Then, we have considered a rigid extension of non-piezoelectric material at the tip of the piezo-actuator to increase the tip deflection. We have an- alytically investigated the effect of thick and thin rigid extension of non-piezoelectric material on the performance of this piezo-actuator. The formulation provides scope for multi-objective optimization for the actuator subjected to mechanical and electrical con- straints, and leads to the findings of some useful pareto optimal solutions. Piezoelectric materials are polarized in a certain direction. Driving a piezoelectric actuator by high electric field in a direction opposite to the polarized direction can destroy the piezo- electric property. Therefore, unipolar high electric field is recommended to drive such actuators. We have discussed the drawbacks of existing switching amplifier based piezo- electric drivers for flapping wing MAV application, and have suggested an active filter based voltage driver to operate a piezoelectric actuator in such cases. The active filter is designed to have a low pass bandwidth, and use Chebyshev polynomial to produce unipolar high voltage of low flapping frequency. Adjustment of flapping frequency by this voltage driver is compatible with radio control communication. To accomplish the flapping-wing mechanism, we have addressed a compatible dis- tributed compliant mechanism, which acts like a transmission between the flapping wing of a micro air vehicle and the laminated piezoelectric actuator, discussed above. The mechanism takes translational deflection at its input from the piezoelectric actuator and provides angular deflection at its output, which causes flapping. The feasibility of the mechanism is investigated by using spring-lever (SL) model. A basic design of the com- pliant mechanism is obtained by topology optimization, and the final mechanism is pro- totyped using VeroWhitePlus RGD835 material with an Objet Connex 3D printer. We made a bench-top experimental setup and demonstrated the flapping motion by actuating the distributed compliant mechanism with a piezoelectric bimorph actuator.
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