A Comprehensive Piezoelectric Bending-Beam Model Inspired by Microaerial Vehicle Applications

摘要

Microaerial vehicles are an up-and-coming area of robotics which is fuelled by modern understanding of the unsteady aerodynamics of insect flight and the development of new actuation technologies. In the past two decades computer simulations have aided in uncovering the lift mechanisms which flying insects use to stay aloft. Using these details, roboticists had begun using lightweight structures and high power density actuators to mimic the physical parameters and flapping kinematics of flying insects with the intent to recreate the dynamics of insect flight. One of the most important aspects of flapping-wing microaerial vehicles is the actuation method. Piezoelectric bending-beam actuators have been scaled up from MEMS technology for use in microaerial vehicle applications owing to their high power density and performance at low mass.\nThe initial development toward the UTIAS Robotic Dragonfly, a microaerial vehicle platform using a piezoelectric-based actuator, is outlined. The components are fabricated from lightweight materials such as a carbon fibre frame, polymide film joints, and polyester film wings while the actuator is a piezoelectric bending-beam which was designed using existing mathematical models. The design and fabrication of the wings, actuator, transmission, and power supply are detailed. The prototypes are measured for lift generation using custom lift sensors which had undergone static and dynamic calibration for low-force, high-bandwidth measurement. Although the resulting lift curves qualitatively correspond with the literature, it was determined that more power was needed for lift-off to be achieved and existing piezoelectric models do not fully account for maximizing the force-deflection relationship.\nAn extension to the existing Ballas model of piezoelectric bending-beam devices is derived. This modified Ballas model incorporates devices beyond constant width. Actuator performance limitations highlighted the need for a more comprehensive piezoelectric bending-beam model. The final contribution is a derivation of a new bending-beam model to permit multiple layers, any continuous width profile, and independent layer excitation. An energy-based approach using the extended Hamilton's principle was used to incorporate the generalities desired in the new piezoelectric bending-beam model. Examples of the new model are compared to both simulation and experiment for verification as well as to showcase its versatility.