Volumetric Energy Density (Laser Powder Bed Fusion)

Take the laser power, divide by the scan speed, the hatch spacing and the layer thickness, and you have the joules spent on each cubic millimetre of powder bed: $E_v = P/(v h t)$. It appears in the first paragraph of most parameter-development papers, on most machine logs, and in most conversations between people comparing settings. It is also, as a design parameter, largely a fiction — and the paper that says so most plainly is the one this page is built on.

In 2017 Bertoli, Wolfer, Matthews, Delplanque and Schoenung published "On the limitations of Volumetric Energy Density as a design parameter for Selective Laser Melting" in Materials & Design. The method was direct: build single tracks at parameter sets chosen so that $E_v$ was identical, and look at what came out. What came out was not identical. Some tracks were continuous and well-formed; others had broken into a row of beads; others had gone into keyhole mode. The energy density said all these processes were the same and they were not remotely the same, because the physics that decides between them lives in the ratios that $E_v$ destroys.

The arithmetic of the destruction is easy to see. Four independent quantities enter and one number leaves, so three degrees of freedom vanish. Halve the power and halve the speed together and $E_v$ does not move by a joule — but the beam now dwells twice as long on each spot at half the intensity, and dwell time and intensity are precisely what set the melt-pool depth, the peak temperature, the Marangoni flow inside the pool and the cooling rate behind it. Triple both instead and $E_v$ is unchanged again, while the track has become a fast, intense cut whose length-to-width ratio may have crossed the Plateau–Rayleigh threshold and pinched itself into beads. That is balling, and it is a single-track instability that no adjustment of hatch or layer can repair.

What is missing from the definition is as important as what is in it. There is no absorptivity: $E_v$ counts joules leaving the laser, not joules entering the metal, and absorptivity swings from roughly 0.3 to 0.7 depending on the alloy, the oxidation and size of the powder, the angle of incidence, and — awkwardly — on whether a keyhole has already opened, since a keyhole traps light and raises its own absorptivity. Two labs quoting 60 J/mm³ on different alloys are not describing comparable processes, and neither are two labs quoting it on the same alloy from different powder lots. There is no spot size either, so a 50 µm beam and a 100 µm beam are treated as one machine. And there is no powder: the layer thickness in the formula is the nominal plate drop, not the depth of powder actually spread, which is greater because loose powder is only about half as dense as solid metal.

So what is it good for? Two things, and they are real. It is a record — a compact way to write down what you ran, which is why it belongs in a build log. And it is a sorting variable within one machine, one alloy, one spot size and one powder lot, where the things it ignores are being held constant anyway and the process window really does trend with it. That is the setting the classic process maps were built in, and inside it $E_v$ behaves respectably.

What it is not good for is the thing everybody wants it for: transferring parameters. A recipe carried from one machine to another at constant $E_v$ is a recipe carried at constant nothing, because the spot size, the beam profile, the gas flow and the absorptivity all changed on the way. The honest procedure has not become any shorter since 2017 — single-track studies to find the stable regime, cross-sections to measure melt-pool depth and width, then hatch and layer chosen from the measured pool, then density coupons. This calculator will give you $E_v$ because you asked for it and because your log wants it. It will not tell you the number means more than it does.