What are the most effective ways to use product engineering tools and frameworks for aerospace R&D projects?

A tool I like a lot to use here is the golden circle. Start with the why, lead over into the how and then the what. This helps visualazing the process behind development. Don't start with the solution, work the problem, and don't skip over approaches that didn't work out, these are also valuable.

You need first to define the problem and the goal independent from solutions, that way you can instead of upgrading solution A to solution AA, you can find a new solution B which is better and/or faster and/or cheaper. Like making a car instead of finding a faster horse.

The domain or science of Decision making is full of different tools for this purpose and the efficacy depends on the setting. My personal favorite is the Quality Function Deployment diagram. These are very flexible, serve extremely well as documentation and can be as robust, in-depth or as light as needed. There are also simpler tools like the Digital Logic Method; this one is highly useful for simply maximizing/minimizing decisions at the outset. Could write a thesis on this topic, but I have 750 characters.

The problem with frameworks is that often, people unused to them start to put the framework ahead of the actual problem to be solved. Whatever is used must be accepted and understood by the people involved and disregarded when it becomes an obstacle. Something like the Double Diamond Framework for mDesign Thinking serves well since it is usually communicated visually and comprehensive enough to be a useful guide and light enough to avoid getting in the way.

What tools are applicable depends on what is being developed. CAD is nigh universal for fast prototype iteration in the early stages, but often with elements of UX prototyping. A physical model, for example, is more informative. Especially when it comes to holistic elements such as size, feel and texture. Generally, using tools that come close to the final product in the later prototyping stages is good. When it comes to early ideation, it is highly dependent on the people involved. Here, good group dynamics are more useful than any ideation tool, and using tools amplifies the existing team cooperation.

The Function and Deployment of Quality Function Deployment (QFD) becomes useful. The tool allows you to cross-examine relationships between engineering and customer requirements and produce numerical scores for comparison and analysis. These diagrams also contain much meta-information on how different criteria interact, what is compromised, and what is preferred in each case. This feature also allows for rapid iteration and saving inapplicable ideas for other projects or problems.

Fair warning on using metrics. Yes, they are useful, but metrics are also abstractions of what they are depending on how they were gathered in raw data and then calculated. They can be quite misleading. The same goes for mathematical models and simulations. You'll need to have a good understanding of the mechanics involved. As well as an understanding of the limitations therein. Other than that, did I mention QFD diagrams? Yeah, it works well for quick trade-offs and more in-depth analysis.

Try to go for ‘good enough’ A lot of engineers at the begining of career in R&D expect to find the perfect solution, so they chase one perfect idea after another. It is important to research, test different ideas, but when you make a decision to go for one idea, make it work. The idea is not to make it work in general case, but in your concrete situation. Then, go for good enough solution which you can improve in version number 2.