A bio-inspired, high-authority actuator for shape morphing structures Dana M. Elzey*, Aarash Y.N. Sofla and Haydn N.G. Wadley ABSTRACT Lightweight structures capable of changing their shape on demand are of interest for a number of applications, including aerospace, power generation, and undersea vehicles. This paper describes a bioinspired cellular metal vertebrate structure which relies on shape memory alloy (SMA) faces to achieve fully reversing shape change. The resulting vertebrate actuators can be combined with flexible face sheets to create a load-bearing, shape morphing panel. Performance of the vertebrate actuator in terms of maximum curvature and moment is analyzed and discussed. A recently constructed, prototype shape morphing airfoil is used to illustrate the concept. Keywords: structural actuator, cellular metal, shape memory alloy, sandwich panel 1. INTRODUCTION Shape morphing structures such as beams and panels should be lightweight yet capable of generating sufficiently high forces and moments to actuate and maintain shape in the presence of external forces. One approach has been to incorporate piezoelectric or shape memory elements into flexible polymer matrix composite structures. However, cellular metals concepts, such as honeycomb, tetrahedral truss and corrugated layer architectures, are ideally suited for the core structures of stiff, strong yet lightweight sandwich beams and panels, with relative densities as low as 2-3%. Replacing the conventional metallic or polymeric face sheets of cellular metal sandwich structures with smart material actuators, e.g. shape memory alloy (SMA), offers the potential for high performance shape morphing structures for aerospace and other demanding applications. We have recently described such a high authority, cellular metal actuator based on a diamond truss core structure (around 10% dense) sandwiched between thin SMA face sheets.1 The core can be manufactured at low cost by corrugating sheet of the desired thickness and then brazing two corrugated layers on either side of a flat center sheet of the same material to form a series of reinforced diamond-shape truss elements. Though lightweight, the core exhibits a high strength and stiffness in longitudinal shear and compression. Prior to the addition of the SMA face sheets however, the core is easy to bend out of plane. This is desirable because any resistance to bending of the core hinders the actuation of the shape morphing beam or panel. In this paper, we explore the concept of a bio-inspired, ‘vertebrate’ core which still exploits a cellular metal architecture, but relies on rotational joints to minimize the core’s bending resistance. The vertebrate actuator concept also relies on SMA face sheets to produce the desired shape change. SMA, such as Ni-Ti and Cu-Zn-Al, rely on a martensitic phase transformation to absorb inelastic strains (as high as 5-8%). Heating above the austenite start transformation temperature enables the material to recover its original shape.2 The spontaneous return of a deformed SMA sample to its original shape (or dimensions) upon heating is referred to as the one-way shape memory effect. A two-way effect is also possible, in which the SMA cycles between two fixed shapes during cycling between an upper and lower transformation temperature. * [email protected]; phone 1 434 982-5796; fax 1 434 982-5799; University of Virginia, 116 Engineer’s Way, P.O. Box 400745, Charlottesville, VA USA 22904-4745 92 Smart Structures and Materials 2003: Active Materials: Behavior and Mechanics, Dimitris C. Lagoudas, Editor, Proceedings of SPIE Vol. 5053 (2003) © 2003 SPIE · 0277-786X/03/$15.00 Most SMA-based actuators operate cyclically between two states and so, if based on the one-way effect, require a biasing force (such as a spring) to return the SMA to its low-temperature (martensitic) state. Such designs are inefficient because the work provided by the shape recovery is partitioned between the bias element, stored (elastically) in the structure, and that available to do work against applied loads (the useful part). Lu et al.3 have proposed and analyzed a lightweight, shape-morphing sandwich panel based on a twoway shape memory effect, in which one shape is acquired at the upper transformation (Austenite finish, Af) temperature and another shape at the lower transformation (Martensite finish, Mf) temperature. This concept is difficult to implement for many applications due to the very low (sub-freezing) temperatures needed to reach the Mf temperature of many SMA’s, and the relatively small (< 2%) length change available via the two-way effect. The vertebrate actuator (and the previous truss core design) is capable of fully reversed, cyclic shape change without the use of any bias elements. The core design ensures that the sandwich faces experience equal, but opposite, strains during actuation. Thus, as one face is heated above Af and contracts as it reverts to the parent (austenite) phase, the opposite (low temperature) face experiences an equal (but opposite) strain, in which stress-induced martensite is formed. The structure of the paper is as follows: after introducing the vertebrate actuator design concept and developing expressions for attainable curvature and moment, we describe a prototype shape morphing panel incorporating vertebrate actuators as ribs. 2. ACTUATOR DESIGN Figure 1 is a schematic illustration of the actuator design. This bio-inspired ‘vertebrate’ actuator consists of a series of tubular elements linked together by cylinder-and-sleeve joints, which allow the elements to rotate relative to one another during actuation. This core design offers the advantages of minimal resistance to bending and can be produced using a relatively simple, low cost manufacturing process. Attached to the top and bottom of the beam are shape memory alloy strips, secured to each vertebra with mechanical fasteners. Each SMA strip is pre-strained at low temperature (i.e. T < As) to approximately one-half of its maximum recoverable shape memory strain (εαβ). Heating either of the SMA face strips causes that strip to contract, resulting in bending of the actuator. The active (i.e. heated) face contracts to its full shape memory strain, while the opposite strip experiences an equal but opposite (tensile) strain. The curvature of the actuator is reversed by heating the opposite SMA face, which now deforms the first face in tension, preparing it for contraction upon heating, and so on. Heating of the SMA may be accomplished by direct resistance (Joule) heating or by means of attached heating elements. The design shown in Fig. 1 illustrates the use of thermal patches, but the prototype described below relies on resistance heating elements wound helically around the SMA. Heating of the entire active SMA strip at once results in a uniform curvature, with center of curvature located on the same side of the actuator as the active face. The opposite face is uniformly stretched in this case. However, individual SMA regions between vertebrae may be selectively heated, with the result that only the region of inactive SMA face directly opposite the heated region is deformed in tension. This selective operation of the vertebrate cells allows the actuator to achieve a wide range of shapes. Attainable curvatures are given as a function of actuator design variables below (see ‘Analysis’ below). The vertebrate core of the actuator may be constructed using thin-walled metal tubing of the desired radius (R) and wall thickness (tw). The center reinforcing may be added by cutting strip from flat sheet of thickness (tc), inserting into the tube and brazing. In addition, a smaller tube (of outer radius, Rh and inner radius, r+) and solid rod (of radius, r-) (which act as hinge sleeve and pin, respectively) are joined to either side of the center section (tube) and a slot (of angle 2φ) cut into the smaller tube to allow for relative motion of the vertebrae. The built-up tube is then sliced into sections (of width, B) (creating individual vertebrae) and the actuator core assembled by inserting the pin of one vertebra into the hinge sleeve of another. Alternatively, metallic or polymeric vertebrae could be produced inexpensively by extrusion. The Proc. of SPIE Vol. 5053 93 prototype actuator cores described later in this paper were constructed of Type 304 stainless steel. Component parts of the vertebrae were joined metallurgically by a transient liquid phase method. Fig. 1: The fully reversing, shape morphing structural actuator is comprised of a cellular flexible core sandwiched between shape memory alloy face sheets. 3. ANALYSIS The performance of the vertebrate actuator concept is characterized by achievable curvature, actuation force (or moment), relative and physical density, cycling frequency, fatigue life, power requirement and cost. In this section, we will analyze density, attainable curvature and actuating moment as a function of geometric design variables. Heating one or the other SMA face strip results in contraction of the heated face by strain, εαβ . The maximum curvature for the actuator (beam) is then given by κ0 = 2ε αβ (1) H where εαβ is the recoverable shape memory strain and H is the nominal actuator height, H = 2 R + t f . The subscript ‘0’ refers to the condition in which no external moments are applied. Figure 2 illustrates the dependence of the dimensionless curvature (κL, where L is actuator length) on aspect ratio, H/L for a shape memory strain, εαβ, of 8%. Greater curvatures are obtained for lower aspect ratio (i.e. reduced actuator height). However, as actuator height is reduced, the available bending moment (M) that can be generated by the actuator is decreased. This follows, since according to the moment-curvature relation for an elastic beam in bending, (2) M = EI (κ 0 − κ ) 94 Proc. of SPIE Vol. 5053 where E is the Youngs modulus of the beam, I is the second area moment of inertia, and κ is the curvature of the actuator beam resulting from application of the moment. Since the curvature scales inversely with actuator height, while as shown below, I scales with the square of H, the moment increases linearly with height. For the composite beam of interest here, EI is replaced by an equivalent ‘flexural rigidity’, (EI)eq. For a face sheet stiffened sandwich panel (or beam), (EI)eq is given by Allen4 as (3) ( EI ) eq ≈ E f BtH 2 2 The approximation equality is used since the core’s resistance to bending and the face strips’ resistance to bending about their own centers have been neglected. The maximum moment which can be applied to the actuator is limited by any one of several potential failure mechanisms, including plastic yielding of the face strip and elastic buckling of the core center reinforcement. The longitudinal bending stress in the face strips is given by Allen4 as (4) σf = ME f ( EI ) eq y where y, the distance from the beam centerline to the face center is taken to be y = H/4. This is used, rather than H/2, since the portion of the beam subjected to compressive loading cannot support any significant load without causing buckling of the thin SMA face strip. The moment is then limited by (5) M yf ≤ BHt f 2 σ yf where σyf is the yield strength of the SMA face strip. Elastic buckling of the core center reinforcement is analyzed using the Euler buckling condition for a slender elastic column. The critical load for buckling is Pcrit = n 2π 2 Ec I c / l 2 , where l is the length of the reinforcing member, l = 2(R-tw), Ec is the core stiffness, Ic the second area moment of inertia of the core sheet ( I c = Bt c3 / 12 ), and n, a constant (taken here as n = 2) determined by the end constraints applied to the column. Buckling is avoided by ensuring that the stress in the core reinforcement, σc = MEc y , does not exceed the critical stress, σ crit = Pcrit / Bt c . With y = H/4 again, ( EI ) eq the limiting moment is given by (6) M bc ≤ BHt π Ec 32 ( R − t w ) 2 2 3 c These expressions for the limiting moment due to face yielding and core center buckling are plotted in dimensionless form (by normalizing using EfBtcLDc) in Fig. 2. The geometric design parameters and material properties used are those given in Table 1. The core relative density is obtained as the ratio of the volume of material per cell to the total volume occupied per cell. This leads to Proc. of SPIE Vol. 5053 95 Vm 2πrt w + 2( R − t w )t c + (π − ϕ )( Rho2 − Rhi2 ) + πr 2 DC = = 2 R(2 R + Rho + r ) V (7) where the parameters are as defined by Fig. 1. Using the parameter values of Table 1, the relative density of the vertebrate actuator core is found to be 0.23. Table 1. Actuator Design Parameters and Material Properties Parameter Symbol Value Tube outer radius 6.35 (mm) [0.25 in.] R Tube wall thickness 0.7 (mm) [0.0275 in.] tw Core center thickness 0.81 (mm) [0.032 in.] tc Hinge sleeve outer radius 2.38 (mm) [0.094 in.] Rho Hinge sleeve inner radius 1.68 (mm) [0.066 in.] Rhi Hinge pin radius 1.59 (mm) [0.063 in.] r Face strip thickness 0.25 (mm) [0.010 in] tf 90 (Gpa) Ef Modulus (SMA-β) 550 (Mpa) σyf Yield strength (SMA-β) Modulus (core) 200 (Gpa) Ec From Fig. 2 it can be seen that the actuator moment is limited by face (SMA) yielding. Though no attempt has been made to optimize the design, it is clear that the core center could be made substantially thinner before elastic buckling would become the limiting failure mechanism. Failure of the tube walls by plastic yielding or buckling should also be considered to determine the optimal tube wall thickness. As mentioned previously, the vertebrate core design is expected to exhibit less resistance to bending than our previous design, based on a truss core consisting of two corrugated layers bonded to a flat center sheet.2 However, the truss core design should be more efficient structurally since the core members are all straight whereas the vertebrate design has curved truss members (i.e. the tube walls). This is confirmed by Figure 2, which includes the predicted limiting moment due to elastic buckling of the core center sheet for the truss core design. The truss core actuator is assumed to have the same overall dimensions as the vertebrate design, the same truss and core center member thickness, and cell length (i.e. one wavelength of the corrugated truss equals the length of one vertebrate cell). The relative density of the truss core design, using the parameters of Table 1, is 0.18, somewhat lower than the density of the vertebrate core. Consequently, the dimensionless moment, which is normalized by the core relative density, is greater than for the vertebrate design. The limiting moment due to face yielding is the same for both designs. 96 Proc. of SPIE Vol. 5053 Fig. 2: Moment and curvature capability as a function of aspect ratio for the vertebrate actuator design using parameters and properties listed in Table 1. The maximum moment is limited by plastic yielding of the SMA face sheet. 4. DISCUSSION - SHAPE MORPHING PANEL An important application area foreseen for this type of actuator is in aero or hydro control surfaces (e.g. aircraft control surfaces, undersea vehicle propulsion and control, wind turbine airfoils, etc.). Figure 3 is a schematic illustration of the concept, based on incorporation of vertebrate actuators as ribs, providing structural and shape changing capability to the control surface. The actuator ribs are held at fixed spacing by tubular spacers connected to vertebrae within the actuator at either end. This allows the actuators freedom to act independently, but ensures that they do not rotate out of plane (roll). Fig. 3: Shape morphing panel concept based on use of vertebrate actuators as structural ribs. A prototype control surface was constructed using a pair of vertebrate actuators consisting of nine vertebrae each. The actuator (rib) dimensions were H = 13 mm, B = 7 mm and L = 145 mm with a center-to-center Proc. of SPIE Vol. 5053 97 spacing of 150 mm. Figures 4 and 5 show a side and three-quarter view of the control surface in two different morphed configurations. The anodized aluminum skin is 0.25 mm thick and is attached by insertion between the C-clips attached to the actuator ribs and the rib surface. The panel skin is thus free to slide relative to the rib surface but must conform to the rib’s changing shape. Actuation is achieved by heating the SMA strips using a coiled resistance heating element (plastic coated wire). Four individually addressable heating circuits are used, corresponding to the upper and lower SMA elements on each of the two ribs. Thermocouples attached to each SMA are used to monitor temperature and to ensure that one SMA element has cooled sufficiently (i.e. to below the start temperature for the austenite phase transformation) before initiating heating of the opposite SMA face strip. Overlooking this precaution can be expected to lead to core failure (either through excessive plastic deformation or buckling) and limits the panel’s actuation frequency.1 (a) (b) Fig. 4: Shape morphing aero control surface in two configurations: (a) both actuator ribs at minimal curvature, (b) both actuators at maximal curvature. 98 Proc. of SPIE Vol. 5053 (a) (b) Fig. 5: Shape morph with ribs actuated unequally: (a) left rib has high curvature, right rib has low curvature, (b) the reverse of configuration (a). 5. SUMMARY A bio-inspired, fully reversing, shape morphing structural actuator is described. The actuator is comprised of a cellular flexible core sandwiched between shape memory alloy face sheets. Heating of either SMA element causes contraction of that face and results in a corresponding curvature of the actuator. The core’s design, which is based on an assembly of modular elements able to rotate relative to one another (‘vertebrate’ structure), enables the actuator to reverse its shape without the use of any bias mechanism (elastic restoring force). Expressions for curvature and moment capability as a function of material and geometric design parameters are developed. Finally, a prototype shape morphing panel is described, in which vertebrate actuators are incorporated as ribs. Proc. of SPIE Vol. 5053 99 ACKNOWLEDGEMENTS The authors would like to thank Mike Shelton for help in constructing the vertebrate actuator core and Peter Schare for help in constructing the panel prototype. Support for this research through DARPA (Leo Christodolou, program manager) and ONR (Steve Fishman, program manager) is also gratefully acknowledged. REFERENCES 1. Elzey, D.M., Sofla, A.Y.N. and Wadley, H.N.G. (2002) “Shape memory-based multifunctional structural actuator panels”, in: Smart Structures and Materials 2002: Industrial and Commercial Applications of Smart Structures Technologies, ed. A-M McGowan, SPIE Conf. Proc. Vol. 4698, pp.192-200. 2. Otsuka, K. and Wayman, C.M. (1998) Shape memory materials, Cambridge University Press, New York. 3. Lu, T.J., Hutchinson, J.W. and Evans, A.G. (2001) “Optimal Design of a Flexural Actuator”, J. Mech. Phys. Solids 49(9), pp.2071-2093. 4. Allen, H.G. (1969) Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford. 100 Proc. of SPIE Vol. 5053
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