Bio-inspired flapper with electromagnetic actuation

Jesse A Roll, Purdue University

Abstract

The design, construction, and testing of a unique 2.6 gram electromagnetic actuator operated at resonance with the specific application to flapping flight is presented. An initial performance evaluation of a commercially available electromagnetic actuator used for static positioning of control surfaces on toy helicopters paired with a fabricated flapping wing was performed. An alternative wedge shaped electromagnetic actuator fitted with "virtual" spring magnets was proposed to address the performance issues associated with the commercial actuator. The unique wedge shape of the proposed actuator allows for a maximum stroke amplitude of 120°. without interface through contact by the wing with the sides of the coil. Additional disc magnets attached to the perimeter of the electromagnetic coil were proposed to increase the systems stiffness, adding an energy storage component to the system and creating a "virtual" spring like effect without the additional of direct mechanical coupling. By selecting the size and quantity of these spring magnets, increases to the stiffness of the system could be manually adjusted increasing the bandwidth of the actuator and allowing for system resonance to be achieved. With the application of a potential difference of alternating polarity across the coil, a driving torque is created by the electromagnetic coil and an opposing counter torque is generated by the displacement of the rotor due to the spring magnets. System resonance could then be achieved by tuning the frequency of the external voltage supply to match that of the primary mode of resonance for the system, resulting in peak amplitudes in the wings stroke dynamics. An analytical model of the system's two degree of freedom dynamics was then derived using a rigid body dynamics, simplified electromagnet relationships based on Maxwells equations, and accepted aerodynamic models for translation and rotational damping of flapping wings. A numerical simulation was then preformed based on these models and used to evaluate the response of the system at multiple voltage frequencies and to gauge the dependency of the coupled system dynamics. A step like response was observed to occur at low voltage frequencies with a steady transition to harmonic motion at higher frequencies near resonance. Simulating a simplified from of the dynamics model, assuming only a single degree of freedom, weak coupling of the systems dynamics near resonance was found by direct comparison of simulated response with the majority of the two degree of freedom model's trajectory and amplitude matching that of simplified model. Independent bench tests preformed on the coil and spring magnets were then used to measure the torque generated for comparison to their derived models. Based on deviation in trends found from this comparison, modifications to the analytical models of the actuator were made to more accurately represent the measured data. Using the simplified model of that actuator dynamics, with modified expressions for the torque generated by the coil and spring magnets, perturbation theory was applied to determine an approximate solution for the maximum stroke of the system operating near resonance finding the amplitude of the stroke dynamics independent of the nonlinear stiffness term. A set of 16 test wings were fabricated for use with the electromagnetic actuator during experimentation. Wing parameters used in to construct these test wings were varied systematically to generate unique wing profiles within the range of parameters of actual biological data. Post fabrication, wing shape parameters were determined using imaging processing software to analyze digital pictures taken of the wings. Compound pendulum experiments then were preformed with the test wing suspended from a fabricated test fixture to determine their period of oscillation resulting from a small perturbation applied to the leading edge. Each test wings center of mass was determined from the intersection of a line along the wing's principle axis and the a reference line defined by balancing the wing on a knife edge. Based on the results of these experiments the moment of inertial for each wing was ascertained and tabulated. Frequency response experiments were conducted on the electromagnetic actuator and wing pair using the entire set of test wings by varying supply voltages and spring configurations. Both course and fine frequency bands of voltage signals were applied to the coil and the response of the wing recorded using a high speed camera to determine the resonance frequency and the maximum stroke amplitude. The results of these test were then compared to the values obtained from approximates solution finding 4.3% error in frequency and 7.2% in amplitude, validating the use of these expressions. With the resonate frequency determined, wing kinematics and mean lift measurements were made for the two best preforming wings operating at resonance, reporting a lift-to-weight ratio of over one at 24V for one of the test wings. (Abstract shortened by UMI.)

Degree

M.S.M.E.

Advisors

Deng, Purdue University.

Subject Area

Engineering|Mechanical engineering|Biomechanics

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