Additive Manufacturing formula solvers

Categories — 58 of them, 1453 solvers in all

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Areal Energy Density (Laser Powder Bed Fusion)

E_a = \frac{P}{v \, h}

Additive ManufacturingThe same beam accounted per unit of scanned AREA rather than per unit volume: power divided by scan speed and hatch spacing. It drops the layer thickness, which is the one term in volumetric energy density that describes the powder rather than the beam — so it is a slightly more honest description of what a single hatched layer receives, and it is still an average over things that are not uniform.

Build Time Estimate

t_b = n \, ( t_s + t_r )

Additive ManufacturingLayers multiplied by what each layer costs: the time the beam spends scanning it plus the time the recoater spends spreading the next one. The estimate every quotation starts from, and the one every scheduler learns to pad.

Carr Compressibility Index

CI = 1 - \frac{\rho_b}{\rho_t}

Additive ManufacturingThe same tapped-and-loose experiment as the Hausner ratio, reported as the percentage of its loose volume the powder gives up when tapped. Ralph Carr published it in Chemical Engineering in 1965. It is not a second measurement and it carries no information the Hausner ratio does not — CI = 100(1 − 1/HR) exactly — but it is the form most pharmaceutical and powder-handling specifications are written in, so both belong on the site.

Fused Filament Extrusion Flow Balance

\frac{\pi}{4} \, d_f^{2} \, v_f = w \, h \, v_p

Additive ManufacturingWhat goes into the hot end must come out of the nozzle: the cross-section of the filament times how fast it is pushed equals the cross-section of the deposited bead times how fast the head moves. The mass balance behind every extrusion multiplier, every E-step calibration and every under-extruded print.

Hausner Ratio

HR = \frac{\rho_t}{\rho_b}

Additive ManufacturingTapped density divided by apparent (bulk) density: how much a powder tightens up when you shake it. Henry Hausner proposed it in 1967 as a one-number flow rating, and it remains the cheapest useful test a powder receives — a ratio near 1.0 means a powder that pours and spreads, and one above 1.35 means a powder that bridges, rat-holes and leaves the recoater with an uneven layer.

Layer Count from Build Height

n = \frac{H}{t}

Additive ManufacturingBuild height divided by layer thickness. The simplest relation in additive manufacturing and the one every schedule rests on, because the layer count multiplies every per-layer cost the machine has — the scan, the recoat, the dwell, the inert-gas sweep.

Normalised Enthalpy and the Keyhole Threshold

\frac{\Delta H}{h_s} = \frac{A \, P}{h_s \, \sqrt{\pi \, D \, v \, \sigma^{3}}}

Additive ManufacturingThe dimensionless group King and colleagues at Lawrence Livermore put forward in 2014 to predict when a laser stops melting and starts drilling. It compares the energy the beam actually deposits into the interaction volume with the energy needed to bring that material to its melting point — and unlike volumetric energy density it keeps power, speed and spot size in the arrangement the heat-conduction physics puts them in, which is why it works and E_v does not.

Powder Consumed by a Build

m = \rho_b \, V

Additive ManufacturingApparent (bulk) density multiplied by the volume of the powder bed. The number that matters is that V is the whole ENVELOPE the build sweeps — plate area times build height — not the volume of the parts. A powder-bed machine fills the entire box whether the parts occupy five per cent of it or fifty.

Relative Density (Per Cent of Theoretical)

\rho_{rel} = \frac{\rho_m}{\rho_{th}}

Additive ManufacturingThe measured density of a built part divided by the density the same alloy has when it is fully solid. The single number the whole parameter-development exercise is trying to move, quoted everywhere as a percentage — and a number that hides more than it reports, because how the porosity is arranged matters far more than how much of it there is.

Scan Time per Layer

t_s = \frac{A}{v \, h}

Additive ManufacturingHow long the beam takes to hatch one layer: the area to be scanned divided by the rate the beam covers area, which is speed times hatch spacing. The per-layer number that the layer count multiplies into a build time.

Staircase Surface Roughness

R_a \approx \frac{t}{4} \, \lvert \cos\theta \rvert

Additive ManufacturingA sloped surface built out of flat layers is a staircase, and this is the arithmetic-mean roughness of those steps: a quarter of the layer thickness, scaled by the cosine of the angle the surface makes with the build plate. Pure geometry — no melting, no powder, no material. It is a floor under the real roughness and never a prediction of it.

Volumetric Energy Density (Laser Powder Bed Fusion)

E_v = \frac{P}{v \, h \, t}

Additive ManufacturingLaser power divided by scan speed, hatch spacing and layer thickness: the joules the beam spends on every cubic millimetre of powder bed. Every machine log records it and every parameter paper quotes it — and it is a bookkeeping number, not a process window. Four independent variables go in and one number comes out, so the information that decides whether the track is sound, balled or keyholing is destroyed on the way through.