Aerospace grade formulations are often composed of several ingredients whose ratios and interactions will impact one or more properties of the final component. Theory and experience can help with the design of these formulations, but sometimes there are interactions or synergies that have not been discovered yet. Therefore, it can be useful to explore a wide experimental space to discover the unexpected.
In this presentation, I share the results and insights obtained after running a mixture design, including how to visualize, normalize, and analyse the data. I also discuss ternary plots, how to communicate technical information to a nontechnical audience, the challenges encountered, and what could have been done better.
Hello, my name is Carlo Campanelli, and this poster is about use of a mixture design to optimize an aerospace formulation. Resin systems for aerospace applications typically compromise multiple components that need to be balanced to simultaneously meet thermomechanical safety and regulatory requirements.
The testing process can be long, expensive, and with multiple sources of variability. Furthermore, there are often time constraints which limit the number of formulations, tests, conditions, samples, and repeats that can be done.
The objective of this work is to improve the specific material properties while maintaining unaltered all other product, the characteristics and performance. This is often challenging as it can be a zero-sum game. And generally, it is a matter of finding the best compromise rather than finding the best formulation. The best compromise can change depending on the specific customer or the specific application.
The approach for this work is to use a mixture design with 3 variables, 15 runs, and 1 repeat. Here on the top right, we can see a picture showing the experimental space of the mixture design containing the 15 formulation tested. The components or variables are X1, X2, and X3, and their sum is always 100%. Here on the right, we can see an image showing how to read the ternary plot and how the sum of the free the component X1, X2, and X3 is actually 100%.
For this work, I've tested several properties, but I've reported they are three in the form of a color-coded ternary plot. Where green and red mean good and bad values, respectively. Starting from property one, we can see how the formulation at the bottom of the ternary plot have a good value, but this property tend to decrease by going up in the ternary plot. By going up, it means that we are increasing the amount of the X1 component. While going from left to right, so changing the amount of the X2 and X3 component, doesn't have an impact on this specific property. This is an example of a property that is dominated mainly by one component, X1 in this case.
Now, looking at the second property, we can see a similar but opposite trend. By going up, this property get better. By increasing the amount of X1, we're improving this specific property. But in this case, going from left to right, we have a decrease in value. Here for this specific properties, we can see that it is influenced by X1 and X3 mainly. This causes us to have three sections where we have good properties, average properties, and bad properties.
Regarding the third property, according to theories extrapolated from literature and direct technical experience, property three should be better for formulation at the bottom of the ternary plot. This is generally true, as we can see here, but there is an exception. This top-right formulation, which is a little bit of an outlier. This highlights the importance of screening a wide space and not having a bias toward certain parameters. Because if we were to follow the theory and only test or analyze the bottom formulation, we would have likely missed on this top-right formulation.
Finally, the Predictor Profiler is useful to compare multiple properties and trends at the same time. Use this ability factor to maximize the most desired properties and visualize the confidence interval. In this case, I've reported or plotted seven properties against the three variables, and we can observe all the trends at the same time. We can also see that for some properties, the confidence intervals are very narrow, while for some other properties, they are very wide. We should be careful when we make conclusions using this data.
About now, the learnings and the future works. This mixture design has highlighted several trends and some unexpected results. This will help with the optimization and tailoring of several products. It would have been beneficial to have more repeats as some properties have quite wide confidence intervals, and it is important to identify and understand the main sources of variability.
A more in-depth study of the data generated is needed to find the correlation between the measured properties, explain outliers, and make connection with previous studies to confirm or disprove theories, and see the bigger picture. In fact, I believe that it is important to make full use work and the data that we have generated.
This is everything for this work. Thank you for your attention.
