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This dissertation presents shape and structural optimization studies on flapping wings for micro air vehicles. The design space of the optimization includes the wing planform and the structural properties that are relevant to the wing model being analyzed. The planform design is parameterized using a novel technique called modified Zimmerman, which extends the concept of Zimmerman planforms to include four ellipses rather than two. Three wing types are considered: rigid, plate-like deformable, and membrane. The rigid wing requires no structural design variables. The structural design variables for the plate-like wing are the thickness distribution polynomial coefficients. The structural variables for the membrane wing control the in-plane distributed forces which modulate the structural deformation of the wing. The rigid wing optimization is performed using the modified Zimmerman method to describe the wing. A quasi-steady aerodynamics model is used to calculate the thrust and input power required during the flapping cycle. An assumed inflow model is derived based on lifting-line theory and is used to better approximate the effects of the induced drag on the wing. A multi-objective optimization approach is used since more than one aspect is considered in flapping wing design. The the epsilon-constraint approach is used to calculate the Pareto optimal solutions that maximize the cycle-average thrust while minimizing the peak input power and the wing mass. An aeroelastic model is derived to calculate the aerodynamic performance and the structural response of the deformable wings. A linearized unsteady vortex lattice method is tightly coupled to a linear finite element model. The model is cost effective and the steady-state solution is solved by inverting a matrix. The aeroelastic model is used to maximize the thrust produced over one flapping cycle while minimizing the input power. / Ph. D.

Au cours des dernières décennies, la possibilité d’exploiter les capacités de vol exceptionnelles des insectes a été à l’origine de nombreuses recherches sur l’élaboration de nano-véhicules aériens (NAVs) à ailes battantes. Cependant, lors de la conception de tels prototypes, les chercheurs doivent analyser une vaste gamme de solutions liées à la grande diversité des insectes volants pour identifier les fonctionnalités et les paramètres adaptés à leurs besoins. Afin d’alléger cette tâche, le but de ce travail est de développer un outil permettant à la fois d’examiner le comportement cinématique et énergétique d’un nano-véhicule aérien à ailes flexibles résonantes, et donc d'évaluer son efficacité. Cet objectif reste néanmoins extrêmement difficile à atteindre car il concerne des objets de très petites tailles. Aussi, nous avons choisi tout d’abord de travailler sur un micro-véhicule aérien (MAV) à ailes battantes. Il s’agit avant tout de valider l’outil de modélisation à travers une comparaison systématique des simulations avec des résultats expérimentaux effectués lors de l’actionnement des ailes, puis au cours du décollage et du vol stationnaire du prototype. Une partie des connaissances et expériences acquises pourra ensuite être utilisée afin de mieux comprendre le fonctionnement et identifier la distribution d'énergie au sein du NAV. Bien que les deux véhicules s’inspirent directement de la cinématique des ailes d'insectes, les mécanismes d'actionnement des ailes artificielles des deux prototypes ne sont pas les mêmes en raison de la différence de taille. Comme le NAV est plus petit, ces ailes ont un mouvement de battement à une fréquence plus élevée que celles du MAV, à l’instar de ce qui existe dans la nature. En conséquence, lorsque l’on passe du MAV au NAV, le mécanisme d’actionnement des ailes doit être adapté et cette différence nécessite d’une part, de revoir la conception, l'approche de modélisation et le processus d'optimisation, et d’autre part, de modifier le procédé de fabrication. Une fois ces améliorations apportées, nous avons obtenu des résultats de simulations en accord avec les tests expérimentaux. Le principal résultat de ce travail concerne l’obtention pour les deux prototypes, le MAV et le NAV, d’une cinématique appropriée des ailes, qui conduit à une force de portance équivalente au poids. Nous avons d’ailleurs démontré que le MAV était capable de décoller et d’avoir un vol stationnaire stable selon l’axe vertical. En tirant parti des modèles basés sur le langage Bond Graph, il est également possible d'évaluer les performances énergétiques de ces prototypes en fonction de la dynamique de l'aile. En conclusion, cette étude contribue à la définition des paramètres essentiels à prendre en compte lors de la conception et l'optimisation énergétique de micro et nano-véhicules à ailes battantes. / In recent decades, the prospect of exploiting the exceptional flying capacities of insects has prompted much research on the elaboration of flapping-wing nano air vehicles (FWNAV). However, when designing such a prototype, designers have to wade through a vast array of design solutions that reflects the wide variety of flying insects to identify the correct combination of parameters to meet their requirements. To alleviate this burden, the purpose of this work is to develop a suitable tool to analyze the kinematic and power behavior of a resonant flexible-wing nano air vehicle. The key issue is evaluating its efficiency. However, this ultimate objective is extremely challenging as it is applied to the smallest flexible FWNAV. However, in this work, we worked first with a flapping-wing micro air vehicle (FWMAV) in order to have a tool for the simulation and experimentation of wing actuation, take-off and hovering. Some of the knowledge and experience acquired will then be transferred to better understand how our FWNAV works and identify the energy, power distribution. Although both of the vehicles employ the insect wing kinematics, their wings actuation mechanisms are not the same due to their sizes difference. Since the FWNAV is smaller, their wings flap at a higher frequency than the FWMAV as inspired by nature. As a consequence, from MAV to NAV, the wing actuation mechanism must be changed. Throughout this work, it can be seen clearly that this difference affects the whole vehicles development including the design, the manufacturing method, the modeling approach and the optimizing process. It has been demonstrated that the simulations are in good correlation with the experimental tests. The main result of this work is the proper wing kinematics of both FWMAV and FWNAV which leads to a lift to the weight ratio bigger and equal to one respectively. The FWMAV is even success to take-off and vertically stable hover. Moreover, taking advantage of the Bond Graph-based models, the evolution power according to the wing dynamic and the efficiency of the subsystem can be evaluated. In conclusion, this study shows the key parameters for designing and optimizing efficiency and the lift generated for two flapping wing vehicles in different size regimes.

In this study the dynamical modeling of the unsteady flow over a flapping wing is considered. The technique is based on collecting instantaneous velocity field data of the flow using Particle Image Velocimetry (PIV), applying image processing to these snapshots to locate the airfoil, filling the airfoil and its surface with proper velocity data, applying Proper Orthogonal Decomposition (POD) to these post-processed images to compute the POD modes and time coefficients, and finally fitting a discrete time state space dynamical model to the trajectories of the time coefficients using subspace system identification (N4SID). The procedure is applied using MATLAB for the data obtained from NACA 0012, SD 7003, elliptic airfoil and flat plate, and the results show that the dynamical model obtained can represent the flow dynamics with acceptable accuracy.

This study seeks to understand the interplay of vorticity and elasto-dynamics that forms the basis for a fluttering flag and flapping wing propulsion, and factors that distinguish one from the other. The fluid dynamics is assumed two dimensional and incompressible, and comprises potential and viscous flow simulations. The elastic solid is one dimensional and governed by the Bernoulli-Euler flexure model. The fluid and elastic solid models are coupled using a predictor-corrector algorithm. Flutter of a flag or foil is associated with drag and we show that the pressure on the foil is predominantly circulatory in origin. The circulatory pressure generated on the foil depends primarily on the slope and curvature. The wake vorticity exhibits a wide range of behavior starting from a Kelvin-Helmholtz type instability to a von Kármán wake. Potential flow simulations do not capture the wake accurately both at high and low mass ratios. This is reflected in the flutter boundary and pressure over the foil when compared with viscous flow simulations. Thrust due to heaving of a flexible foil shows maxima at a set of discrete frequencies that coincide with the frequencies at which the flapping velocity of the foil tip is a maximum. The propulsive efficiency shows maxima at a set of discrete frequencies that are close but distinct from the thrust maxima set of frequencies. These discrete frequencies are close to the natural frequencies of vibration of a cantilevered foil vibrating in vacuum. At low frequencies thrust is a consequence of a strong leading edge vortex developed over the foil and it remains attached to the foil as it is convected due to the favorable pressure gradient presented by the time and spatially varying shape of the foil. At moderate and high frequencies of oscillation the pressure, and consequently the thrust, generated by the foil is non-circulatory in origin and they are high where the accelerations of the foil are high. At high frequencies the leading edge vortex is weak. Except in the low frequency range, potential flow simulations qualitatively compares well with viscous flow predictions. We show that thrust and drag on a flexible foil oscillating in a flow is caused by the phase difference between the slope of the foil and the fluid pressure on it. Propulsive efficiency though is governed by the phase difference between foil velocity and fluid pressure and inertia forces. Thus, the interplay of vorticity and elasto-dynamics determine the behavior of a flutter and propulsion of a flexible foil in a fluid flow.

Ce travail de thèse s'inscrit dans le contexte des drones vise à réaliser à terme un Nano-dispositif volant (Nano Aerial Vehicle) capable d'imiter le vol des insectes. Ce mode de locomotion est privilégié car il présente des caractéristiques très adaptées au vol en milieu confiné. La solution proposée consiste à développer un drone de la taille d'un insecte s'appuyant sur des ailes vibrantes pour se mouvoir et à utiliser les technologies MEMS pour répondre aux problématiques de fabrication et de réduction d'échelle. La réussite d'un tel projet soulève néanmoins de nombreux défis scientifiques et technologiques, en particulier, les aspects aéro-élastiques des ailes et l'autonomie du drone. Pour répondre à ces défis, nous proposons dans un premier temps de mettre en œuvre des concepts comme la résonance et la torsion passive sur des prototypes en polymère (SU-8) réalisés par photolithographie. Dans un second temps, les différents composants de la chaîne de puissance sont optimisés, notamment l'actionneur électromagnétique, la liaison et les ailes de manière à maximiser la force de portance générée. Suite à ces améliorations, nous démontrons de façon expérimentale que le prototype était capable non seulement de reproduire une cinématique complexe mais également de compenser 75% de son poids. / This manuscript reports a work which aims to develop a tiny flying robots inspired by natural flyers. Our main objective is to devise a flying robot mimicking insects in terms of kinematics and scale using MEMS technologies in order to answer the scale challenges: the large-scale manufacturing and the system's small scale. The success this project faces different challenges such as aeroelastic aspects of wings and drone autonomy.In this work we propose the use of original concepts like resonance and passive torsion of the wings which are implemented on all-polymer prototypes obtained using a micromachining SU-8 photoresist process. In order to achieve a better efficiency of the prototype, each element of the energy transduction has been carefully examined and optimized. Especially, the actuation, the transmission and the wings in order to increase the lift. These improvements demonstrate experimentally that the prototype is able to produce a complex kinematic and compensate 75 % of its weight.

The unsteady aerodynamic and aeroelastic analysis of flapping flight under various kinematics and flow parameters is presented in this dissertation. The main motivation for this study arises from the challenges facing the development of micro air vehicles. Micro air vehicles by requirement are compact with dimensions less than 15-20 cm and flight speeds of around 10-15 m/s. These vehicles operate in low Reynolds number range of 10,000 to 100,000. At these low Reynolds numbers, the aerodynamic efficiency of conventional fixed airfoils significantly deteriorates. On the other hand, flapping flight employed by birds and insects whose flight regime coincides with that of micro air vehicles offers a viable alternate solution. For the analysis of flapping flight, a boundary fitted moving grid algorithm is implemented in a flow solver, GenIDLEST. The dynamic movement of the grid is achieved using a combination of spring analogy and trans-finite interpolation on displacements. The additional conservation equation of space required for moving grid is satisfied. The solver is validated with well known flow problems such as forced oscillation of a cylinder, a heaving airfoil, a moving indentation channel, and a hovering fruitfly. The performance of flapping flight is analyzed using Large Eddy Simulation (LES) for a wide range of Reynolds numbers and under various kinematic parameters. A spiral Leading Edge Vortex (LEV) forms during the downstroke due to the high angle of attack, which results in high force production. A strong spanwise flow of the order of the flapping velocity is observed along the core of the LEV. In addition, the formation of a negative spanwise flow is observed due to the tip vortex, which slows down the removal of vorticity from the LEV. This leads to the instability of the LEV at around mid-downstroke. Analysis with different rotation kinematics shows that a continuous rotation results in better propulsive efficiency as it generates thrust during the entire flapping cycle. Analysis with different angles of attack shows that a moderate angle of attack which results in complete shedding of the LEV offers high propulsive efficiency. The analysis of flapping flight at Reynolds numbers ranging from 100 to 100,000 shows that higher lift and thrust values are obtained for Re?100. The critical reasons are that at higher Reynolds numbers, the LEV is closer to the surface and as it sheds and convects it covers most of the upper surface. However, the Reynolds number has no or little effect on the lift and thrust as identical values are obtained for Re=10,000 and 100,000. The analysis with different tip shapes shows that tip shapes do not have a significant effect on the performance. Introduction of stroke deviation to kinematics leads to drop in average lift as wing interacts with the LEV shed during the downstroke. A linear elastic membrane model with applied aerodynamic load is developed for aeroelastic analysis. Analysis with different wing stiffnesses shows that the membrane wing outperforms the rigid wing in terms of lift, thrust and propulsive efficiency. The main reason for the increase in force production is attributed to the gliding of the LEV along the camber, which results in a high pressure difference across the surface. In addition, a high stiffness along the spanwise direction and low stiffness along the chordwise direction results in a uniform camber and high lift and thrust production. / Ph. D.

The objective of this research is to verify the three degree of freedom capabilities of a bio-inspired quad flapping-wing micro aerial vehicle in simulation and in hardware. The simulation employs a nonlinear plant model and input-output feedback linearization controller to verify the three degree of freedom capabilities of the vehicle. The hardware is a carbon fiber test bench with four flapping wings and an embedded avionics system which is controlled via a PD linear controller. Verification of the three degree of freedom capabilities of the quad flapping-wing concept is achieved by analyzing the response of both the simulation and test bench to pitch, roll, and yaw attitude commands.

The conventional Mini and Large scale Unmanned Aerial Vehicle systems span anywhere from approximately 12 inches to 12 feet; endowing them with larger propulsion systems, batteries/fuel-tanks, which in turn provide ample power reserves for long-endurance flights, powerful actuators, on-board avionics, wireless telemetry etc. The limitations thus imposed become apparent when shifting to Micro Aerial Vehicles (MAVs) and trying to equip them with equal or near-equal flight endurance, processing, sensing and communication capabilities, as their larger scale cousins. The conventional MAV as outlined by The Defense Advanced Research Projects Agency (DARPA) is a vehicle that can have a maximum dimension of 6 inches and weighs no more than 100 grams. Under these tight constraints, the footprint, weight and power reserves available to on-board avionics and actuators is drastically reduced; the flight time and payload capability of MAVs take a massive plummet in keeping with these stringent size constraints. However, the demand for micro flying robots is increasing rapidly. The applications that have emerged over the years for MAVs include search&rescue operations for trapped victims in natural disaster succumbed urban areas; search&reconnaissance in biological, radiation, natural disaster/hazard succumbed/prone areas; patrolling&securing home/office/building premises/urban areas. VTOL capable rotary and fixed wing flying vehicles do not scale down to micro sized levels, owing to the severe loss in aerodynamic efficiency associated with low Reynolds number physics on conventional airfoils; whereas, present state of the art in flapping wing designs lack in one or more of the minimum qualities required from an MAV: Appreciable flight time, appreciable payload capacity for on-board sensors/telemetry and 6DoF hovering/VTOL performance. This PhD. work is directed towards overcoming these limitations. Firstly, this PhD thesis presents the advent of a novel Quad-Wing MAV configuration (called the QV). The Four-Wing configuration is capable of performing all 6DoF flight maneuvers including VTOL. The thesis presents the design, conception, simulation study and finally hardware design/development of the MAV. Secondly, this PhD thesis proves and demonstrates significant improvement in on-board Energy-Harvesting resulting in increased flight times and payload capacities of the order of even 200%-400% and more. Thirdly, this PhD thesis defines a new actuation principle called, Fixed Frequency, Variable Amplitude (FiFVA). It is demonstrated that by the use of passive elastic members on wing joints, a further significant increase in energy efficiency and consequently reduction in input power requirements is observed. An actuation efficiency increase of over 100% in many cases is possible. The natural evolution of actuation development led to invention of two novel actuation systems to illustrate the FiFVA actuation principle and consequently show energy savings and flapping efficiency improvement. Lastly, but not in the least, the PhD thesis presents supplementary work in the design, development of two novel Micro Architecture and Control (MARC) avionics platforms (autopilots) for the application of demonstrating flight control and communication capability on-board the Four-Wing Flapping prototype. The design of a novel passive feathering mechanism aimed to improve lift/thrust performance of flapping motion is also presented.

This thesis contributes to the state of the art in integrated design of insect-scale piezoelectric actuated flapping wing vehicles through the development of novel theoretical models for flapping wing aerodynamics and piezoelectric actuator dynamics, and integration of these models into a closed form design process. A comprehensive literature review of available engineered designs of miniature rotary and flapping wing vehicles is provided. A novel taxonomy based on wing and actuator kinematics is proposed as an effective means of classifying the large variation of vehicle configurations currently under development. The most successful insect-scale vehicles developed to date have used piezoelectric actuation, system resonance for motion amplification, and passive wing pitching. A novel analytical treatment is proposed to quantify induced power losses in normal hover that accounts for the effects of non uniform downwash, wake periodicity and effective flapping disc area. Two different quasi-steady aerodynamic modelling approaches are undertaken, one based on blade element analysis and one based on lifting line theory. Both approaches are explicitly linked to the underlying flow physics and, unlike a number of competing approaches, do not require empirical data. Models have been successfully validated against experimental and numerical data from the literature. These models have allowed improved insight into the role of the wing leading-edge vortex in lift augmentation and quantification of the comparative contributions of induced and profile drag for insect-like wings in hover. Theoretical aerodynamic analysis has been used to identify a theoretical solution for the optimum planform for a flapping wing in terms of chord and twist as a function of span. It is shown that an untwisted elliptical planform minimises profile power, whereas a more highly tapered design such as that found on a hummingbird minimises induced power. Aero-optimum wing kinematics for hovering are also assessed. It is shown that for efficient flight the flapping velocity should be constant whereas for maximum effectiveness the flapping velocity should be sinusoidal. For both cases, the wing pitching at stroke reversal should be as rapid as possible. A dynamic electromechanical model of piezoelectric bending actuators has been developed and validated against data obtained from experiments undertaken as part of this thesis. An expression for the electromechanical coupling factor (EMCF) is extracted from the analytical model and is used to understand the influence of actuator design variables on actuator performance. It is found that the variation in EMCF with design variables is similar for both static and dynamic operation, however for light damping the dynamic EMCF will typically be an order of magnitude greater than for static operation. Theoretical contributions to aerodynamic and electromechanical modelling are integrated into a low order design method for propulsion system sizing. The method is unique in that aside from mass fraction estimation, the underlying models are fully physics based. The transparency of the design method provides the designer with clear insight into effects of changing core design variables such as the maximum flapping amplitude, wing mass, transmission ratio, piezoelectric characteristics on the overall design solution. Whilst the wing mass is only around 10% of the actuator mass, the effective wing mass is 16 times the effective actuator mass for a typical transmission ratio of 10 and hence the wing mass dominates the inertial contribution to the system dynamics. For optimum aerodynamic effectiveness and efficiency it is important to achieve high flapping amplitudes, however this is typically limited by the maximum allowable field strength of the piezoelectric material used in the actuator.