A Black Box Design Approach to Avian-Inspired SMA Coil Actuated Wearable Morphing Angel Wings

Black box design is a constraint driven design approach that distills essential elements of a physical process into inputs and outputs. This paper details the black box design implementation and validation of shape memory alloy (SMA) coil actuators as active members in a Watt I six bar avian-inspired wearable morphing angel wing mechanism. SMA coil actuators leverage the unique characteristics of high energy density SMA wire by providing a compact structural platform for large actuation displacement applications. The moderate force and displacement performance of low spring index coil actuators paired with their virtually silent actuation performance made them an attractive actuator solution to an avian-inspired wearable morphing wing mechanism for the University of Minnesota Department of Theatre Arts and Dance production of ‘Marisol’. The wing design constraints (extended span of 7.5 ft, a closed span of 3 ft) required a tailorable actuator system with capacity to perform at particular target force and strain metrics cyclically. A low spring index parameter study was conducted to facilitate an accelerated phase of design prototyping. The parameter study featured six SMA coil actuator prototypes made with 0.012” diameter Dynalloy Flexinol® wire of varying spring indexes (C = 2.5–4.9). The coil actuators were manufactured through a CNC winding process, shape set in a furnace at 450 °C for 10 minutes, and water quenched for hardening. A series of thermomechanical actuation tests were conducted to experimentally characterize the low spring index actuation performances. The coil actuation characterizations demonstrated increased force and decreased actuator displacement corresponding to decreased spring indexes. Scaling these results aided an accelerated design of an actuator system. The actuator system consisted of four C = 3.05 coil actuators wound with 0.02” diameter SMA that were integrated into each Watt I mechanism. The characterization of the force-displacement profiles for low index SMA coil actuators provides an effective empirical design strategy for scaling actuator performance to mechanical systems requiring moderate force, moderate displacement actuators.

Acoustoelastic-Based Stress Measurement Utilizing Low-Frequency Flexural Waves

Current acoustoelastic-based stress measurement techniques operate at the high-frequency, weakly-dispersive portions of the dispersion curves. The weak dispersive effects at such high frequencies allow the utilization of time-of-flight measurements to quantify the effects of stress on wave speed. However, this comes at the cost of lower sensitivity to the state-of-stress of the structure, and hence calibration at a known stress state is required to compensate for material and geometric uncertainties in the structure under test. In this work, the strongly-dispersive, highly stress-sensitive, low-frequency flexural waves are utilized for stress measurement in structural components. A new model-based technique is developed for this purpose, where the acoustoelastic theory is integrated into a numerical optimization algorithm to analyze dispersive waves propagating along the structure under test. The developed technique is found to be robust against material and geometric uncertainties. In the absence of calibration experiments, the robustness of this technique is inversely proportional to the excitation frequency. The capabilities of the developed technique are experimentally demonstrated on a long rectangular beam, where reference-free, un-calibrated stress measurements are successfully conducted.

Semi-Active Helicopter Ground Resonance Suppression Using Magnetorheological Technology

This paper discusses the semi-active control of helicopter ground resonance using magnetorheological (MR) damper. A dynamic model of a MR damper with bi-fold flow mode is built based on the hyperbolic tangent model and experimental data on mechanical properties; and its inverse model is derived for the control. An approximate analytical solution of a linear system is provided and a critical stability area is calculated according to the classical model of ground resonance and the method of determining the linear system stability. Then, Simulations are performed on the helicopter ground resonance model with three semi-active control strategies and the control performance is compared. Simulation results show that the comprehensive performance of the fuzzy skyhook control algorithm is superior to the on-off skyhook and continuous skyhook control algorithms.

Analytical Model for a Superelastic SMA Beam

We propose an analytical model for a superelastic shape memory alloy (SMA) beam. The model considers reversible phase transformation between austenite and a single martensite variant driven by mechanical loading/unloading. In particular, we consider a cantilever beam subjected to a concentrated transverse force acting at the tip. The force is gradually increased from zero to a maximum value sufficient to cause complete transformation of the initially austenitic phase into martensite away from the beam core. The force is then gradually removed, resulting in complete strain recovery. In each stage of the loading/unloading process, an analytical relation is established between bending moment and curvature in terms of position along the axis of the beam. The model is compared to a uniaxial numerical beam model and to finite element analysis (FEA) results for the same beam in 3D, with very good agreement in each case. The moment-curvature relation is then integrated to obtain a nonlinear expression for the deflection and stress distribution in terms of position along the length of the beam. The expression is validated against 3D simulation results.

Exploitation of Adaptive Trailing Edge Architectures to Small Aircraft

Airfoil camber adaptation may be the key for the performance improvement of wings for many specific applications, including shorter take-off distance, compensation of weight variation and so on. Following the successful experiences gained in SARISTU, where an adaptive trailing edge device was developed for medium to large size commercial aircraft, the authors propose to exploit the developed architecture to a small aircraft wing. The basic reasons behind that mainly rely on the associated possibility to access easier implementation onto a real aircraft instead of referring to wing segments for wind tunnel or ground tests. In this way, many operative problems are faced, that would be otherwise neglected in usual lab experimentation. First of all, the integration of the proposed device onto a flying machine, that in turn pose the problem of facing the interface with the existing systems. Secondly, the necessity of including the device into the flap while fully preserving its current functionality. Furthermore, the necessity of developing a robust design process that allows having the release of the permit-to-fly. Each of the above steps, non-exhaustive in illustrating the difficulty of the addressed challenge, is structured in many other sub-segments, ranging from a suitable FHA analysis to a full re-design of the existing high lift systems or the adaptation of the architecture of the reference morphing trailing edge itself. This last item poses the classical challenge of the scaling issues, requiring the structural and the actuation subsystems to entirely fit into the new geometry. The objective of the present research is then to verify the feasibility of applying a certain architectural morphing philosophy onto a real aircraft, taking into account all the operational difficulties related to such an operation. This paper reports the activities related to the exploitation of the reference adaptive structural architecture, to the geometry of a flap of a small aircraft. In detail, the system layout is presented, followed by a FE analysis of the structural system under the operational loads and an estimation of the weight penalty associated to this transformation. Interfaces of the flap system with the main aircraft body are considered as constraints to the design development, so that the only flap is affected.

Induced Strain Actuation for Solid-State Ornithopters: Pitch and Heave Coupling

This paper investigates the heaving and pitching of a wing-like parameterized cantilevered plate with a leading edge stiffener and clamp variation when actuated with a surface-bonded piezoelectric actuator. The response is analyzed using a finite element model that is validated by comparison with known analytical solutions. The validated finite-element model is subjected to a harmonic excitation parametric analysis. The parameters varied in the model are the root clamped percentage, leading edge stiffener thickness, and the aspect ratio of the plate. The model is examined at the first two Eigen frequencies. Metrics of heaving and pitching are developed using surface fitting methods and their amplitudes and phases are reported throughout the parameter space. Emphasis is placed on the interaction and coupling of the first two modes of vibration with respect to the parameters. A piezo-composite wing prototype is fabricated and actuated harmonically with a Macro-Fiber Composite actuator while leading edge stiffener thickness and root clamped percentage is varied. The resulting experimental data is used to further validate the theoretical models.

Nonlinear Structural Dynamics of Macro-Fiber Composite Cantilevers for Resonant Actuation

Macro-fiber composite (MFC) piezoelectric materials are used in a variety of applications employing the converse piezo-electric effect, ranging from bioinspired actuation to vibration control. Most of the existing literature to date considered linear material behavior for geometrically linear oscillations. However, in many applications, such as bioinspired locomotion using MFCs, material and geometric nonlinearities are pronounced and linear models fail to represent and predict the governing dynamics. The predominant types of nonlinearities manifested in resonant actuation of MFC cantilevers are piezoelectric softening, geometric hardening, inertial softening, as well as internal and external dissipative effects. In the present work, we explore nonlinear actuation of MFC cantilevers and develop a mathematical framework for modeling and analysis. An in vacuo actuation scenario is considered for a broad range of voltage actuation levels to accurately identify the sources of dissipation. Several experiments are conducted for an MFC bimorph cantilever, and model simulations are compared with nonlinear experimental frequency response functions under resonant actuation. The resulting experimentally validated framework can be used for simulating the dynamics of MFCs under resonant actuation, as well as parameter identification and structural optimization for nonlinear operation regime.

Non-Chaotic Cross-Well State Transfer of Duffing-Holmes Type Bistable Systems

A control strategy called hybrid position feedback control is applied to a bistable system to prevent multiple crossovers during actuation from one stable equilibrium to the other. The hybrid controller is based on a conventional positive position feedback controller. The controller uses the inertial properties of the structure around the stable positions to achieve large displacements by destabilizing a positive position feedback controller. Once the unstable equilibrium is reached, the controller is stabilized to converge to the target stable equilibrium. The bistable system under harmonic excitation and hybrid controller are investigated for its behavior. In addition, energy analysis of the system controlled by the hybrid controller is investigated using numerical time domain methods. The energy variance by parameters and the comparison between the open-loop system with harmonic excitation and the controlled system is investigated.

Two Stage Design of Compliant Mechanisms With Superelastic Compliant Joints

The design of compliant mechanisms made of Nickel Titanium (NiTi) Shape Memory Alloys (SMAs) is considered to exploit the superelastic behavior of the material to achieve tailored high flexibility on demand. This paper focuses on two-stage design optimization of compliant mechanisms, as a systematic method for design of the composition of the functionally graded NiTi material within the compliant mechanism devices. The location, as well as geometric and mechanical properties, of zones of high and low flexibility will be selected to maximize mechanical performance. The proposed two-stage optimization procedure combines the optimization of an analytical model of a single-piece functionally graded unit, with a detailed FEA of a continuous compliant mechanism. In the first stage, a rigid-link model is developed to initially approximate the behavior of the compliant mechanism. In the second stage the solution of the rigid-link problem serves as the starting point for a continuous analytical model where the mechanism consists of zones with different material properties and geometry, followed by a detailed FEA of a compliant mechanism with integrated zones of superelasticity. The two-stage optimization is a systematic approach for compliant mechanism design with functional grading of the material to exploit superelastic response in controlled manner. Direct energy deposition, as an additive manufacturing technology, is foreseen to fabricate assemblies with multiple single piece functional graded components. This method could be applied to bio-inspired structures, flapping wings, flexible adaptive structures and origami inspired compliant mechanisms.

Cross-Well Actuation of Bistable Structures Subjected to Noise Disturbance

Large loads due to fluid-structure interaction can lead to high bending stresses and fatigue failure in wings and wind turbine blades. A solution for the mentioned problem is using a bistable composite laminate for load alleviation. A bistable composite laminate is capable of attaining two statically stable shapes, and it can be designed to alleviate a critical load, such as wind gust, by snapping from one stable position to the other. Piezocomposite actuators can be used to reverse the snap-through and bring back the structure to its original optimal aerodynamic shape, after the gust load is alleviated. However, there will always be a limit on the size of the piezocomposite actuator used; hence, severe force and energy constraints exist to achieve the snap-through. In this context, this paper focuses on the minimum required actuation energy for performing snap-through of a bistable structure. The paper shows how the required energy for cross-well transfer varies as a function of damping ratio and frequency ratio at specific harmonic force amplitude when the system is externally disturbed with a band-limited noise signal. A band-limited noise signal is chosen to model external/ambient disturbances. This paper uses the Duffing-Holmes equation as a one-degree-of-freedom representative model of a bistable structure. This equation is numerically solved to calculate the required energy for cross-well oscillation under different system and forcing conditions. Various non-dimensional parameters are used to highlight interesting phenomena. It is found that the domain of low energy regions decreases by increasing the level of noise.