3D Print Quality Tuning

Summary

This experiment investigates 3d print quality tuning. Central composite design to maximize surface quality and minimize print time by tuning layer height, print speed, nozzle temperature, and infill percentage.

The design varies 4 factors: layer height mm (mm), ranging from 0.1 to 0.3, print speed (mm/s), ranging from 30 to 80, nozzle temp c (C), ranging from 190 to 220, and infill pct (%), ranging from 10 to 50. The goal is to optimize 2 responses: surface quality (pts) (maximize) and print time min (min) (minimize). Fixed conditions held constant across all runs include material = PLA, bed temp = 60C.

A Central Composite Design (CCD) was selected to fit a full quadratic response surface model, including curvature and interaction effects. With 4 factors this produces 32 runs including center points and axial (star) points that extend beyond the factorial range.

Quadratic response surface models were fitted to capture potential curvature and factor interactions. The RSM contour plots below visualize how pairs of factors jointly affect each response.

Key Findings

For surface quality, the most influential factors were nozzle temp c (39.4%), infill pct (30.2%), layer height mm (15.4%). The best observed value was 10.1 (at layer height mm = 0.2, print speed = 55, nozzle temp c = 172.137).

For print time min, the most influential factors were nozzle temp c (47.0%), print speed (25.2%), infill pct (21.5%). The best observed value was 27.0 (at layer height mm = 0.2, print speed = 0.227744, nozzle temp c = 205).

Recommended Next Steps

Run confirmation experiments at the predicted optimal settings to validate the model.
Consider whether any fixed factors should be varied in a future study.

Experimental Setup

Factors

Factor	Low	High	Unit
`layer_height_mm`	0.1	0.3	mm
`print_speed`	30	80	mm/s
`nozzle_temp_c`	190	220	C
`infill_pct`	10	50	%

Fixed: material = PLA, bed_temp = 60C

Responses

Response	Direction	Unit
`surface_quality`	↑ maximize	pts
`print_time_min`	↓ minimize	min

Configuration

use_cases/146_3d_print_quality/config.json

{
  "metadata": {
    "name": "3D Print Quality Tuning",
    "description": "Central composite design to maximize surface quality and minimize print time by tuning layer height, print speed, nozzle temperature, and infill percentage"
  },
  "factors": [
    {
      "name": "layer_height_mm",
      "levels": [
        "0.1",
        "0.3"
      ],
      "type": "continuous",
      "unit": "mm"
    },
    {
      "name": "print_speed",
      "levels": [
        "30",
        "80"
      ],
      "type": "continuous",
      "unit": "mm/s"
    },
    {
      "name": "nozzle_temp_c",
      "levels": [
        "190",
        "220"
      ],
      "type": "continuous",
      "unit": "C"
    },
    {
      "name": "infill_pct",
      "levels": [
        "10",
        "50"
      ],
      "type": "continuous",
      "unit": "%"
    }
  ],
  "fixed_factors": {
    "material": "PLA",
    "bed_temp": "60C"
  },
  "responses": [
    {
      "name": "surface_quality",
      "optimize": "maximize",
      "unit": "pts"
    },
    {
      "name": "print_time_min",
      "optimize": "minimize",
      "unit": "min"
    }
  ],
  "settings": {
    "operation": "central_composite",
    "test_script": "use_cases/146_3d_print_quality/sim.sh"
  }
}

Experimental Matrix

The Central Composite Design produces 32 runs. Each row is one experiment with specific factor settings.

Run	`layer_height_mm`	`print_speed`	`nozzle_temp_c`	`infill_pct`
1	0.2	55	205	-13.8178
2	0.1	80	190	50
3	0.3	30	220	10
4	0.3	80	220	50
5	0.2	55	237.863	30
6	0.3	30	220	50
7	0.2	0.227744	205	30
8	0.1	80	220	10
9	0.2	55	205	30
10	0.3	80	190	10
11	0.2	55	205	30
12	0.3	30	190	50
13	0.2	55	205	30
14	0.3	80	220	10
15	0.2	55	172.137	30
16	-0.019089	55	205	30
17	0.2	55	205	30
18	0.1	30	190	50
19	0.3	80	190	50
20	0.2	55	205	30
21	0.1	30	220	10
22	0.2	55	205	30
23	0.419089	55	205	30
24	0.1	30	220	50
25	0.2	55	205	30
26	0.1	80	190	10
27	0.2	55	205	73.8178
28	0.2	55	205	30
29	0.3	30	190	10
30	0.2	109.772	205	30
31	0.1	30	190	10
32	0.1	80	220	50

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/146_3d_print_quality/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/146_3d_print_quality/config.json \
    --output use_cases/146_3d_print_quality/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/146_3d_print_quality/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/146_3d_print_quality/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/146_3d_print_quality/config.json

6

Multi-objective optimization

With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.

Terminal

$ doe optimize --config use_cases/146_3d_print_quality/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/146_3d_print_quality/config.json \
    --output use_cases/146_3d_print_quality/results/report.html

Features Exercised

Feature	Value
Design type	`central_composite`
Factor types	`continuous` (all 4)
Arg style	`double-dash`
Responses	2 (surface_quality ↑, print_time_min ↓)
Total runs	32

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: surface_quality

Top factors: nozzle_temp_c (39.4%), infill_pct (30.2%), layer_height_mm (15.4%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
layer_height_mm	4	3.8679	0.9670	0.255	0.9021
print_speed	4	8.7079	2.1770	0.574	0.6856
nozzle_temp_c	4	13.6650	3.4162	0.901	0.4878
infill_pct	4	11.5404	2.8851	0.761	0.5666
Lack	of	Fit	8	32.3352	4.0419
Pure	Error	7	26.5388
Error	15	58.8739	3.7913
Total	31	96.6550	3.1179

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for surface_quality

Half-Normal Plot of Effects

Model Diagnostics

Response: print_time_min

Top factors: nozzle_temp_c (47.0%), print_speed (25.2%), infill_pct (21.5%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
layer_height_mm	4	229.3929	57.3482	0.085	0.9859
print_speed	4	1942.8214	485.7054	0.716	0.5941
nozzle_temp_c	4	2353.0714	588.2679	0.867	0.5062
infill_pct	4	425.5000	106.3750	0.157	0.9569
Lack	of	Fit	8	2245.2143	280.6518
Pure	Error	7	4750.0000
Error	15	6995.2143	678.5714
Total	31	11946.0000	385.3548

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for print_time_min

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

3D surfaces fitted with quadratic RSM. Red dots are observed data points.

print time min layer height mm vs infill pct

print time min layer height mm vs nozzle temp c

print time min layer height mm vs print speed

print time min nozzle temp c vs infill pct

print time min print speed vs infill pct

print time min print speed vs nozzle temp c

surface quality layer height mm vs infill pct

surface quality layer height mm vs nozzle temp c

surface quality layer height mm vs print speed

surface quality nozzle temp c vs infill pct

surface quality print speed vs infill pct

surface quality print speed vs nozzle temp c

Multi-Objective Optimization

When responses compete, Derringer–Suich desirability finds the best compromise. Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.

Overall Desirability

D = 0.7093

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`surface_quality`	1.5	0.6712	7.70 0.6712 7.70 pts	↑
`print_time_min`	1.0	0.7704	43.00 0.7704 43.00 min	↓

Recommended Settings

Factor	Value
`layer_height_mm`	0.2 mm
`print_speed`	55 mm/s
`nozzle_temp_c`	205 C
`infill_pct`	30 %

Source: from observed run #1

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`print_time_min`	43.00	27.00	+16.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#11	0.6134	layer_height_mm=0.3, print_speed=80, nozzle_temp_c=190, infill_pct=50
#8	0.6089	layer_height_mm=0.1, print_speed=80, nozzle_temp_c=190, infill_pct=10

Model Quality

Response	R²	Type
`print_time_min`	0.0767	linear

Full Multi-Objective Output

doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================

Overall desirability: D = 0.7093

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
surface_quality              1.5       0.6712        7.70 pts   ↑
print_time_min               1.0       0.7704       43.00 min   ↓

Recommended settings:
  layer_height_mm = 0.2 mm
  print_speed = 55 mm/s
  nozzle_temp_c = 205 C
  infill_pct = 30 %
  (from observed run #1)

Trade-off summary:
  surface_quality: 7.70 (best observed: 10.10, sacrifice: +2.40)
  print_time_min: 43.00 (best observed: 27.00, sacrifice: +16.00)

Model quality:
  surface_quality: R² = 0.1341 (linear)
  print_time_min: R² = 0.0767 (linear)

Top 3 observed runs by overall desirability:
  1. Run #1 (D=0.7093): layer_height_mm=0.2, print_speed=55, nozzle_temp_c=205, infill_pct=30
  2. Run #11 (D=0.6134): layer_height_mm=0.3, print_speed=80, nozzle_temp_c=190, infill_pct=50
  3. Run #8 (D=0.6089): layer_height_mm=0.1, print_speed=80, nozzle_temp_c=190, infill_pct=10

Full Analysis Output

doe analyze
=== Main Effects: surface_quality ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
nozzle_temp_c            4.7000       0.3121            39.4%
infill_pct               3.6000       0.3121            30.2%
layer_height_mm          1.8357       0.3121            15.4%
print_speed              1.8000       0.3121            15.1%

=== ANOVA Table: surface_quality ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
layer_height_mm              4       3.8679       0.9670      0.255     0.9021
print_speed                  4       8.7079       2.1770      0.574     0.6856
nozzle_temp_c                4      13.6650       3.4162      0.901     0.4878
infill_pct                   4      11.5404       2.8851      0.761     0.5666
Lack of Fit                  8      32.3352       4.0419      1.066     0.4729
Pure Error                   7      26.5388       3.7913
Error                       15      58.8739       3.7913
Total                       31      96.6550       3.1179

=== Summary Statistics: surface_quality ===

layer_height_mm:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -0.019089           1     5.1000     0.0000     5.1000     5.1000
  0.1                 8     6.4750     1.0990     4.0000     7.3000
  0.2                14     6.9357     1.9832     3.6000    10.1000
  0.3                 8     6.6000     2.1778     2.4000     9.5000
  0.419089            1     6.4000     0.0000     6.4000     6.4000

print_speed:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0.227744            1     7.6000     0.0000     7.6000     7.6000
  109.772             1     7.7000     0.0000     7.7000     7.7000
  30                  8     7.1750     1.2453     6.0000     9.5000
  55                 14     6.6643     2.0140     3.6000    10.1000
  80                  8     5.9000     1.8655     2.4000     7.3000

nozzle_temp_c:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  172.137             1     5.4000     0.0000     5.4000     5.4000
  190                 8     6.5250     2.3206     2.4000     9.5000
  205                14     6.6500     1.7819     3.6000     9.8000
  220                 8     6.5500     0.7578     5.1000     7.3000
  237.863             1    10.1000     0.0000    10.1000    10.1000

infill_pct:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -13.8178            1     3.6000     0.0000     3.6000     3.6000
  10                  8     6.4375     1.6151     4.0000     9.5000
  30                 14     6.9857     1.8305     4.5000    10.1000
  50                  8     6.6375     1.8244     2.4000     8.6000
  73.8178             1     7.2000     0.0000     7.2000     7.2000

=== Main Effects: print_time_min ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
nozzle_temp_c           59.0000       3.4702            47.0%
print_speed             31.6250       3.4702            25.2%
infill_pct              27.0000       3.4702            21.5%
layer_height_mm          8.0000       3.4702             6.4%

=== ANOVA Table: print_time_min ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
layer_height_mm              4     229.3929      57.3482      0.085     0.9859
print_speed                  4    1942.8214     485.7054      0.716     0.5941
nozzle_temp_c                4    2353.0714     588.2679      0.867     0.5062
infill_pct                   4     425.5000     106.3750      0.157     0.9569
Lack of Fit                  8    2245.2143     280.6518      0.414     0.8803
Pure Error                   7    4750.0000     678.5714
Error                       15    6995.2143     678.5714
Total                       31   11946.0000     385.3548

=== Summary Statistics: print_time_min ===

layer_height_mm:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -0.019089           1    69.0000     0.0000    69.0000    69.0000
  0.1                 8    61.8750     6.7281    58.0000    78.0000
  0.2                14    62.7143    24.0590    27.0000   100.0000
  0.3                 8    68.1250    23.5277    39.0000   106.0000
  0.419089            1    61.0000     0.0000    61.0000    61.0000

print_speed:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0.227744            1    63.0000     0.0000    63.0000    63.0000
  109.772             1    43.0000     0.0000    43.0000    43.0000
  30                  8    74.6250    18.5391    58.0000   106.0000
  55                 14    64.4286    23.4315    27.0000   100.0000
  80                  8    55.3750     8.1053    39.0000    63.0000

nozzle_temp_c:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  172.137             1    27.0000     0.0000    27.0000    27.0000
  190                 8    70.5000    22.2068    39.0000   106.0000
  205                14    63.9286    20.9925    29.0000   100.0000
  220                 8    59.5000     7.6718    47.0000    75.0000
  237.863             1    86.0000     0.0000    86.0000    86.0000

infill_pct:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -13.8178            1    46.0000     0.0000    46.0000    46.0000
  10                  8    64.7500    15.4064    47.0000    98.0000
  30                 14    63.5000    23.4906    27.0000   100.0000
  50                  8    65.2500    19.5868    39.0000   106.0000
  73.8178             1    73.0000     0.0000    73.0000    73.0000

Optimization Recommendations

doe optimize
=== Optimization: surface_quality ===
Direction: maximize

Best observed run: #21
  layer_height_mm = 0.2
  print_speed = 55
  nozzle_temp_c = 172.137
  infill_pct = 30
  Value: 10.1

RSM Model (linear, R² = 0.0173, Adj R² = -0.1283):
  Coefficients:
    intercept                      +6.6625
    layer_height_mm                -0.0450
    print_speed                    +0.2136
    nozzle_temp_c                  +0.0989
    infill_pct                     -0.0878

RSM Model (quadratic, R² = 0.3625, Adj R² = -0.1626):
  Coefficients:
    intercept                      +5.9080
    layer_height_mm                -0.0450
    print_speed                    +0.2136
    nozzle_temp_c                  +0.0989
    infill_pct                     -0.0878
    layer_height_mm*print_speed    -0.1000
    layer_height_mm*nozzle_temp_c  -0.0375
    layer_height_mm*infill_pct     -0.2000
    print_speed*nozzle_temp_c      -0.0375
    print_speed*infill_pct         -0.7250
    nozzle_temp_c*infill_pct       +0.5125
    layer_height_mm^2              +0.1993
    print_speed^2                  +0.1889
    nozzle_temp_c^2                +0.6577
    infill_pct^2                   -0.1027

  Curvature analysis:
    nozzle_temp_c                  coef=+0.6577  convex (has a minimum)
    layer_height_mm                coef=+0.1993  convex (has a minimum)
    print_speed                    coef=+0.1889  convex (has a minimum)
    infill_pct                     coef=-0.1027  concave (has a maximum)

  Notable interactions:
    print_speed*infill_pct         coef=-0.7250  (antagonistic)
    nozzle_temp_c*infill_pct       coef=+0.5125  (synergistic)

  Predicted optimum (from linear model, at observed points):
    layer_height_mm = 0.2
    print_speed = 109.772
    nozzle_temp_c = 205
    infill_pct = 30
    Predicted value: 7.1305

  Surface optimum (via L-BFGS-B, linear model):
    layer_height_mm = 0.1
    print_speed = 80
    nozzle_temp_c = 220
    infill_pct = 10
    Predicted value: 7.1079

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. nozzle_temp_c  (effect: 3.8, contribution: 38.1%)
  2. print_speed  (effect: 3.5, contribution: 34.9%)
  3. infill_pct  (effect: 1.7, contribution: 17.0%)
  4. layer_height_mm  (effect: 1.0, contribution: 10.0%)

=== Optimization: print_time_min ===
Direction: minimize

Best observed run: #14
  layer_height_mm = 0.2
  print_speed = 0.227744
  nozzle_temp_c = 205
  infill_pct = 30
  Value: 27.0

RSM Model (linear, R² = 0.0866, Adj R² = -0.0488):
  Coefficients:
    intercept                      +64.0000
    layer_height_mm                -0.2717
    print_speed                    +6.1356
    nozzle_temp_c                  -0.2081
    infill_pct                     +1.6222

RSM Model (quadratic, R² = 0.3891, Adj R² = -0.1141):
  Coefficients:
    intercept                      +60.7728
    layer_height_mm                -0.2717
    print_speed                    +6.1356
    nozzle_temp_c                  -0.2081
    infill_pct                     +1.6222
    layer_height_mm*print_speed    -2.6250
    layer_height_mm*nozzle_temp_c  +2.7500
    layer_height_mm*infill_pct     -1.2500
    print_speed*nozzle_temp_c      -6.3750
    print_speed*infill_pct         -6.6250
    nozzle_temp_c*infill_pct       +3.7500
    layer_height_mm^2              -0.6842
    print_speed^2                  -1.6217
    nozzle_temp_c^2                +6.0867
    infill_pct^2                   +0.2533

  Curvature analysis:
    nozzle_temp_c                  coef=+6.0867  convex (has a minimum)
    print_speed                    coef=-1.6217  concave (has a maximum)
    layer_height_mm                coef=-0.6842  concave (has a maximum)
    infill_pct                     coef=+0.2533  convex (has a minimum)

  Notable interactions:
    print_speed*infill_pct         coef=-6.6250  (antagonistic)
    print_speed*nozzle_temp_c      coef=-6.3750  (antagonistic)
    nozzle_temp_c*infill_pct       coef=+3.7500  (synergistic)
    layer_height_mm*nozzle_temp_c  coef=+2.7500  (synergistic)
    layer_height_mm*print_speed    coef=-2.6250  (antagonistic)
    layer_height_mm*infill_pct     coef=-1.2500  (antagonistic)

  Predicted optimum (from linear model, at observed points):
    layer_height_mm = 0.2
    print_speed = 109.772
    nozzle_temp_c = 205
    infill_pct = 30
    Predicted value: 77.4424

  Surface optimum (via L-BFGS-B, linear model):
    layer_height_mm = 0.3
    print_speed = 30
    nozzle_temp_c = 220
    infill_pct = 10
    Predicted value: 55.7625

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. print_speed  (effect: 58.0, contribution: 51.4%)
  2. nozzle_temp_c  (effect: 39.2, contribution: 34.8%)
  3. infill_pct  (effect: 8.0, contribution: 7.1%)
  4. layer_height_mm  (effect: 7.6, contribution: 6.8%)