Process windows from first principles
A closed-form analytical model for melt pool geometry, made interactive — so you can see the failure modes rather than just label them.
Every additive engineer has a spreadsheet somewhere with laser power and scan speed combinations they’ve tried. The parameter space is large and the physics underneath it isn’t always obvious, so they end up picking a DoE range that they have used before. If applied blindly, the process development is mostly trial and error dressed up as engineering.
First-principles models have existed for decades that tell you what your melt pool is doing. They’re just rarely the starting point.
The Rosenthal solution is a closed-form analytical model for the temperature field around a moving point heat source. What it gives you is melt pool geometry — depth, width, length — directly from laser power, scan speed, and material properties. No simulation required, gives an instant result.
I’ve built a tool that uses this to make the process window interactive. Adjust laser power or scan speed and you see the melt pool update in real time, along with where you’re sitting relative to the keyholing and lack-of-fusion boundaries. The view shows the melt pool geometry in the context of layer thickness and hatch spacing, so the failure modes are visible rather than just labelled.
It’s not a replacement for real process development. The Rosenthal model is a first-principles approximation — it assumes a semi-infinite substrate and ignores latent heat. But it’s fast enough to give you an intuition for the physics before you commit to a build, and honest enough to show you where its assumptions break down.
Material properties for a handful of common alloys are included. I find this first-principles view useful to see how the melt pool can change in broad strokes — though I’m interested to know if others find the approximations too limited.