Multicolour Printing Cost: AMS vs Dual Nozzle vs Toolchanger

The comparison order is always AMS/MMU, dual nozzle, nozzle swap, full toolchanger. It describes architectures, not a ranking of models.

For active layers $L_m$ and changes per active layer $n_l$, $N=L_m n_l$, or enter an exact sliced change count. Directional relative frequencies $w_{ij}$ give $\bar V=\sum w_{ij}V_{ij}/\sum w_{ij}$. In additive mode, $V_{ij}=U_i+D_j$; direct mode accepts all 12 off-diagonal entries for four slots. A/B use Prusa's worked black/white example. C/D and equal transition frequencies are illustrative.

For architecture $k$, reload share $r_k$ and calibration factor $f_k$ give gross clearing mass $F_k=N r_k f_k\bar V\rho$. All volumes are explicitly converted to consistent units. Flush replacing useful material is $R_k=\min(F_k p, m_{capacity})$. Tower mass is $T_k=N V_{prime,k}\rho+L_t V_{structure,k}\rho$, or an entered complete tower mass. Fixed startup/brim mass is $S_k$. Total consumed is $M_{model}+F_k-R_k+T_k+S_k$. The material-balance residual is checked.

Weighted all-in change time is $t_k=(1-r_k)t_{dedicated,k}+r_k t_{reload,k}$. Plate time adds model-only time with its machine multiplier, $N t_k$, fixed setup time, and extrusion time for tower material outside the change allowance. That extra tower mass is $\max(T_k-N V_{prime,k}\rho,0)$, so measured towers do not count priming time twice. No time reduction is credited for flush reuse: this is conservative when infill replaces an already timed purge.

Electricity is average wall power × total hours. Cash cost is filament + electricity. Valued cost adds occupied hours × the entered time rate. Annual totals multiply plate quantities by annual plates; ownership curves add purchase cost once. For a positive toolchanger premium and positive per-plate savings, whole-plate payback is $\lceil\Delta P/\Delta C\rceil$. A lower initial cost with higher running cost is identified separately and has no recovery-of-premium result.

Reference checks verify Prusa's two worked directional examples, CNC Kitchen's roughly 40 s inclusive H2C change cycle, and the independently reported Tom's Hardware frog material budget. These validate directional averaging, time conversion and material accounting; they do not establish predictive accuracy for every machine/profile.

• Scenario date: 2026-10-27. Purchase amounts (600 / 1000 / 1600 / 2000 USD), 150 W average power, 6 min setup, tower structure 20 mm³/layer, 0.5 g fixed waste, equal base print speeds and dual reload share 33% are illustrative editable assumptions, not vendor specifications or measured product comparisons.
• A 90 s shared-nozzle cycle is an illustrative midpoint of CNC Kitchen's reported 1–2 minute range. The nozzle-swap scenario uses its reported roughly 40 s inclusive cycle; 12 s for loaded tools is an illustrative point inside its 10–15 s range. The 45 mm³ separate prime is Orca's documented Type 2 example, not universal across profiles.
• All-in change times already include change-associated flushing, priming, motion and heating. Sparse structure is added separately. Retune inclusive times when changing flush volumes. Startup mass and time are independent budgets.
• Each architecture's reload percentage describes actual occupied-nozzle reloads, not colour count or a simple nozzle-crossing fraction. No automatic route optimization is attempted. Common matrix weights approximate its reload-pair mix; use per-machine calibration factors or separate runs for dissimilar mixes.
• Density and price are blended effective values. Useful reuse capacity is material already budgeted inside model/support/object mass. The same capacity limit is applied independently to each candidate printer.
• Identical copies share the colour schedule and tower. Model mass and model-only time scale with copies. Extra travel and geometric packing effects are excluded.
• When using a purge-to-tower MMU workflow, count clearing material once: a measured tower must exclude its clearing fraction if the flush matrix already counts it. Separate prime volume is only extra pressure stabilization.
• The colour-matrix custom switch must stay enabled to use its edits. Machine scenario selectors offer Enter own values for every numeric parameter and the measurement/firmware date; selecting the illustrative row restores that row.

Planning for 2–4 represented slots with nonnegative, calibrated budgets. Variable layer height is supported through actual layer and change counts, not geometric inference. Tower-supporting layers are independent of layers with colour changes and of total model layers. Enter 0 supporting layers or 0 structural volume to omit tower structure; per-change priming is still counted. A physical layer can have several changes.

A full toolchanger or nozzle-swap system can still flush if it has fewer dedicated loaded paths than colours: enter the actual reload share. XL, INDX, U1 and H2C firmware/mechanical implementations differ; these are architecture examples, not identical mechanisms or interchangeable factory profiles.

Colour cleanliness and inter-material strength are not predicted. Wipe-to-infill can contaminate light walls or incompatible materials. Determine safe volumes and reuse experimentally. Default power, purchase cost and tower structure are not measurements. Firmware/slicer revisions require remeasurement; record the revision alongside your local scenario.

Positive time-valued savings need usable released capacity. Set the time rate to zero or select cash basis for out-of-pocket payback. Annual production is demand, not automatically constrained by calendar availability; a capacity condition flags more than 8760 occupied hours on one machine. Zero annual plates has no finite payback in years. There is no finite recovery when a positive purchase premium meets zero or negative savings; the status explains this and numeric payback is blank.

The frog checks reproduce published accounting, with distinct sliced and weighed values. Their difference is real measurement uncertainty, not a reason to tune the predictive model. Failed prints, material-specific prices, dryers, extraction, labour, maintenance differences, financing, taxes, residual value and discounted cash flow are outside the model.