Wing Compliance Research Articles

Non-Linear Analysis in Post-Buckling Regime of a Tilt Rotor Composite Wing Structure Using Detailed Model and Robust Loading Approach

The design and development of a wing for a completely brand-new aircraft represents, in aeronautics, one of the highest challenges from an engineering point of view. The present work describes a novel methodology devoted to execute numeric simulation in a non-linear post-buckling regime to verify the composite wing compliance under the design load conditions. The procedure was developed as part of a wing design and research activity and was motivated by the need to have more realistic results, without standard conservatisms like the no-buckling up to ultimate load, to be of use for achieving further weight savings. To carry this out, it was obviously necessary to ensure that the structural integrity was also guaranteed in the post-buckling regime, above the limit load, and therefore in a highly non-linear regime. The present work illustrates a numerical approach based on non-linear finite element analysis which uses the inertia relief option in order to have a more realistic representation of the structural response of the wing in its real context. All that represents a novelty since, at present, the commercial FE codes allow us to use the inertia relief option exclusively for linear analysis. Obviously, the approach can be applied to any other structural component with similar needs. The obtained results show that the differences between linear and non-linear regime are not negligible and, above all, that it is possible to design a wing (or other structural components) considering, at the same time, the large deformation due to the post-buckling regime, the material non-linearities due to the failures and any other non-linearities in order to achieve the challenging weight requirement of the new aircraft generation.

Coupled Aeroelastic Study of a Flexible Micro Air Vehicle-Scale Flapping Wing in Hovering Flight

Instantaneous force and structural deformation experiments were performed on a flexible, structurally characterized, low-aspect-ratio representative flapping wing. A six-component force balance was used to measure aerodynamic-force time history over a flap cycle. A VICON motion capture setup tracked the wing deformations while flapping. Measured aerodynamic forces and wing deformations were compared against coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) aeroelastic analysis results. The CFD solver is an unsteady Reynolds-averaged Navier–Stokes solver. The CSD solver is a general-purpose multibody dynamics solver capable of modeling geometrically nonlinear beam and shell elements. The CFD/CSD results were able to capture the overall trend in aerodynamic forces and wing deformations. Although predicted and measured variations in lift were similar, the drag-force magnitudes tended to be underpredicted by the coupled aeroelastic solver. The coupled CFD/CSD solver was used to evaluate the influence of wing flexibility on wing performance. Results showed that, in particular instances, decreasing wing stiffness increased the time-averaged aerodynamic lift and lift-to-power ratio. Decreased wing stiffness led to reduced leading-edge vortex circulation strength. This suggests that the increased wing performance is mainly due to a redirection of the resultant force vector allowed by the increased wing compliance.

Morphological diversification has led to inter-specific variation in elastic wing deformation during flight in scarab beetles.

Insect wing shapes and the internal wing-vein arrangement are remarkably diverse. Although the wings lack intrinsic musculature to adjust shape actively, they elastically deform due to aerodynamic and inertial loads during flapping. In turn, the deformations alter the shape of the wing profile affecting the aerodynamic force. To determine how changes in wing-vein arrangement affect elastic wing deformation during free flight, we compared elastic wing deformations between free-flying rose chafers (Protaetia cuprea) and dung beetles (Scarabaeus puncticollis), complementing the comparison with wing static bending measurements. The broader relevance of the results to scarab beetle divergence was examined in a geometric morphometric (GM) analysis of wing-vein arrangement in 20 species differing in phylogeny and ecology. Despite rose chafers and dung beetles demonstrating similar flapping kinematics and wing size, the rose chafer wings undergo greater elastic deformation during flapping. GM analyses corrected for phylogenetic relatedness revealed that the two beetles represent extremes in wing morphology among the scarab subfamilies. Most of the differences occur at the distal leading edge and the proximal trailing edge of the wing, diversifying the flexibility of these regions, thereby changing the pattern of elastic wing deformation during flapping. Changes to local wing compliance seem to be associated with the diversification of scarab beetles to different food sources, perhaps as an adaptation to meet the demands of diverse flight styles.

Elastic wing deformations mitigate flapping asymmetry during manoeuvres in rose chafers (Protaetia cuprea).

ABSTRACTTo manoeuvre in air, flying animals produce asymmetric flapping between contralateral wings. Unlike the adjustable vertebrate wings, insect wings lack intrinsic musculature, preventing active control over wing shape during flight. However, the wings elastically deform as a result of aerodynamic and inertial forces generated by the flapping motions. How these elastic deformations vary with flapping kinematics and flight performance in free-flying insects is poorly understood. Using high-speed videography, we measured how contralateral wings elastically deform during free-flight manoeuvring in rose chafer beetles (Protaetia cuprea). We found that asymmetric flapping during aerial turns was associated with contralateral differences in chord-wise wing deformations. The highest instantaneous difference in deformation occurred during stroke reversals, resulting from differences in wing rotation timing. Elastic deformation asymmetry was also evident during mid-strokes, where wing compliance increased the angle of attack of both wings, but reduced the asymmetry in the angle of attack between contralateral wings. A biomechanical model revealed that wing compliance can increase the torques generated by each wing, providing higher potential for manoeuvrability, while concomitantly contributing to flight stability by attenuating steering asymmetry. Such stability may be adaptive for insects such as flower chafers that need to perform delicate low-speed landing manoeuvres among vegetation.

Kinematic and Aerodynamic Enhancement of a Robotic Hummingbird

This paper reports a study aiming at improving the flight quality and aerodynamic performance of a robotic hummingbird. The first part of the paper addresses the issue of the parasitic roll and pitch bias moments resulting from the small asymmetry (left/right and front/back) in the wing trajectory. This is achieved with a new string-based mechanism that reduces by 90% the asymmetry associated with the previous mechanism of our robot (known as COLIBRI). The second part of the paper aims at increasing the lift and reducing the mechanical power. An experimental study is conducted with leading edge bars of various diameters and it is found that wing flexibility may contribute to smooth the transition at wing reversal (less twisting oscillations) and leads to a significant increase of the lift force and a significant reduction of the mechanical power. As a side effect, the wing compliance contributes to reducing the noise in the inertial sensor and the acoustic noise produced by the flying robot.

Thrust, drag and wake structure in flapping compliant membrane wings

We present a theoretical framework to characterize the steady and unsteady aeroelastic behaviour of compliant membrane wings under different conditions. We develop an analytic model based on thin airfoil theory coupled with a membrane equation. Adopting a numerical solution to the model equations, we study the effects of wing compliance, inertia and flapping kinematics on aerodynamic performance. The effects of added mass and fluid damping on a flapping membrane are quantified using a simple damped oscillator model. As the flapping frequency is increased, membranes go through a transition from thrust to drag around the resonant frequency, and this transition is earlier for more compliant membranes. The wake also undergoes a transition from a reverse von Kármán wake to a traditional von Kármán wake. The wake transition frequency is predicted to be higher than the thrust–drag transition frequency for highly compliant wings.

Analytical results on the role of flexibility in flapping propulsion

AbstractWing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop small-amplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing’s emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviours and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. The simple robust estimates afforded by our theory may prove valuable even in situations where details of the flapping motion and wing geometry differ.

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings and can therefore aid in understanding the complex aircraft design process that must eventually consider all these metrics and load cases simultaneously.

Aerodynamic Characterization of a Wing Membrane with Variable Compliance

Membrane wings with variable compliance have a great potential to improve the maneuverability and performance of micro air vehicles. Moreover, changes in membrane wing compliance might be used by flying animals, such as bats, to control aerodynamic performance. In this work, the mechanical properties and aerodynamic performance of a low-aspect-ratio membrane wing with variable compliance was characterized. The membrane was made of dielectric material coated with compliant electrodes and supported by a rigid frame. The compliance of the wing was controlled by applying a voltage across a membrane. The wing model was tested in a wind tunnel. It was found that, when a fixed voltage is applied across the wing membrane, the camber increases, accompanied by a small increase in lift. However, lift is significantly increased when the wing is forced with an oscillating field at specific frequencies. In addition, stall is delayed, and for a range of angle of attacks, there is an increase in lift-to-drag ratio. Fluid dynamics measurements are needed to analyze the fluid–membrane interaction.

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance

Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior--in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics.

Flapping Wing Structural Deformation and Thrust Correlation Study with Flexible Membrane Wings

This experimental study investigates the relationship between flapping wing structure and the production of aerodynamic forces for micro air vehicle hovering flight by measuring full-field structural deformation and thrust generation. Results from four flexible micromembrane wings with different skeletal reinforcement demonstrate that wing compliance is crucial in thrust production: only certain modes of passive aeroelastic deformation allow the wing to effectively produce thrust. The experimental setup consists of a flapping mechanism with a single-degree-of- freedom rotary actuation up to 45 Hz at 70 deg stoke amplitude and with power measurement, a force and torque sensor that measures the lift and thrust, and a digital image correlation system that consists of four cameras capable of capturing the complete stroke kinematics and structural deformation. Several technical challenges related to the experimental testing of microflapping wings are resolved in this study: primarily, flapping wings less than 3 in. in length produce loads and deformations that are difficult to measure in an accurate and nonintrusive manner. Furthermore, the synchronization of the load measurement system, the vision-based wing deformation measurement system, and the flapping mechanism is demonstrated. Intensive data analyses are performed to extract useful information from the measurements in both air and vacuum.

How wing compliance drives the efficiency of self-propelled flapping flyers

Wing flexibility governs the flying performance of flapping-wing flyers. Here, we use a self-propelled flapping-wing model mounted on a "merry go round" to investigate the effect of wing compliance on the propulsive efficiency of the system. Our measurements show that the elastic nature of the wings can lead not only to a substantial reduction in the consumed power, but also to an increment of the propulsive force. A scaling analysis using a flexible plate model for the wings points out that, for flapping flyers in air, the time-dependent shape of the elastic bending wing is governed by the wing inertia. Based on this prediction, we define the ratio of the inertial forces deforming the wing to the elastic restoring force that limits the deformation as the elastoinertial number N(ei). Our measurements with the self-propelled model confirm that it is the appropriate structural parameter to describe flapping flyers with flexible wings.

Measurement of Thrust and Lift Forces Associated With Drag of Compliant Flapping Wing for Micro Air Vehicles Using a New Test Stand Design

Compliant wing designs have the potential of improving flapping wing Micro-Air Vehicles (MAVs). Designing compliant wings requires a detailed understanding of the effect of compliance on the generation of thrust and lift forces. The low force and high-frequency measurements associated with these forces necessitated a new versatile test stand design that uses a 250 g load cell along with a rigid linear air bearing to minimize friction and the dynamic behavior of the test stand while isolating only the stationary thrust or lift force associated with drag generated by the wing. Moreover, this stand is relatively inexpensive and hence can be easily utilized by wing designers to optimize the wing compliance and shape. The frequency response of the wing is accurately resolved, along with wing compliance on the thrust and lift profiles. The effects of the thrust and lift force generated as a function of flapping frequency were also determined. A semi-empirical aerodynamic model of the thrust and lift generated by the flapping wing MAV on the new test stand was developed and used to evaluate the measurements. This model accounted for the drag force and the effects of the wing compliance. There was good correlation between the model predictions and experimental measurements. Also, the increase in average thrust due to increased wing compliance was experimentally quantified for the first time using the new test stand. Thus, our measurements for the first time reveal the detrimental influence of excessive compliance on drag forces during high frequency operation. In addition, we were also able to observe the useful effect of compliance on the generation of extra thrust at the beginning and end of upstrokes and downstrokes of the flapping motion.

Aerodynamic and functional consequences of wing compliance

A growing body of evidence indicates that a majority of insects experience some degree of wing deformation during flight. With no musculature distal to the wing base, the instantaneous shape of an insect wing is dictated by the interaction of aerodynamic forces with the inertial and elastic forces that arise from periodic accelerations of the wing. Passive wing deformation is an unavoidable feature of flapping flight for many insects due to the inertial loads that accompany rapid stroke reversals—loads that well exceed the mean aerodynamic force. Although wing compliance has been implicated in a few lift-enhancing mechanisms (e.g., favorable camber), the direct aerodynamic consequences of wing deformation remain generally unresolved. In this paper, we present new experimental data on how wing compliance may affect the overall induced flow in the hawkmoth, Manduca sexta. Real moth wings were subjected to robotic actuation in their dominant plane of rotation at a natural wing beat frequency of 25 Hz. We used digital particle image velocimetry at exceptionally high temporal resolution (2,100 fps) to assess the influence of wing compliance on the mean advective flows, relying on a natural variation in wing stiffness to alter the amount of emergent deformation (freshly extracted wings are flexible and exhibit greater compliance than those that are desiccated). We find that flexible wings yield mean advective flows with substantially greater magnitudes and orientations more beneficial to lift than those of stiff wings. Our results confirm that wing compliance plays a critical role in the production of flight forces.