The Pennsylvania State University The Graduate School FLAPPING WING MECHANISMS FOR PICO AIR VEHICLES USING PIEZOELECTRIC ACTUATORS A Dissertation in Electrical Engineering by Kiron Mateti ' 2012 Kiron Mateti Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2012 UMI Number: 3521284 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent on the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3521284 Copyright 2012 by ProQuest LLC. All rights reserved. This edition of the work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 The dissertation of Kiron Mateti was reviewed and approved∗ by the following: Srinivas Tadigadapa Professor of Electrical Engineering Dissertation Co-Advisor, Co-Chair of Committee Christopher D. Rahn Professor of Mechanical and Nuclear Engineering Dissertation Co-Advisor, Co-Chair of Committee Zhiwen Liu Professor of Electrical Engineering Qiming Zhang Professor of Electrical Engineering George A. Lesieutre Professor of Aerospace Engineering Kultegin Aydin Professor of Electrical Engineeing Head of Electrical Engineering ∗Signatures are on file in the Graduate School. Abstract Swarms of flying robotic insects could revolutionize hazardous environment explo- ration, search and rescue missions, and military applications. Reducing size to insect scale enables entrance into extremely narrow spaces with inherent stealth advantages. For mass production, these vehicles must have reliable and repeatable fabrication processes that define flapping wing mechanisms with microscale fea- tures and produce large flapping amplitudes at frequencies in the range of many insects. This thesis focuses on the design and fabrication processes of flapping wing mechanisms for these types of robots. First, the design, fabrication, modeling, and experimental validation of the Penn State Nano Air Vehicle (PSNAV), a NAV scale piezoelectrically actuated clapping wing mechanism, is presented. A flexure hinge allows passive wing ro- tation for the clapping wing mechanism. Analytical models of wing flapping and rotation are derived and validated using experimental wing trajectory results. The PSNAV prototype is experimentally shown to provide approximately 54 deg. peak to peak wing rotation, 14 deg. peak to peak flapping angle, and 0.21 mN of thrust at 9.5 Hz. At 25.5 Hz, the prototype produces a maximum of 1.34 mN of thrust. The PSNAV model accurately predicts the wing resonances in the experimental iii prototype. Model-predicted thrust is lower than the experimentally measured val- ues, however. Towards a compliant mechanism, the next stage of this research introduces a simple process to monolithically fabricate flying robotic insects at the pico air ve- hicle (PAV) scale from SUEX dry film, an epoxy based negative photoresist similar to SU-8. The developed process has fewer steps compared to other methods, does not use precious metals, and greatly reduces processing time and cost. It simul- taneously defines the PAV airframe, compliant flapping mechanism, and artificial insect wing using photolithography. Using this process, we designed and fabricated the LionFly, a flapping wing prototype actuated by a PZT-5H bimorph actuator. Several LionFly prototypes were fabricated and experimentally tested. Theoret- ical and experimental results have excellent agreement validating the compliant mechanism kinematics and aerodynamic added mass and damping. High voltage tests show a peak to peak flapping angle of 55 deg. at 150 V amplitude with 150 V DC offset at 51 Hz resonance. Consistent performance from multiple prototypes demonstrate the reliable and repeatable nature of the fabrication process. Lastly, this research presents detailed modeling and experimental testing of wing rotation and lift in the LionFly. A flexure hinge along the span of the wing allows the wing to rotate in addition to flapping. A linear vibrational model is developed and augmented with nonlinear aerodynamic forces using the blade el- ement method. This model is validated using experimental testing with a laser vibrometer and accurately predicts small amplitude wing dynamics in air and vac- uum. Strobe photography and high definition image processing is used to measure high amplitude wing trajectories. At higher amplitudes, the model can sufficiently iv predict wing trajectory amplitudes, but phase measurement and simulation have slight error. The LionFly produces 46 deg. flap and 44 deg. rotation peak to peak with relative phase of 12 deg., and maximum lift of 71 µN at 37 Hz. By reducing theinertiaofthewingandtuningtherotationalhingestiffness, aredesigneddevice is simulated to produce lift to weight ratio of one. v Table of Contents List of Figures ix List of Tables xii Acknowledgments xiii Chapter 1 Introduction 1 1.1 Background of Flapping Wing Mechanisms . . . . . . . . . . . . . . 2 1.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Component Selection . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Current Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Contribution and Organization of Thesis . . . . . . . . . . . . . . . 11 Chapter 2 Clapping Wing Nano Air Vehicle Actuated By Piezoelectric T-beams 13 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Design and Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 T-Beam Actuators . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 Amplification Mechanism . . . . . . . . . . . . . . . . . . . 18 2.2.3 Wing Design . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Experimental Testing and Results . . . . . . . . . . . . . . . . . . . 27 Chapter 3 Monolithic SUEX Flapping Wing Mechanisms for Pico Air Ve- hicle Applications 33 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Material Choice and Fabrication . . . . . . . . . . . . . . . . . . . . 34 vi 3.2.1 Material Choice for Compliant Mechanisms . . . . . . . . . 34 3.2.2 Monolithic Multilevel Fabrication of SUEX . . . . . . . . . . 37 3.2.3 Actuator Selection . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Compliant Mechanism Design and Modeling . . . . . . . . . . . . . 41 3.3.1 Mechanism Design . . . . . . . . . . . . . . . . . . . . . . . 41 3.3.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 48 3.4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . 48 Chapter 4 Wing Rotation in the LionFly 56 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.2 Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2.3 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2.3.1 Aerodynamic Forces . . . . . . . . . . . . . . . . . 63 4.2.3.2 Aerodynamic Moments . . . . . . . . . . . . . . . . 65 4.2.3.3 Added Mass . . . . . . . . . . . . . . . . . . . . . . 65 4.3 Experimental Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . 69 4.4 Model-Based Redesign . . . . . . . . . . . . . . . . . . . . . . . . . 78 Chapter 5 Conclusions and Future Work 83 5.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.1.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.1.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Appendix A Piezoelectric Materials and Actuators 89 A.1 Piezoelectric Actuators . . . . . . . . . . . . . . . . . . . . . . . . . 89 A.1.1 Piezoelectric Materials . . . . . . . . . . . . . . . . . . . . . 89 A.1.2 Cantilever Beam Bending Actuators . . . . . . . . . . . . . 92 A.1.3 T-beam Actuators . . . . . . . . . . . . . . . . . . . . . . . 94 A.1.3.1 Operation . . . . . . . . . . . . . . . . . . . . . . . 94 A.1.4 Static and Dynamic Modeling of T-Beam Actuators . . . . . 96 A.1.4.1 Fabrication and Experimental Setup . . . . . . . . 96 A.1.4.2 Static Results and Modeling . . . . . . . . . . . . . 97 vii A.1.4.3 Dynamic Modeling . . . . . . . . . . . . . . . . . . 103 A.1.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . 105 Appendix B Design and Extra Results of the Lionfly 107 B.1 Single Degree of Freedom Design . . . . . . . . . . . . . . . . . . . 107 B.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 B.1.2 Static Response . . . . . . . . . . . . . . . . . . . . . . . . . 109 B.1.3 Amplitude Dependent Linear Aerodynamic Drag Force . . . 112 B.1.4 Rotational Hinge Stiffness . . . . . . . . . . . . . . . . . . . 115 B.2 Additional LionFly Data . . . . . . . . . . . . . . . . . . . . . . . . 117 B.3 Review of SU-8 Material Properties . . . . . . . . . . . . . . . . . . 119 Bibliography 123 viii List of Figures 2.1.1 Conceptual Drawing of Clapping Winged PSNAV . . . . . . . . . . 14 2.2.1 T-beam Fuselage Fabrication Process . . . . . . . . . . . . . . . . . 15 2.2.2 Schematic of the PSNAV, a Four Winged Clapping NAV . . . . . . 16 2.2.3 T-beam Maximum Mechanical Energy Output Optimization . . . . 18 2.2.4 Drawing of Revolute Joint . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.5 Photograph of Fabricated Wings for the PSNAV . . . . . . . . . . 20 2.2.6 Schematic of Fabricated Clapping Wing Amplification Mechanism . 20 2.3.1 Schematic of Clapping Winged LionFly System Model . . . . . . . 21 2.3.2 Aerodynamic Forces and Torques on Wing . . . . . . . . . . . . . . 25 2.4.1 Photograph of Experimental Setup . . . . . . . . . . . . . . . . . . 27 2.4.2 T-beam Static Displacement . . . . . . . . . . . . . . . . . . . . . 28 2.4.3 T-beam Blocking Force Measurement . . . . . . . . . . . . . . . . 29 2.4.4 Flapping of Clapping Winged PSNAV . . . . . . . . . . . . . . . . 30 2.4.5 Wing Rotation of Clapping Wing PSNAV . . . . . . . . . . . . . . 30 2.4.6 Frequency Response of Clapping Wing PSNAV . . . . . . . . . . . 31 2.4.7 Average Value Lift Frequency Response of Clapping Winged LionFly 32 3.1.1 Conceptual Drawing of the Penn State LionFly . . . . . . . . . . . 34 3.2.1 Schematic of a Flexure Hinge . . . . . . . . . . . . . . . . . . . . . 35 3.2.2 Transmission Spectrum of SUEX . . . . . . . . . . . . . . . . . . . 38 3.2.3 Fabrication Process of SUEX Flexure Hinges . . . . . . . . . . . . 39 3.2.4 Flexure Thickness vs. 310 nm Exposure Dose . . . . . . . . . . . . 40 3.2.5 Cross Section of Fabricated Flexure Hinge . . . . . . . . . . . . . . 41 3.3.1 Pseudo Rigid Body Model of Slider Rocker Mechanism . . . . . . . 42 3.3.2 Link Diagram of Slider Rocker Mechanism . . . . . . . . . . . . . . 44 3.4.1 Photograph of Fabricated LionFly . . . . . . . . . . . . . . . . . . 47 3.4.2 Photograph of Experimental Testing Setup . . . . . . . . . . . . . 49 3.4.3 Quasi-Static Response of Flapping Wing Mechanism . . . . . . . . 50 3.4.4 Frequency Response of Φ(s)/V(s) . . . . . . . . . . . . . . . . . . 51 3.4.5 Frequency Response of X(s)/V(s) . . . . . . . . . . . . . . . . . . 52 3.4.6 Flapping Angle at High Voltage at Resonance . . . . . . . . . . . . 53 ix