Piezoelectric Microfiber Composite Actuators for Morphing Wings

Morphing wing technologies provide expanded functionality in piloted and robotic aircraft, extending particular vehicle mission parameters as well as increasing the role of aviation in both military and civilian applications. However, realizing control surfaces that do not void the benefits of morphing wings presents challenges that can be addressed with microfiber composite actuators (MFCs). We present two approaches for realizing control surfaces. In one approach, flap-like structures are formed by bonding MFCs to each side of a metal substrate. In the other approach, MFCs are bonded directly to the wing. Counter intuitively, the flap approach resulted in larger voltage actuation curvatures, with increased mass load. Actuation performance, defined as the ratio of curvature per applied voltage, was as large as (kV·mm)−1. The direct bonding approach reveals that at zero wing pressure, up to μm of displacement could be realized.


Introduction
Traditional piezoelectric actuators, oen referred to as "stack" actuators, have been used in numerous applications, including aeronautical applications [1,2]. Traditional piezoelectric actuators are typically capable of exerting high pressures, but with small strains. is has limited their applicability. Newer actuator designs overcome the limitations of small displacements typical of traditional piezoelectric actuators by trading the characteristic high pressures for larger displacements. is is usually accomplished through various composite structures rather than expensive, high precision micromachined leveraging designs. Some of these newer composite actuator designs include Moonies [3], Rainbow [4], THUNDER [5], LIPCA [6], ECLIPSE [7], and MFCs [8]. Although several actuators show promise in other applications, micro-robotics [9]; for example, MFCs were chosen for this application because they are more �exible. In addition, they have been used in other aeronautical applications [10,11]. A review of morphing aircra can be found in [12].
e MFC actuators are formed by sandwiching piezoelectric �bers between polyimide layers. e polyimide layers have interdigitated electrodes that are a key feature of MFCs. ey allow the utilization of the higher d 33 piezoelectric coupling constants rather than the lower transverse d 31 coupling constant. e high dielectric constant of the piezoelectric �ber concentrates, or condenses, the applied electric �eld inside the ceramic. More detailed information about MFCs can be found in the literature [8,13,14]. In this study we focus on an important aeronautical application of MFC actuators, speci�cally, morphing wings.
Morphing wings exhibit signi�cant advantages over �xed wing aircra in many applications. In this investigation, we focus on an extreme example of morphing wing technology, in�atable wings, in particular, one developed by ILC Dover. In�atable wings provide unique capabilities, for example, the ability to fold the de�ated wings into a cylinder for quick deployment via conventional artillery or aerial drop assemblies [15,16]. Upon reaching the target area, the wings are deployed and the aircra can loiter for long periods. However, one challenge is that of realizing control surfaces for these in�atable wings.
We present experimental results applicable to two alternate approaches for realizing control surfaces that incorporate MFCs. e �rst approach utilizes the MFC in a traditional �ap con�guration. is approach provided large DC displacements. Further optimization should result in the full range of displacements found in conventional �aps. In the second approach, successful procedures were developed for bonding MFC actuators directly to the surface of an in�atable wing. e experimental results show that the DC displacements are tension load limited, resulting in small displacements at higher wing pressures. However, modi�cations to this approach are suggested for enhancing performance.

Theory
Numerous theoretical treatments of MFCs can be found in the literature. Studies that highlight the importance of prestress [17] and its nonlinear aspects [18,19] are particularly relevant. In addition, Classical Laminate eory has been applied to MFCs [20]. Additionally, computer models have been developed [21,22].
For our �ap design, the MFC was mounted to a metal substrate. e details are given in the experimental procedures section. A characteristic curvature is realized when an electrical �eld is applied to the actuator. e electric response displacement of these curved actuators can be expressed in a variety of ways, including tip displacement, dome height ℎ [23], or normalized dome height [24]. We represent the voltage response displacement in terms of curvature , where is the radius of curvature. e curvature can be related to the dome height ℎ via (1) [25].
Here, is the arc length of the piezoelectric patch and is the length of the tab on each end of the actuator. e tab is a portion of the substrate le uncovered by the piezoelectric patch on some actuator designs. e curvature is zero for a �at actuator and increases for a more curved actuator. A negative (−) curvature corresponds to curvature up and a positive (+) curvature corresponds to curvature down. For example, simply hanging a mass on the end of the cantilevermounted actuator produces a positive (+) curvature.
e tip displacements were obtained from the micrometer measurements described in the experimental procedures section. For a �at actuator, . e distance is measured from the point on the actuator where the tip displacement measurements were made to the cantilever pivot point. Equation (2) relating and to the radius of curvature can be derived from simple geometry: Other �ap con�gurations include �aps with tabs of length extending well beyond the piezoelectric patch. In this case, the tip de�ection angle is given by If a mass load is applied to the actuator prior to applying the electric �eld, an initial curvature results. e situation can be treated analytically, by adapting a well-known mechanical engineering beam problem [26]. e piezoelectric actuator can be approximated as a passive column or simply supported horizontal beam of length with pinned ends. e piezoelectric force is represented as an external force acting inward on each end of the beam. Further, assume that the beam has an initial curved shape ( ), where is the coordinate along the length of the beam. e applied point mass is not directly included in this analysis. It is indirectly incorporated by virtue of the fact that the initial shape is due to the applied point mass load.
e second order inhomogeneous differential equation that characterizes the shape ( ) of the actuator is given by Here is Young's modulus and is the area moment of inertia. Based on experimental results, the actual initial shape of the actuator is a circle segment. However, a closed form solution can easily be found if we approximate the initial actuator curvature by the following expression ( ) .
Here, is the initial displacement at the center of the actuator and is related to the radius of curvature by (1) with substituted for ℎ. Aer applying the appropriate boundary conditions, the general solution is Here cr can be recognized as the critical load for an initially straight beam and is given by the following expression: e relevant point for our discussion can be seen in (6). For a given piezoelectric force , subsequent deformations ( ) are proportional to initial displacements ( ).

Experimental Details
e initial approach for realizing control surfaces in morphing wings was to bond the MFC to metal substrates and then use them in a �ap con�guration as depicted in Figure 1. is con�guration is similar to a conventional �ap and provided large displacements under mass load conditions. Although similar to conventional �aps, one big advantage of the piezoelectric �ap over the conventional �ap, for in�atable wings, is that the piezoelectric �ap is controlled by electrical leads rather than hydraulics or mechanical linkages. For the �ap measurements, two custom actuators were constructed by Smart Material Corporation. One actuator  Table 1. e rationale for bonding MFC sheets to both the bottom and top was to create a push-pull effect. e push-pull effect is a result of applying the voltages to both actuators with opposite voltage polarities. One electrical lead combination and voltage polarity tended to produce a concave up curvature, whereas the opposite combination tended to produce concave down curvatures. e actuators were mounted in cantilever mode for experimental convenience. A custom mass hanger was affixed near the free end of the cantilever so load masses could be applied. e applied mass loads are intended to simulate aerodynamic drag forces on the �aps. erefore, an upward tip actuation simulates the �aps acting against the drag forces and a downward tip actuation simulates the �aps acting with the drag forces. e experimental arrangement is depicted in Figure 2. A low frequency (2 Hz) sinusoidal signal was produced by a function generator and then ampli�ed by a Kepco BP 1000 high voltage ampli�er. Care must be taken that the electrical power source is not only capable of supplying the required voltages, but it must also supply the peak currents to a very reactive, mostly capacitive, load. e applied peak-topeak voltage was independently monitored by both a digital oscilloscope, and by a DAQ card (National Instruments model PCI 6024E). e current output of the micrometer was applied to the current sensing resistor. e voltage across the resistor was monitored by a separate channel on the same DAQ card and was monitored independently by a separate channel of the digital oscilloscope. e DAQ inputs were buffered by a high impedance buffer circuit. e maximum resolution was limited by the 12-bit vertical resolution of the DAQ card to 5 micrometers.
e experimental data acquisition and control was accomplished with LabVIEW Virtual Instruments (VIs) interfacing soware with both the GPIB and DAQ systems. LabVIEW VIs were written in-house and designed to collect the output from both the laser micrometer and the power  supply acquired from the DAQ. e VIs captured 512 data points over one complete cycle of the displacement and applied voltage. A full range of applied voltages was acquired for each load mass ranging from 9.1 grams to 309.1 grams ± 0.1 gram. e minimum load represents the mass of the hanger. Measurements were repeated for increasing and decreasing masses and were repeated several times for each actuator substrate, aluminum, and steel. e measurements were very reproducible.
e displacement measurements were made in a noncontact manner with a Micro-Epsilon model 1400-5 laser micrometer. is micrometer has a measurement range of 5 mm and a resolution of 3 micrometers. e micrometer outputs a current in the range of 4-19 mA that is proportional to the displacement. e micrometer was calibrated and checked for linearity across the entire range against a computer automated Michelson interferometer. e interferometer was constructed in-house. At high mass loads an additional long range (20 centimeters), but lower resolution (40 m), micrometer (Micro-Epsilon model number 1400-200) was used. e uncertainties of the displacement measurements were below 5% relative uncertainty.
For the direct bonding approach, the initial bonding tests were conducted on a small sample of Kevlar, the same Kevlar used in the construction of the airfoil. ILC Dover provided an in�atable airfoil for use in this pro�ect. See Figure 3. e airfoil is a 0018 symmetric design and has a maximum operating pressure of 69 kPa (10 psi) relative pressure. e wing is 0.8133 m (32.02 inches) long and 0.4318 m (17.00 inches) wide at the root, tapering down to 0.2809 m (11.06 inches) at the tip. e wing is constructed from Kevlar fabric that is sewn into an airfoil shape with multiple spars running along its span. e spars provide structural support when the wing is in�ated as well as maintaining well-de�ned volumes into which a polymeric bladder is inserted (similar to a hand being inserted into a glove) to act as the air retention mechanism. e root of the wing was attached to an aluminum mounting plate �tted with a gas inlet. More details about the wing can be obtained from [15,16].
e actuator chosen for the direct bonding measurements was the MFC model 26E03-006B manufactured by Smart Material Corporation. e actuator dimensions are 74.2 mm × 98.7 mm ± 0.2 mm. A location near the outermost trailing edge of the wing, spanning the four wing spars closest to the trailing edge, not including the spar that constitutes the trailing edge itself, was identi�ed as the location on the wing that could provide the greatest change in aerodynamic li for given actuator displacements. Unfortunately, this location could not be utilized because three of the spars were inactive (i.e., not pressurized) due to knotting that occurred in the air bladder in the interior of the wing. e actuator was bonded to the wing as close to the trailing edge as possible while avoiding the knotted areas. e actuator then had to be moved slightly closer to the root of the wing so that the entire length of the actuator would span exactly three spars. e center of this location is 141±1 mm from the tip and 142± 1 mm from the trailing edge. e adhesive used to bond the actuator to the airfoil was EP 31 developed by Master Bond Incorporated. is two-part epoxy has a 20 kN (4500 lb) shear strength, which greatly reduces compliance problems that may limit the performance of the actuator/Kevlar system. Both the actuator and the airfoil (depressurized) were cleaned with acetone. e importance of cleaning the bonding surfaces cannot be overstressed. In preparation for bonding the actuator to the airfoil, the de�ated airfoil was held in place and pressed �at. e adhesive was allowed to cure for 28 hours at room temperature before the airfoil was repressurized. Bonding reliability was tested by repeatedly applying sinusoidal voltage signals to the actuators over a range of frequencies from below one Hertz to above one kilohertz with amplitudes less than 1500 Volts peak to peak with a 500 Volt offset. At higher frequencies (higher ramp rates) the current demands on the high voltage ampli�er becomes signi�cant. e reason for the voltage asymmetry is due to the preferred direction produced during the initial piezoelectric poling preparation. Electric breakdown is the effective limit on voltages in the same direction as the poling direction. e limiting factor in the reverse direction is depoling. e applied voltages in this investigation were below 75% of the rated voltage capacity of the MFC actuator. e bond was visually inspected periodically with no evidence of bond degradation. Aer realizing successful bonding of the MFC to the wing, displacements were measured at various points shown in Figure 3. During measurements, the frequency of the applied voltage was one Hertz, which is well below any electrical or mechanical resonances. Initial applications of the voltage indicated that the displacement was very small. Even small displacements may be useful for active boundary layer control techniques, thus an in-depth investigation of the displacements was conducted. Figure 4 shows two representative data sets for the steel substrate acting against the applied load, upward. e arrows in the �gure indicate the direction around the loop as a function of applied voltage. e lower curve is with the load of the mass hanger (9.1 g). e upper curve is with a total load of 3 9.1 ± .1 g. Focusing �rst on the low mass load curve, the actuator starts out with a slight downward (+) curvature ( .749×1 −4 mm −1 ) due to the mass at zero applied voltage. As the voltage is increased, the actuator becomes �at at 0.35 kV then becomes curved upward (−) until at 1 kV applied voltage the curvature is −3.4 ± .1 × 1 −3 mm −1 . For the upper curve, (309.1 g) the actuator starts with a downward curve (+) due to the mass and becomes less curved with applied voltage. Both curves show signi�cant hysteresis, which is expected for piezoelectric devices, even for small applied electric �elds well below those required to repole the piezoelectric ceramic. However, other sources of hysteresis such as mechanical losses should also be considered. A more detailed treatment of nonlinear responses of piezoelectric composite actuators can be found elsewhere [18,27,28]. If the actuator response is approximated to �rst order by a linear �t, a performance can be de�ned as curvature per applied voltage and can be read as the effective slope from the curvature versus applied voltage plots. e fact that the slopes are negative is an artifact of the sign convention chosen to de�ne curvature up and down. Figure 5 shows the magnitude of the performance as a function of mass load for several masses. e performance increases linearly with increased load mass. e slope is 4.9 ± 0.2 × 10 −7 (mm⋅kV⋅g) −1 . e actuator, in fact, produces a larger change in curvature with greater loads for a given applied voltage. At �rst glance, this may seem counter intuitive. However, larger mass loads produce larger initial curvatures that favor greater performance. is can be seen from (6). ere are competing effects here. Of course, the larger mass loads require more force to move. However, the mass loads also provide an initial curvature, which tends to enhance the performance. e result is a slight net increase of the performance. Figure 6 shows a family of curves for a variety of mass loads. e expected Hooke's law type behavior for zero applied voltages is evident. e aluminum substrate showed similar results. However, the performance was less predictable for the aluminum substrate. e magnitude of the performance increased linearly from an initial value of 1.14 × 10 −3 to a value of 1.30 × 10 −3 for a 150 g load. e performance, as a function of mass, increased up to 150 g and then decreased linearly back to the original value at 250 g and remained there until the maximum load of 300 g. Furthermore, as seen in Figure 7 the hysteresis was also less predictable. Another interesting phenomenon was the looping at the end of the hysteresis curves near mass loads of 120 g. is was evident in both aluminum and steel. However, it was more predominate for the aluminum substrate.

Results and Discussion
e �ap approach produced signi�cant displacements. It is interesting to ask how these results compare with traditional �aps. A straight comparison is not possible because, unlike traditional �aps that remain rigid, the piezoelectric �aps �ex along their entire length. However, it is reasonable to compare the tangent angle of the piezoelectric near the tip. A simple geometric proof shows that the angle of the tip , in radians, relative to horizontal, is equal to the ratio of the actuator arc length to the radius of curvature . e arc length is equal to the length of the actuator when �at. �sing the dimensions of the steel substrate actuator ( 10 .2 mm) and the change in curvature Δ 4.123 × 10 −4 mm −1 for a 9.1 g mass load and 1 kV applied voltage we get a tip angle de�ection of 2.48 ± 0.0 degrees which is small compared to traditional �aps. However, with optimization of parameters like the substrate thickness and length, larger angles should be obtainable. Other �ap con�gurations include �aps with tabs of length extending beyond the piezoelectric patch. In this case, the tip de�ection angle given by (3) would be much greater.
For the direct bonding approach, baseline data on the depressurized wing (0 psi) while laying �at was obtained. Voltage was applied and displacement measurements taken at 3 points on the actuator. For zero mechanical loads (tension), maximum displacements of 63 ± 3 m were recorded. e next pressure measurement was at 34 kPa (5 psi). e wing system would not sustain lower constant pressures. Measurements were made at the same three points as in the 0 psi test, plus two additional points on the wing located at the tip of the wing and at the tip of the trailing edge of the wing. e results are shown in Figure 8. Displacement data was also acquired at 48 kPa (7 psi). At this pressure, the displacements were approaching the resolution of the micrometer at every point except test point 1. Displacement measurements at pressures greater than 48 kPa (7 psi) were below experimental uncertainty. Bonding reliability was tested by cycling the MFC through thousands of actuations over several days. e experimental measurements were duplicated several times with reproducible results.
Although the actuator did not bond completely to the seams of the wing, the majority of the area of the actuator (>90%) formed a strong bond with the wing. In future work, it may be advantageous to raise the temperature of the bonding  area in order to achieve an even stronger bond with shorter curing times. Ideally, the actuators would be incorporated into the wing during construction of the wing, rather than retro�tting them. e observed displacements at high pressures were small, resulting in only slight changes in the cross-sectional shape of the wing, thereby limiting the effect on �ight characteristics of the airfoil during �ight. However, the low pressure and fabric sample tests did produce appreciable displacements. e displacements were strongly dependent on pressure, indicating that the displacements are load (mechanical) limited by the fabric tension. One solution to this problem is to stack the actuators to increase the force generated and/or use larger actuators. In addition, the possibility of using the actuators to generate wing twist may prove useful. Another approach would be to alter the wing design to take speci�c advantage of the actuators. A portion of the outer trailing edge of the wing could be �removed� and replaced by an in�atable section hinged on a strip of Kevlar fabric. is would provide a free moving portion of the wing for use in altering li. Without having to work against the tension in the fabric across the entire length of the wing, the actuator would then only have to work against aerodynamic forces. is could be accomplished without compromising the advantage of a small deployment volume.

Conclusions
Piezoelectric MFC sheets can be successfully incorporated into in�atable wings. Two approaches were explored. In one approach, MFC sheets were bonded to metal substrates and affixed to the trailing edge of the wing in a manner similar to traditional wing �aps. e voltage dependent displacements were characterized in terms of curvature ( ). Mass loading the actuator produced a counter intuitive increase in the performance of the actuator. Flap tip angle de�ections of 2.48 ± 0.05 degrees were obtained. In the other approach, MFCs were attached directly to the upper surface of the wing. At zero pressure, displacements as high as 63 ± 3 micrometers were obtained. As the pressure of the wing increased the displacements diminished toward zero within experimental uncertainty at a pressure of 48 kPa (7 psi). e main advantage of the direct attachment method is that it better maintains the �exibility of the wing. However, problems of tension loading with increased wing pressure need to be addressed. e �ap approach produces greater displacements although it diminishes the �exibility of the wing. is is not an insurmountable problem depending on the application. For example, the �aps could be segmented so that they can be folded with the wing when de�ated. However, once the �exibility of the MFC sheet has been diminished by bonding it to a metal substrate other composite actuators such as THUNDER actuators should be considered. ey may provide larger displacements and they have been considered for other aeronautical applications [29]. ey are also slightly more mature and are more easily modeled with Finite Element Methods [30] even though FEM models for MFCs have been published [22]. ese FEM models can be used to optimize performance and incorporate them into wing designs. Additionally, wind tunnel tests need to be performed to verify the models under dynamic conditions.