Materials for Morphing Wings
As an undergraduate student I conducted research to identify materials and technologies that might help design airplane wings that can change shape. I received the President's Undergraduate Research Award which funded much of the research. I was advised by Dr. David Bucknall of the School of Polymer Textile and Fiber Engineering (now School of Material Science and Engineering) at Georgia Tech and Dr. Chris Lynch of the Woodruff School of Mechanical Engineering at Georgia Tech. Here is some interesting information about the study.
The Wright brothers used a system called “wing warping” to control the roll of an airplane while flying. They used a system of pulleys and cables to twist the trailing edges of the wings in opposite directions. However, wing warping was difficult to control, and potentially dangerous, and the idea was soon dropped in favor of the stiff wing with an aileron.
For over a century since, wings have generally been stiff rigid structures with morphing capability limited to a few joints and flaps. Various factors have been responsible for this limitation. Most importantly, wings experience tremendous aerodynamic and frictional forces during flight, and contemporary developments in material science proved the stiff wing to be the best option in order to withstand these. Additionally, by using a rigid wing approach, the equations for flight can be kept relatively simple and forces acting on wings can be explained and calculated with relative ease.
However modern knowledge of materials allows us to create structures that are light, flexible, and at the same time withstand greater forces than those previously at the disposal of aerospace engineers. In addition, computing capabilities available today allow us to work with far more complex aerodynamic equations, and simulate forces and other variables in atmospheric flight with greater ease and accuracy. We are thus able to explore newer wing technologies that can enhance our control over aerial flight, and can once again consider wing morphing technologies, such as wing warping.
The performance of air vehicles can be improved and flight efficiency increased, by allowing wings to morph into structures best suited to each mode of flight since different airfoils are more appropriate for different flight regimes. For instance, a low camber supercritical airfoil reduces transonic drag divergence, while a symmetric airfoil may better suit frequent inverted flight, and an airfoil with a more angular shape would be better suited to supersonic flight. The ability to change the shape of the airfoil would allow an airplane to fly more efficiently over a range of flight modes.
This was the inspiration for the study, and the goal was to consider a few concepts and identify potential areas for further research.
A few different concepts were considered and explored to study their feasibility. They include:
- A foam with a thermally morphable resin coating
- A jointed cell like structure consisting of carbon fiber and resin
Each of these concepts and some of the early research I conducted into them is described below.
Concept 1 - foam with a thermally morphable resin coating
One of the concepts considered was a flexible open cell foam with a thermally morphable resin (rigid at room temperature, flexible when heated) coating the pores. The polymer on heating will become flexible and the foam can be bent into a different shape. Once the desired shape has been achieved, the polymer can be rapidly cooled into a rigid form. The foam will then maintain its new shape due to the stiffness of the cooled polymer.
1B. Test Samples
Three commercially sold open celled foams, each with different properties and pore sizes, were considered. Open celled foams are foams in which the pores are not entirely isolated from each other, and they are interconnected by tiny passageways. Open celled foams were used for the experiments since the resin solutions would need to soak all the way through the foams to line the pores.
The 3 foams were purchased from a site called www.thefoamfactory.com These 3 foams may or may not be available from other sources. They are referred to as Poly foam, Lux-R foam, and Dryfast foam.
1C. Measuring foam dimensions
The visible characteristics of 3 foams were studied under an optical microscope to measure the initial dimensions of the pores (so that subsequent changes after addition of the resin could be compared with the initial state). To find the cell thickness and the diameters of the pores, numerous photos were taken of the 3 foams using an optical microscope and these photos were then processed using Image Pro, Microsoft Paint, and Adobe Photoshop.
The photographs taken using the optical microscope were downloaded to Image Pro, and the software was calibrated with the correct scale for the lens being used. It was used to insert a scale at the bottom right of the images.
The images were then opened in Adobe Photoshop where the cell boundaries were measured using the Measure tool. The readings returned by the Measure tool were in inches, and were compared with the thickness of the scale on the figure in order to get the thickness in micrometers. 5 readings were taken, and averaged, for the thickness of the cell boundaries.
Finding the average diameter of the pores was a little more challenging as the pores were of different sizes and shapes and it was hard to determine which diagonal to measure their diameters along. A feature of Photoshop was used, which makes it possible to count the number of pixels of a certain color, or range of colors, in an image. However, the pores in the image were not all white, but had blurry outlines of the underlying layers of the foam, and the software had trouble differentiating the underlying layers from the one on top. Hence the insides of some pores were erased using the Eraser tool.
Then the color range selection tool was opened using Select > ColorRange.. (in Photoshop CS2). The range was set to brown, and the fuzziness adjusted to select the right shades of brown.
The dark (brown) regions of the image were selected, and the number of brown pixels was displayed in the histogram window.
Number of white pixels = Total number of Pixels – Number of brown pixels
The number of white pixels could be converted to an area in inches squared (using the image dimensions to calculate how many pixels are in an inch). The image dimensions were accessed from Image > Image Size…
Once the area in square inches was found, it was divided by the number of pores to give the average area of each pore. Then rearranging the formula for area of a circle, that the diameter of each pore becomes
Square root of ((avg area of pores x 4 )/PI)
The average diameter in inches was converted to micrometers using the length in inches of the scale marked on the image.
No. of cells: 25
Total Pixels: 1738880
Total area: 19.30778 sq inches
No. of brown pixels: 641915
No. of white pixels = 1738880-641915
Area of white color = (1096965 x 19.30778)/ 1738880
= 12.18023031 sq in
Avg area of each pore = 12.18023031 / 25
=0.487209212 sq in
Avg Diameter of pores = sqrt ((0.487209212 x 4)/PI)
= 0.787612871 in
Converting to micrometers
Avg Diameter of pores = 319.5184064 micro meters
1D. Coating Process
To prove it is in fact possible to coat the inner walls of the pores of a foam with polymer layer of certain thickness, we dissolve a polymer that is solid at room temperature in water, soaked the foams in it so that they absorb the solution and then allowed the foams to dry. It was expected that when the water evaporates the polymer in the solution should line the inside of the pores. Experiments were conducted to find if a higher concentration of the polymer in solution would result in the formation of a thicker polymer layer in the foam pores.
The polymer used was polyethylene oxide (PEO), a commercially used polymer which has the following structure HO-(CH2-CH2-O)n-H. A PEO of high molecular weight was used which is a solid at room temperature. Multiple solutions of PEO in water were created for testing, including 1% by weight, 7% by weight, 15% by weight, and 25% by weight.
Sample Preparation 1% by weight:
Weight of cup = 19.4174 g
Weight of cup + water = 264.2233 g
Weight of water = (264.2233-19.4174)g = 244.8059 g
Weight of PEO required = 0.01 x 244.8059g
= 2.448059 g
It is hard to measure out this exact weight of PEO powder accurately but a very close value was used (it measured at 2.4479 g).
The other 3 solutions were created in the same manner.
PEO does not however dissolve easily in water. The 1% and 7% mixtures were stirred using a magnetic stirrer. The 15% and 25% PEO by weight solutions were too thick to be properly dissolved by just the magnetic stirrer, so they were also sonicated. (A sonicator is an instrument that agitates solutions by bombarding them with ultrasound. The molecules of the solution are made to vibrate, and this helps dissolve the solution.)
The 3 test foams were dissolved in each of these solutions, and were then left out to dry. The solution was not squeezed out of them as this might cause some pores to have solution left in them and others to have less solution. So they were allowed to drain excess solution out themselves while drying.
The foams were then viewed under an optical microscope.
Here are some sample images:
On a single cell level, it can be seen that in some cases the thickness of the PEO layer increases with increase in percentage of PEO by weight in the solution, while in other cases the entire cell is filled with it rather than just having a coating layer, as can be seen in the image for 15% PEO. Also the PEO layer within a cell does not seem to maintain a uniform thickness, narrowing in some regions and broadening in others. However if we look at the averages across many cells, there is a trend where a greater percentage of PEO by weight results in a higher average coating thickness of the cells. So at the macro level it can be concluded that increasing the percentage of PEO in the solution will result in a thicker coating.
1E. Result of Coating
DMA analysis was then conducted on each of the 3 foams, soaked in each of the solutions, as well as without the PEO coating. Dynamic mechanical analysis (DMA) is a technique used to observe the viscoelastic nature of polymers. An oscillating force is applied to a material, and the resulting displacement is recorded. Thus the stiffness of the material can be determined and the modulus can be calculated. As a result of the DMA analysis graphs were plotted for amplitude vs displacement, and the modulus was taken as the average of the y values.
|Index||t||Ts||Tr||x value||y value|
Modulus = 0.110036 MPa
It was observed that the modulus increases with % PEO. In other words the foams with a higher percentage of PEO were stiffer.
One of the challenges discovered in the coating process was that the bottom layers of the foam were lined with more PEO than the top layers, because after the foams are soaked in the solution and left out to dry the solution drains downward due to the effect of gravity. This could be an issue to study further for the manufacturing of such coated foams.
1F. Changing the stiffness
The next step was to consider how the modulus of the polymer coating could be made to change with temperature. A quantity of interest was the glass transition temperature. Glass transition temperature is the temperature below which the physical properties of amorphous materials vary in a manner similar to those of a crystalline phase (glassy state), and above which amorphous materials behave like liquids (rubbery state). So it helps understand over what range of temperatures there will be a large change in the modulus, and helps determine at what temperatures the PEG will be stiff or flexible.
Differential scanning calorimetry (DSC) was used to find the glass transition. DSC is a thermoanalytic technique in which the difference in the amount of heat required to increase the temperature of a sample and a reference are measured as a function of temperature. The sample and the reference are maintained at very nearly the same temperature throughout the experiment. When the sample undergoes a physical transformation such as phase transitions, more (or less) heat will need to flow to it than the reference to maintain more at the same temperature. By observing the difference in heat flow between the sample and the reference, differential scanning calorimeters are able to measure the amount of heat absorbed or released during such transactions. More subtle phase changes, such as glass transitions can also be observed using DSC.
On using the DSC, the following plot was obtained. The bump indicates the change, giving a general idea of where the glass transition temperature for the POE is.
This information was important for further experiments to study the change in modulus of the cell with temperature.
1G. Exploring literature for a Simple model
From an engineering standpoint, it will be beneficial to have a model or relation to approximate the stiffness of a piece of coated foam based on the properties of the foam and the coating.
The model proposed in the book Cellular Solids - Structure and Properties (by Gibson and Ashby) appeared to be a good starting point. In this model, forces are applied at 2 opposite faces to cause deflection of those faces while the other faces remain rigid. This deflection will reach a point where it will offer resistance to additional force
Here is a 2D view of deflection under this same model
Gibson and Ashby proposed the following simple equation with their model.
E* = Youngs modulus for foam
Es = Youngs modulus of material of beam
P* = density of foam
Ps = density of material of foam
C1 = constant
1H. Expanding upon the model
An effort was made to expand this model so it can be applied to foams with a coating on the inner walls. It was decided to model the cells with coating in a finite-element analysis software to help come up with a more advanced model.
As a first step, it was necessary to verify the model proposed by Gibson and Ashby model, and also use it to calibrate the FEA model (such as figuring out how the loads and constraints should be applied to replicate the simple model).
The foam cell was modeled in SolidWorks.
It was then simulated using the FEA add-on package COSMOSWorks (now known as SolidWorks Simulation).
Initially constraints were applied at the ends of the arms.
It was observed that both sets of arms deformed in the same way as the theoretical model proposed by Gibson and Ashby; however the vertical columns of the cell buckle outwards as well (which is what one would realistically expect) whereas in the theoretical model they remain perfectly straight. Since the goal here was to verify their model and calibrate the FEA models for further research, it was decided to make the same approximation, and change the boundary conditions to bring them more in line with this theoretical model. To achieve this the edges of the vertical columns were fixed as well.
The deformation of this model is quite similar to the theoretical one.
Subsequently, the model was altered to add a coating on the inside.
It was also decided to model an assembly rather than a single cell.
Numerous simulations were run and trends observed, and some closed form solutions were found, although none of them matched the simplicity of the original theoretical model proposed by Gibson and Ashby.
Concept 2 - Jointed Cell Structure
Another concept considered was that of a jointed cell like structure. This structure was a closed frame of bars of carbon fiber coated with resin joined together with an elastomer. The carbon fibers coated with resin formed a hard supporting material whereas the connective elastomeric bits formed the joints.
2B. Experimenting with curing conditions
Experiments were conducted to find optimum resin + hardener mixing ratio, and also to find the optimum curing conditions (curing temperature and curing time), and to find a suitable surface material on which curing can occur without bonding. HTR-212 was used as the resin, the hardener was HT-360, and the surface was a Teflon sheet. Various samples were cured in an oven at 130C for 48 hours. The resin and hardner combination was found to work satisfactorily when mixed in a ratio of 10:3.3 by weight. However there was some discoloring (likely due to oxidation) and some trapped air bubbles. Curing the samples in a vacuum did not help solve either of these issues. After more experimentation it was discovered that a lower temperature of 65C was much more ideal and resulted in few air bubbles and less discoloring.
2C. Carbon Resin composite plate connected with elastic bands
A simple prototype was created of two carbon resin composite plates, connected together with three flexible elastic bands. The composite plates were both approximately 79.5 mm in length, 52 mm in width, and 2.35 mm thick. Each was made of 4 sheets of carbon fiber coated with resin. Three elastic bands of length approx 135 mm were used to connect the composite plates to each other. They were embedded at both ends into the composite plates, such that 2 sheets of carbon fiber were above them and 2 below, and the elastic bands went a distance of approx 35 mm into each composite plate to ensure a firm grip.
In order to create the prototype an apparatus was machined out of Teflon sheets. It consisted of a flat base on which to put the carbon fiber sheets at either end. A vertical support was placed in the center to hold the elastic bands up so that any resin that spread out from the carbon resin composite during curing would not creep along the elastic bands and coat them.
The setup was cured for 48 hours at around 65C.
2D. Tensile testing with prototype
The elastic band connected composite plate structure was subjected to tensile tests. These tests were aimed at finding:
- Whether the elastic bands would break first or get pulled out from between the carbon fiber sheets.
- The stress strain curve of the composite plates and the Young’s modulus
The plot above was obtained from a tensile test on the entire structure (composite plates connected with elastic bands). The plot is not linear but rather is curved; this happened because the elastic bands were slowly sliding out of the carbon fiber resin composite, and thus the rate of loading seems to decrease exponentially with time. The 3 sharp drops in load were when the each of the 3 elastic bands slips out of the composite plate. This was undesired behavior; the elastic bands should stay firmly embedded in the composite so that they snap and break rather than slide out, and it indicated that the geometry will need to be improved.
The plot above was obtained from a tensile test on just the composite plates. The load increased fairly steadily as can be seen in the first half of the graph. The second half is jagged because the composite plate started to crack, but did not break apart instantly due to the reinforcement provided by the carbon fibers. Upon plotting the stress vs strain it was found to be fairly linear, and the Young's modulus was calculated from it.
2E. Molds for improved prototypes
The tensile tests indicated that the resin needed to be applied evenly over the carbon fibers so that the strength of the material is uniform, and the elastomers needed to be better bonded to the composite. Molds were created in which the carbon composite plates could be produced and cured and the elastomers would be cured into the carbon plates at the same time as the carbon composite itself is cured. The molds were specifically designed to make sure the resin does not travel down the elastomers while curing, as it did with the first prototype.
I designed the molds in SolidEdge. Here is the bottom part of the mold that cures the carbon resin composite
And here is the top part of the same mold. It plugs into the bottom in such a way that chambers are created in which to pour the resin over the carbon fibers. The interlocking prongs of the top and bottom prevent the resin from flowing along the elastomer.
Other molds were created for other parts of the structure, including one which helps bring the ends of the strip together to complete a loop by curing another carbon composite plate connecting the ends.
The molds were machined out of a material called delrin which was easier to work with in the machine shop. They were subsequently used to create improved prototypes for further experimentation.