A breadboard system has been developed for demonstrating nonmechanical zoom using flexible thin films. The project consists of three major task areas: material characterization, diagnostic system development, and imaging system development. The material characterization phase involves two components: development of modeling tools, and measurement of material properties for use in the tools. The diagnostic system development phase will apply the tools and knowledge developed in the first phase to build algorithms for modeling and testing one-dimensional films with multiple actuators. These models will then be compared to experimental results and modified as needed. The imaging system development phase will conclude the effort by building a sensor system with variable zoom based on optical-quality PVDF films.

A COMSOL deformation plot for an initial gradient Piezoelectric Model (deformation is exaggerated by 7.5X). Overall dimensions are 2 mm × 2 mm × 50 μm.
The modeling tools are based on interaction among three commercial software packages: SolidWorks, COMSOL Multiphysics, and ZEMAX optical design. SolidWorks is a computer-aided design package, which has a live interface to COMSOL, which is a finite element analysis/partial differential equation solver. ZEMAX is an optical design package. Both COMSOL and ZEMAX have live interfaces to MATLAB. A model in SolidWorks can be updated in COMSOL, an FEA calculation performed in COMSOL, and data exported to MATLAB. Independently, surface profile data has been exported from MATLAB into ZEMAX. The next step will be to connect a single model from SolidWorks to ZEMAX. From MATLAB, the optical data will be used to alter the voltages driving the surfaces in COMSOL, and the cycle repeated. This will enable the development of approximations at a future time.

Modeling has focused on developing an empirical model for the film behavior and incorporating it into COMSOL. In the past, PVDF actuators were formed by combining two layers of materials that were poled with different orientations. The materials then act like a bimetallic strip used in a thermostat. Given the same field, one layer of the bimorph material would expand and one layer would contract, resulting in a curvature. This process is not amenable to opticalquality films because of the distortion created by attaching the two films.

A process was developed that generates a curvature from a unimorph film that can be fabricated with an opticalquality surface. The current focus is on actual material characterization. In the test fixture for characterizing the material properties, an upper bracket is used to connect the film to high voltage and hold it rigidly. A lower bracket is balanced on a knife edge, and will be used to connect the film to ground and apply a load to the film. There is a mirror mount on one end of the lower bracket. A laser will be reflected off this mount to measure deformations of the film as voltage is applied and the load is varied. Initial modeling using material constants for PVDF indicate a deformation of ~0.4% in length can be expected with 1 kV applied. For test samples with a 50-mm active area, that yields a deformation of 200 μm. This deformation will result in a 4-mrad deflection of the laser spot, or about 10× larger than the estimated uncertainty using the laser diode available in the lab.

One example of COMSOL results is shown in the figure. This figure was from a model that included a gradient in the piezoelectric constant that couples the zaxis electric field to the x-axis strain. This particular model included the x = 0 surface constrained in the x direction. In addition to the negative curvature in the xz plane, there is a slight positive curvature in the yz plane. This curvature is seen from the curved lines of equal z-axis displacement, and results from Poisson’s ratio. Poisson’s ratio for a material relates the strain in one direction to the negative strain in the orthogonal direction. To confirm this explanation, another model was run with Poisson’s ratio set to zero. The resulting surface had the lines of constant z-displacement straight and parallel to the y-axis.

Of the 18 evaluation samples provided, one sample has been briefly assessed by allowing the sample to hang freely and applying voltages to the electrodes. In contrast with previous films, this film showed very little deformation, even with the application of 4.5 kV. A laser was used to measure the angle of the surface deflection, with the deflection equal to roughly 5º at 3 kV. This is the order of magnitude of response expected when the film is constrained at the edges. There are several potential explanations for the behavior. The difference could be due to the smaller sample size and the linear configuration (previous films were substantially larger and circular), reducing the effects of the border around the active area of the film.

This work was done by Greg A. Finney of Kratos Defense and Security Solutions for the Office of Naval Research. ONR-0025

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This article first appeared in the February, 2012 issue of Defense Tech Briefs Magazine.

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