Wood Glue Joint Strength

Summary

This experiment investigates wood glue joint strength. Box-Behnken design to maximize joint strength and minimize cure time by tuning glue spread rate, clamping pressure, and open assembly time.

The design varies 3 factors: spread g m2 (g/m2), ranging from 100 to 250, clamp psi (psi), ranging from 50 to 250, and open time min (min), ranging from 1 to 10. The goal is to optimize 2 responses: shear strength mpa (MPa) (maximize) and cure hrs (hrs) (minimize). Fixed conditions held constant across all runs include glue type = PVA, wood = red_oak.

A Box-Behnken design was chosen because it efficiently fits quadratic models with 3 continuous factors while avoiding extreme corner combinations — requiring only 15 runs instead of the 8 needed for a full factorial at two levels.

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 shear strength mpa, the most influential factors were open time min (68.6%), spread g m2 (18.1%), clamp psi (13.3%). The best observed value was 9.7 (at spread g m2 = 250, clamp psi = 150, open time min = 10).

For cure hrs, the most influential factors were clamp psi (68.9%), spread g m2 (23.9%), open time min (7.2%). The best observed value was 3.4 (at spread g m2 = 250, clamp psi = 150, open time min = 1).

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
`spread_g_m2`	100	250	g/m2
`clamp_psi`	50	250	psi
`open_time_min`	1	10	min

Fixed: glue_type = PVA, wood = red_oak

Responses

Response	Direction	Unit
`shear_strength_mpa`	↑ maximize	MPa
`cure_hrs`	↓ minimize	hrs

Configuration

use_cases/199_wood_glue_joint/config.json

{
  "metadata": {
    "name": "Wood Glue Joint Strength",
    "description": "Box-Behnken design to maximize joint strength and minimize cure time by tuning glue spread rate, clamping pressure, and open assembly time"
  },
  "factors": [
    {
      "name": "spread_g_m2",
      "levels": [
        "100",
        "250"
      ],
      "type": "continuous",
      "unit": "g/m2"
    },
    {
      "name": "clamp_psi",
      "levels": [
        "50",
        "250"
      ],
      "type": "continuous",
      "unit": "psi"
    },
    {
      "name": "open_time_min",
      "levels": [
        "1",
        "10"
      ],
      "type": "continuous",
      "unit": "min"
    }
  ],
  "fixed_factors": {
    "glue_type": "PVA",
    "wood": "red_oak"
  },
  "responses": [
    {
      "name": "shear_strength_mpa",
      "optimize": "maximize",
      "unit": "MPa"
    },
    {
      "name": "cure_hrs",
      "optimize": "minimize",
      "unit": "hrs"
    }
  ],
  "settings": {
    "operation": "box_behnken",
    "test_script": "use_cases/199_wood_glue_joint/sim.sh"
  }
}

Experimental Matrix

The Box-Behnken Design produces 15 runs. Each row is one experiment with specific factor settings.

Run	`spread_g_m2`	`clamp_psi`	`open_time_min`
1	175	50	1
2	175	150	5.5
3	250	150	10
4	250	150	1
5	175	150	5.5
6	175	150	5.5
7	100	150	10
8	250	50	5.5
9	175	50	10
10	250	250	5.5
11	100	150	1
12	175	250	10
13	100	50	5.5
14	100	250	5.5
15	175	250	1

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/199_wood_glue_joint/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/199_wood_glue_joint/config.json \
    --output use_cases/199_wood_glue_joint/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/199_wood_glue_joint/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/199_wood_glue_joint/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/199_wood_glue_joint/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/199_wood_glue_joint/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/199_wood_glue_joint/config.json \
    --output use_cases/199_wood_glue_joint/results/report.html

Features Exercised

Feature	Value
Design type	`box_behnken`
Factor types	`continuous` (all 3)
Arg style	`double-dash`
Responses	2 (shear_strength_mpa ↑, cure_hrs ↓)
Total runs	15

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: shear_strength_mpa

Top factors: open_time_min (68.6%), spread_g_m2 (18.1%), clamp_psi (13.3%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
spread_g_m2	2	0.9413	0.4706	0.214	0.8121
clamp_psi	2	0.4827	0.2413	0.110	0.8976
open_time_min	2	14.1823	7.0912	3.218	0.0943
Lack	of	Fit	6	9.7044	1.6174
Pure	Error	2	4.4067
Error	8	14.1110	2.2033
Total	14	29.7173	2.1227

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for shear_strength_mpa

Half-Normal Plot of Effects

Model Diagnostics

Response: cure_hrs

Top factors: clamp_psi (68.9%), spread_g_m2 (23.9%), open_time_min (7.2%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
spread_g_m2	2	0.1698	0.0849	0.322	0.7334
clamp_psi	2	0.8702	0.4351	1.652	0.2508
open_time_min	2	0.0127	0.0063	0.024	0.9763
Lack	of	Fit	6	1.9780	0.3297
Pure	Error	2	0.5267
Error	8	2.5046	0.2633
Total	14	3.5573	0.2541

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

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

cure hrs clamp psi vs open time min

cure hrs spread g m2 vs clamp psi

cure hrs spread g m2 vs open time min

shear strength mpa clamp psi vs open time min

shear strength mpa spread g m2 vs clamp psi

shear strength mpa spread g m2 vs open time min

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 = 0.8527

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`shear_strength_mpa`	1.5	0.7909	8.80 0.7909 8.80 MPa	↑
`cure_hrs`	1.0	0.9545	3.40 0.9545 3.40 hrs	↓

Recommended Settings

Factor	Value
`spread_g_m2`	100 g/m2
`clamp_psi`	50 psi
`open_time_min`	5.5 min

Source: from observed run #4

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`cure_hrs`	3.40	3.40	+0.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#15	0.7783	spread_g_m2=250, clamp_psi=250, open_time_min=5.5
#10	0.7370	spread_g_m2=100, clamp_psi=150, open_time_min=10

Model Quality

Response	R²	Type
`cure_hrs`	0.1926	linear

Full Multi-Objective Output

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

Overall desirability: D = 0.8527

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
shear_strength_mpa           1.5       0.7909        8.80 MPa   ↑
cure_hrs                     1.0       0.9545        3.40 hrs   ↓

Recommended settings:
  spread_g_m2 = 100 g/m2
  clamp_psi = 50 psi
  open_time_min = 5.5 min
  (from observed run #4)

Trade-off summary:
  shear_strength_mpa: 8.80 (best observed: 9.70, sacrifice: +0.90)
  cure_hrs: 3.40 (best observed: 3.40, sacrifice: +0.00)

Model quality:
  shear_strength_mpa: R² = 0.8290 (quadratic)
  cure_hrs: R² = 0.1926 (linear)

Top 3 observed runs by overall desirability:
  1. Run #4 (D=0.8527): spread_g_m2=100, clamp_psi=50, open_time_min=5.5
  2. Run #15 (D=0.7783): spread_g_m2=250, clamp_psi=250, open_time_min=5.5
  3. Run #10 (D=0.7370): spread_g_m2=100, clamp_psi=150, open_time_min=10

Full Analysis Output

doe analyze
=== Main Effects: shear_strength_mpa ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
open_time_min            2.2250       0.3762            68.6%
spread_g_m2              0.5857       0.3762            18.1%
clamp_psi                0.4321       0.3762            13.3%

=== ANOVA Table: shear_strength_mpa ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
spread_g_m2                  2       0.9413       0.4706      0.214     0.8121
clamp_psi                    2       0.4827       0.2413      0.110     0.8976
open_time_min                2      14.1823       7.0912      3.218     0.0943
Lack of Fit                  6       9.7044       1.6174      0.734     0.6747
Pure Error                   2       4.4067       2.2033
Error                        8      14.1110       2.2033
Total                       14      29.7173       2.1227

=== Summary Statistics: shear_strength_mpa ===

spread_g_m2:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  100                 4     7.6000     1.5811     6.0000     9.7000
  175                 7     7.0143     1.7985     4.7000     8.8000
  250                 4     7.0750     0.7890     6.2000     8.0000

clamp_psi:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  150                 7     7.0429     1.1267     5.9000     8.8000
  250                 4     7.1500     1.6902     4.9000     8.8000
  50                  4     7.4750     2.0855     4.7000     9.7000

open_time_min:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  1                   4     5.5750     0.9430     4.7000     6.7000
  10                  4     7.7250     1.0996     6.2000     8.8000
  5.5                 7     7.8000     1.2410     5.9000     9.7000

=== Main Effects: cure_hrs ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
clamp_psi                0.6500       0.1302            68.9%
spread_g_m2              0.2250       0.1302            23.9%
open_time_min            0.0679       0.1302             7.2%

=== ANOVA Table: cure_hrs ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
spread_g_m2                  2       0.1698       0.0849      0.322     0.7334
clamp_psi                    2       0.8702       0.4351      1.652     0.2508
open_time_min                2       0.0127       0.0063      0.024     0.9763
Lack of Fit                  6       1.9780       0.3297      1.252     0.5075
Pure Error                   2       0.5267       0.2633
Error                        8       2.5046       0.2633
Total                       14       3.5573       0.2541

=== Summary Statistics: cure_hrs ===

spread_g_m2:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  100                 4     4.0000     0.4082     3.4000     4.3000
  175                 7     4.2000     0.5477     3.4000     4.8000
  250                 4     3.9750     0.6021     3.4000     4.8000

clamp_psi:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  150                 7     4.0429     0.4198     3.4000     4.7000
  250                 4     3.8000     0.6164     3.4000     4.7000
  50                  4     4.4500     0.4041     4.1000     4.8000

open_time_min:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  1                   4     4.1000     0.5354     3.4000     4.7000
  10                  4     4.1250     0.5852     3.4000     4.8000
  5.5                 7     4.0571     0.5255     3.4000     4.8000

Optimization Recommendations

doe optimize
=== Optimization: shear_strength_mpa ===
Direction: maximize

Best observed run: #10
  spread_g_m2 = 250
  clamp_psi = 150
  open_time_min = 10
  Value: 9.7

RSM Model (linear, R² = 0.2853, Adj R² = 0.0903):
  Coefficients:
    intercept                      +7.1867
    spread_g_m2                    -0.0250
    clamp_psi                      +0.7875
    open_time_min                  +0.6625

RSM Model (quadratic, R² = 0.6422, Adj R² = -0.0018):
  Coefficients:
    intercept                      +5.8000
    spread_g_m2                    -0.0250
    clamp_psi                      +0.7875
    open_time_min                  +0.6625
    spread_g_m2*clamp_psi          +0.6250
    spread_g_m2*open_time_min      +0.1750
    clamp_psi*open_time_min        +0.2500
    spread_g_m2^2                  +1.1500
    clamp_psi^2                    +0.3750
    open_time_min^2                +1.0750

  Curvature analysis:
    spread_g_m2                    coef=+1.1500  convex (has a minimum)
    open_time_min                  coef=+1.0750  convex (has a minimum)
    clamp_psi                      coef=+0.3750  convex (has a minimum)

  Notable interactions:
    spread_g_m2*clamp_psi          coef=+0.6250  (synergistic)

  Predicted optimum (from linear model, at observed points):
    spread_g_m2 = 175
    clamp_psi = 250
    open_time_min = 10
    Predicted value: 8.6367

  Surface optimum (via L-BFGS-B, linear model):
    spread_g_m2 = 100
    clamp_psi = 250
    open_time_min = 10
    Predicted value: 8.6617

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

Factor importance:
  1. open_time_min  (effect: 1.6, contribution: 38.1%)
  2. clamp_psi  (effect: 1.6, contribution: 36.8%)
  3. spread_g_m2  (effect: 1.1, contribution: 25.1%)

=== Optimization: cure_hrs ===
Direction: minimize

Best observed run: #1
  spread_g_m2 = 250
  clamp_psi = 150
  open_time_min = 1
  Value: 3.4

RSM Model (linear, R² = 0.0049, Adj R² = -0.2665):
  Coefficients:
    intercept                      +4.0867
    spread_g_m2                    -0.0250
    clamp_psi                      +0.0125
    open_time_min                  +0.0375

RSM Model (quadratic, R² = 0.8063, Adj R² = 0.4576):
  Coefficients:
    intercept                      +4.3667
    spread_g_m2                    -0.0250
    clamp_psi                      +0.0125
    open_time_min                  +0.0375
    spread_g_m2*clamp_psi          -0.3250
    spread_g_m2*open_time_min      +0.1750
    clamp_psi*open_time_min        -0.4500
    spread_g_m2^2                  -0.4583
    clamp_psi^2                    +0.2667
    open_time_min^2                -0.3333

  Curvature analysis:
    spread_g_m2                    coef=-0.4583  concave (has a maximum)
    open_time_min                  coef=-0.3333  concave (has a maximum)
    clamp_psi                      coef=+0.2667  convex (has a minimum)

  Notable interactions:
    clamp_psi*open_time_min        coef=-0.4500  (antagonistic)
    spread_g_m2*clamp_psi          coef=-0.3250  (antagonistic)

  Predicted optimum (from quadratic model, at observed points):
    spread_g_m2 = 175
    clamp_psi = 50
    open_time_min = 10
    Predicted value: 4.7750

  Surface optimum (via L-BFGS-B, quadratic model):
    spread_g_m2 = 100
    clamp_psi = 50
    open_time_min = 1
    Predicted value: 3.2167

  Model quality: Good fit — general trends are captured, some noise remains.

Factor importance:
  1. spread_g_m2  (effect: 0.5, contribution: 40.9%)
  2. open_time_min  (effect: 0.4, contribution: 30.5%)
  3. clamp_psi  (effect: 0.3, contribution: 28.7%)

Run	`spread_g_m2`	`clamp_psi`	`open_time_min`
1	175	50	1
2	175	150	5.5
3	250	150	10
4	250	150	1
5	175	150	5.5
6	175	150	5.5
7	100	150	10
8	250	50	5.5
9	175	50	10
10	250	250	5.5
11	100	150	1
12	175	250	10
13	100	50	5.5
14	100	250	5.5
15	175	250	1

Run	`spread_g_m2`	`clamp_psi`	`open_time_min`
1	175	50	1
2	175	150	5.5
3	250	150	10
4	250	150	1
5	175	150	5.5
6	175	150	5.5
7	100	150	10
8	250	50	5.5
9	175	50	10
10	250	250	5.5
11	100	150	1
12	175	250	10
13	100	50	5.5
14	100	250	5.5
15	175	250	1

Run	`spread_g_m2`	`clamp_psi`	`open_time_min`
1	175	50	1
2	175	150	5.5
3	250	150	10
4	250	150	1
5	175	150	5.5
6	175	150	5.5
7	100	150	10
8	250	50	5.5
9	175	50	10
10	250	250	5.5
11	100	150	1
12	175	250	10
13	100	50	5.5
14	100	250	5.5
15	175	250	1