drafts/process-map-literature.md

---
title: Process-map conventions for polymer SLS (PA12)
summary: Canonical axes (Andrew number, VED, EMR), the two process windows (bed-temperature sintering window vs stable sintering region), property-vs-energy curve shape, and the published precedent for percent-based relative energy axes on desktop machines.
---

> **DRAFT — PENDING HUMAN REVIEW.** Synthesized from a 2026-07-26 literature
> pass (primary-source verified where noted, incl. both Vasquez papers and
> Bourell CIRP 2017 read in full). Grounds the dashboard Process Map page.

# Process maps for polymer SLS of PA12

## Canonical axes

Published PA12 parameter studies vary laser power P [W] as the primary knob
(scan speed v, hatch h, layer t, beam size held constant — Bourell 2017);
part-bed temperature is treated as a *window constraint*, not a map axis.
Derived quantities:

- **Andrew number (areal ED)**: A_N = P/(v·h) [J/mm²]. Defined from the
  start as a *relative* measure (Nelson 1993; Williams & Deckard, SFF 1996).
  PA12 working range ~0.01–0.04 J/mm² (Bourell 2017); optima are
  machine/powder-specific (one Formiga study: 0.048–0.067 J/mm²) — do not
  hard-code a single number. Omits layer thickness.
- **Volumetric ED**: E_v = P/(v·h·t) [J/mm³]. Collapses layer-thickness
  variation. PA12 anchors (Bourell 2017): density knee ~0.12 J/mm³; UTS
  peaks 51 MPa, declines to ~47 MPa above ~0.3 J/mm³. PA12/CF optimum
  0.23–0.24 J/mm³ (Lupone 2021). Typical optimum band ~0.2–0.35 J/mm³.
  ⚠ VED conventions differ across papers — match the formula before comparing.
- **Energy Melt Ratio**: EMR = applied VED ÷ E_m, where
  E_m = [C_p·(T_m − T_bed) + h_f]·ρ·φ (Starr, Gornet & Usher 2011 — NOT
  "Starr/Rios/Fulcher"; that citation circulating in older notes is wrong).
  The literature's accepted cross-machine / cross-bed-temperature
  normalizer. PA12 on the Vasquez 2013 convention (EOS P100, bed 172 °C,
  φ≈0.5): E_m = 0.069 J/mm³, E_deg = 0.43 J/mm³, degradation at EMR ≈ 6.2,
  practical optimum EMR ≈ 4–5 (Lupone 2021). ⚠ "EMR ≈ 1–3" folklore is not
  supported on this convention. Bierwisch 2021 extends to AMR (optical
  absorption correction) — relevant for blue diodes on white PA12.

## Two distinct process windows (don't conflate)

1. **Bed-temperature sintering window** (Goodridge 2012 / Schmid 2014):
   T_bed between crystallization onset and melt onset. PA12: T_m 184.8 °C,
   T_c,peak 146.5 °C, window ≈ 27.6 °C wide, typical setpoint ≈ 168 °C.
   Too low → curl/warp/delamination; too high → caking.
2. **Stable sintering region** on the laser-energy axis (Vasquez 2011/2013):
   floor = full particle melt (E_m), ceiling = degradation onset (TGA 1 %
   mass loss 322–325 °C; laser can drive local powder >300 °C). Regions:
   unsintered (EMR <~1) → rising properties (1–4) → stable optimum (4–5) →
   degradation (≳6.2: chain scission, gas porosity, orange peel, Bonus-Z
   growth, property decline). Raising T_bed lowers E_m and shifts the whole
   usable band down — exactly what EMR normalizes. No keyhole regime in
   polymer SLS; balling is marginal, not a canonical region.

## Property-vs-energy overlay

Universal shape: rise → plateau → decline. Strength/modulus plateau first;
**elongation-at-break keeps rising to higher EMR and is the most
energy-sensitive property** (Starr 2011) — best single process-health
indicator. Anchors: Vasquez 2013 peak UTS 53.9 MPa at 18 W, −3.5 % at
22–25 W; EOS PA2200 datasheet UTS 45±3 MPa, modulus 1700±150 MPa,
elongation 20±5 % X/Y (Z 4–9 %). Desktop diodes (Sinterit Lisa 5 W:
UTS 45–48 MPa but elongation 2–6 %) sit on the rising flank.

## Relative (percent) energy axes are publishable practice

Sinterit Lisa exposes only a "Laser Power Ratio" multiplier; peer-reviewed
studies (Olejarczyk 2020, Gharate 2023, Joch 2025) report the relative
setting as the energy axis directly. Stronger option: one-time optical
power-meter calibration of % → W (would exceed the literature standard for
desktop SLS), then compute A_N/EMR physically.

## Inova MK1 specifics

- Firmware `LaserFillEnergyDensity` is **linear** ED (mJ per mm of scan
  path ≈ P/v), globally scaled by `TotalEnergyDensityPercent`. Divide by
  hatch spacing to get A_N; by hatch × layer for VED. Spot ~250–350 µm
  (hackaday/sls4all sources, unverified); hatch = spot × (1 −
  HotspotOverlapPercent/100).
- Laser: 5 W optical (dev) / 10 W (production), 445–450 nm, PWM control.
- At 445 nm neat white PA12 absorbs poorly (Gueche 2021) — absolute
  absorbed energy is uncertain, which itself argues for the relative /
  EMR-band presentation.

## Recommended map views (dashboard)

1. EMR-normalized energy strip with property overlay + literature bands
   (needs DSC params + bed setpoint + calibrated watts).
2. P–v (or relative-ED) plane with iso-A_N contours, points colored by
   outcome — implemented as the Process Map page's Map view using
   EffectiveLineEnergyDensity.
3. Bed-temperature window strip (146.5 / 168 / 184.8 °C) — companion, kept
   separate from the energy views.

Full citation list (33 refs incl. DOIs): see the 2026-07-26 research
transcript; load-bearing ones: Nelson 1993; Williams & Deckard SFF 1996 /
RPJ 1998; Starr RPJ 17(6) 2011 doi:10.1108/13552541111184143; Vasquez
Proc IMechE B 2011 doi:10.1177/0954405411414994; Vasquez Polym Eng Sci
2013 doi:10.1002/pen.23386; Bourell CIRP Annals 66 (2017)
doi:10.1016/j.cirp.2017.04.128; Lupone eXPRESS Polym Lett 2021
doi:10.3144/expresspolymlett.2021.16; Han Int J Extreme Manuf 2022
doi:10.1088/2631-7990/ac9096; Olejarczyk Appl Sci 2020
doi:10.3390/app10186184; Bierwisch Mater Des 2021
doi:10.1016/j.matdes.2020.109432; Sommer Polymers 2024
doi:10.3390/polym16101366.

## Discrepancies with existing drafts

- `energy-density-cheatsheet.md` quotes "PA12 AED ≈ 0.02–0.1 J/mm²"; the
  verified Bourell 2017 dataset spans ~0.005–0.04 J/mm² with secondary
  sources at 0.02–0.035. Reconcile before promoting either draft.
- Any note citing "Starr/Rios/Fulcher" for EMR should be corrected to
  Starr/Gornet/Usher (RPJ 2011).