Transcript Slide 1
Design and Development of Piezoelectric Sensors/Actuators for Morphing Aircraft David Pisani and Christopher S. Lynch I. Motivation Morphing structures are an emerging and growing technology. An early driver for this technology was the DARPA funded Northrop Grumman smart wing program and the subsequent morphing aircraft structures (MAS) program at NextGen Aeronautics. Morphing of the N-MAS was initially going to be handled through the implementation of smart materials technology. But, the available smart materials each had drawbacks that prevented their implementation. NextGen Morphing Aircraft demonstrating cruise and combat configurations Civil and military aircraft are typically designed to a few optimal aerodynamic flight conditions. As the roles of drones expand such as with HALE aircraft. The flight conditions of a mission can vary significantly over its flight. HALE aircraft have a larger proportion of fuel weight then other aircraft. The use of shape morphing technology would be advantageous for this type of aircraft by changing its aeroelastic shape throughout the mission and increasing its fuel efficiency. Micromechanics Phase Field Ferroelectric finite elements using a micromechanical model is important to morphing actuator designs on the structural level. It allows insight to the overall device design. The finite element code uses linear piezoelectric elements coupled with a micromechanical switching routine to simulate ferroelectric/ferroelastic interactions. Linear Piezoelectric Finite Element Formulation In order to evaluate the effects of IDE geometry, a 3-D non-linear finite element program with a ferroelectric/ferroelastic polarization reorientation material model was developed. To achieve hysteretic behavior, a linear piezoelectric finite element formulation was combined with a micromechanical switching model. Linear Piezoelectric Discretized Governing Equations: Kuu ik ab E r u K u i b cijkl òkl N au, j d bi N au d ti N au d b k ab Ku k ukb K b eiklòklr Pi r N a,i d N a d ab ab Micromechanical Switching Routine The micromechanical switching routine serves as a check for when polarization orientations of grains switch. When they do, constitutive tensors along with remnant polarization and strain are updated and fed back into the linear piezoelectric code. Northrop Grumman Global Hawk HALE (High-altitude, long-endurance) Aircraft Switching Criterion Ei Pi r kl òklr Wab Exploring and fabricating different ferroelectric compositions allows one to use the best materials for a specific application. After characterizing these materials under stress, electric field and temperature, their material properties can be fed into computational codes to explore the compositions effect on the structure. In this phase field model, the ABO3 perovskite structure is represented by a linearly interpolated hexahedron (brick) element where the element nodes represent the A (a) Perovskite unit cells. (b) Finite element representation site atoms. Each element retains an of a poled perovskite unit cell using hexahedron (brick) Eigen-polarization and Eigen-strain. element showing the unbalanced charges at the nodes. The Eigen-polarization is expressed as an unbalanced charge on each of the brick element’s eight nodes. The Eigen-strain of each element is represented by an unbalanced force vector on each of the nodes. The finite element code is used to find the potential and displacement of each of the nodes so that mechanical and electrical compatibility are achieved. Different PZT compositions with dopants can be fabricated to obtain controllable non-180 degree switching and to obtain field controllable phase transformations. Electric field driven polarization and strain curves. R1 through R3 show an increase in barium concentration Using this finite element method to determine electric potentials and displacements of the system, the Gibbs elastic free energy can be found and used to evolve the domain structures using the timedependent Ginzburg-Landau equation (TDGL) Electric Field (b) Micromechanical model example on unpoled specimen (a). The arrows represent polarization orientation of grains. When a large enough electric field is applied the polarization directions align with the electric field (b). Compositional Development Phase Field Model Work energy switching criterion used in micromechanical model (a) Gibbs elastic free energy density for a tetragonal material under: (a) no load. (b) externally applied stress, (c) externally applied electric field. (a) (c) (d) (b) Pi n Fn n in t Pi One dopant to the PLSnZT family that is worth exploring is Barium modification. Adding barium acts as a ferroelectric phase stabilizer. Thus increasing barium concentrations shifts the morphotropic phase boundary and causes a decrease in both switching field and a decrease in hysteresis. The simulation was conducted using a modified form of the timedependent Ginzburg-Landau method such that the maximum change in polarization for each time step did not exceed 10% of the spontaneous polarization magnitude. An example simulation is shown on the right of an open circuited rectangular structure. This phase field model will help gain insight into morphing structures on the domain level and determine the effects of various 20 × 20 element simulation of tetragonal ferroelectric material compositions. (e) PZT powder is prepared via a conventional mixed-oxide route by using PbO, TiO2 and ZrO2. and various dopants. Calcination is done at 890ºC for 2 hrs. Disc specimens are prepared and formed using a hydraulic press. The discs are then sintered at 1200ºC with a heating rate of 5ºC/min. Lead lanthanum stannate zirconate titanta (PLSnZT) ceramics are of interest for wing morphing applications. The stable antiferroelectric tetragonal phase can be switched to a ferroelectric rhombohedral phase using electric field. This phase transition has large strain changes due to the larger ferroelectric rhombohedral unit cell. These large strains can prove useful for morphing structures. Time-dependent Ginzburg-Landau equation (TDGL) Combining the linear piezoelectric finite element formulation with the micromechanical switching routine, a non-linear 3D finite element code with ferroelectric/ferroelastic elements is formed. A test example shown below with electric field applied in the z direction. The figure above shows several needs for actuation systems that is not currently met by existing technology and can be met by smart structures technology. Ferroelectric / ferroelastic behavior offers the capability of using an electrical signal to permanently switch a remnant strain, and the manipulation of geometry enables the ability to control in-plane anisotropic behavior. In order to develop actuation systems based on ferroelectric / ferroelastic behavior and phase transformation behavior, computational research such as micromechanical modeling and phase field modeling along with compositional development must be used in conjunction of one another. Characterization of material under stress, electric field and temperature. These results can then be fed into computational codes. with unconstrained open circuit boundary conditions. Twenty seven element example of ferroelectric finite element code. A bipolar electric field is cycled to exhibit switching behavior. Morphing Technology This switchable ferroelectric composite designs can be combined with the idea of a bimorph to create large curvature bending and large angle twisting piezolaminates. Examples of the proposed bend and twist coupling are shown subfigures a and b in the figure below. These can be combined to produce a wave like motion as shown in subfigure c below. Piezo fiber geometries with interdigitated electrodes can be designed using the three techniques above, 3D finite elements with micromechanics, phase field and compositional developments. Although IDEs are not new, they only exploit the linear range of material behavior. The linear material behavior is shown in the figure to the right. The material under the electrodes does not pole and the material between the electrodes is poled along the length. This can be switched to poling through the thickness by running the voltage from top to bottom instead of left to right. With proper electrode spacing this will result in a hysteretic change of length of the fibers. (a) Interdigitated electrodes on piezoelectric fibers. Field lines drawn are electric field. HENRY SAMUELI SCHOOL OF ENGINEERING AND APPLIED SCIENCE (b) Bimorph beam bending example The waveforms show the total voltage applied to an electrode. (c) Piezolaminates with a) Bending Coupling, b) twist coupling using a +/- 45° piezo fiber layup, and c) a morphing surface using multiple elements NSF CMMI Engineering Research and Innovation Conference 2012