drafts/process-map-literature.md

metadata

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).