Non Skid Coating Formulation Utilizing a Design of Experiments (DOE) Approach
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Non Skid Coating Formulation Utilizing a Design of Experiments (DOE)
Approach
TRFA Annual Meeting, Fort Lauderdale FL14 November 2005Charles S. Tricou
Applied Research LaboratoryThe Pennsylvania State University
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Repair and Replacement
• Repair is time-, material-, and labor-intensive.
• Repair costs Range from $13- $25 /ft2
– CV 63 (November 2000)» 116,000 ft2
» Labor: $22.50 / ft2
» Material: $ 2.80 / ft2
– CVN 72 (April 2004)» 70,000 ft2
» Cost: $1.4 Million ($20 / ft2 )
Durability• Approximately 80% of CVN flight deck nonskid coatings
are replaced following each deployment. Extending the durability and functionality of nonskid coatings to last through 2 full deployments will save the Navy ~ $5M per year.
• Nonskid coatings in arrested landing areas are removed and replaced 2 or 3 times per deployment cycle.
• Flight deck coatings have degraded during deployment to an extent necessitating repair. Repairs at foreign ports are very expensive and result in temporary loss of platform availability.
Overview
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Approach
Develop a High-Performance Epoxy / Urethane Polymer
• A design of experiments (DOE) approach was used to optimize coating performance in corrosion resistance, chemical resistance, impact resistance, and long-term coefficient of friction (COF) retention.
• This approach offers the potential of achieving maximum performance from an organic-based nonskid coating. After qualification, such a system may be used as a drop-in replacement for current epoxy-based systems.
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Performance Measurements (Outputs)
Coating performance measurements Adhesion
Corrosion (QUV, Salt Fog, Immersion, etc.)
Service-specific durability tests• Erosion / Wear
• Impact Resistance
• Chemical Resistance
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Performance Measurements (Outputs)
Coating performance measurements Adhesion
Corrosion (QUV, Salt Fog, Immersion, etc.)
Service-specific durability tests• Erosion / Wear
• Impact Resistance
• Chemical Resistance
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DOE Approach – What is it?
Design of Experiments (DOE) is a scientific approach to experimentation. A good DOE will yield the following benefits:
Aid in the selection and isolation of the important variables to be studied
Minimize the number of experiments that must be carried out to yield meaningful results
Maximize the amount of information that can be extracted from the experiments
Minimize the cost of product development and process control
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DOE – How it Works2-Factor (full factorial) Linear
Linear Design 2 levels for each factor 2n trials For 2 factors n = 2
→ 4 trials required
Factor 1
Fac
tor
2
Provides information aboutinteractions between factors (variables)
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2-Factor (full factorial) Quadratic
Factor 1
Fac
tor
2
Non-Linear Design 3 levels for each factor 3n trials For 2 factors (n = 2)
→ 9 trials required
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3-Factor (full factorial) Linear
Factor 1
Factor 2Linear Design 2 levels for each factor 2n trials For 3 factors n = 3
→ 23 trials required
Factor 3
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Mixture Designs
Constraints C1 + C2 + C3 = Fixed % Component 1
Component 3Component 2
Binary Blend
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Non Skid Polymer FormulationComponents & Levels
Components (Levels)A. Polyamine Curing Agent #1 (Stoich)B. Polyamine Curing Agent #2 (Stoich)C. Modifier #1 (0% – 30% by weight of base resin)D. Modifier #2 (0% – 30% by weight of base resin)E. Modifier #3 (0% – 30% by weight of base resin)F. Adhesion Promoter #1 (0% – 0.5% by weight of Resin)G. Adhesion Promoter #2 (0% – 0.5% by weight of Resin)H. Base Resin (100 grams)
Constraints: Total Modifier cannot exceed 30%0 ≤ C + D + E ≤ 30 grams
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Design Strategy
In total, there are 8 potential components that may be used in the coating formulation. However, the amount of base resin used in each trial is held constant at 100 grams. Since the amount of resin does not vary, the base resin may be eliminated as a variable, reducing the number of variables to 7.
To maintain stoichiometry, the amount of one curing agent used will depend upon the amount of the other curing agent used. By expressing the amount of one of the curing agents as a fraction of the total curing agent used, the other curing agent is eliminated as a variable, reducing the total number of variables from 7 to 6.
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Design Strategy
A quadratic D-Optimal design was chosen for this experiment. The D-Optimal design provides substantial information with a a minimum number of trials.
Components (Levels)A. Polyamine Curing Agent #1 (Fraction of total curing agent used: 0 - 1)B. Polyamine Curing Agent #2 (Stoich, based on amount of PCA1)C. Modifier #1 (0% – 30% by weigh of Resin)D. Modifier #2 (0% – 30% by weight of Resin)E. Modifier #3 (0% – 30% by weight of Resin)F. Adhesion Promoter #1 (0% – 0.5% by weight of Resin)G. Adhesion Promoter #2 (0% – 0.5% by weight of Resin)H. Base Resin (100 grams)
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D-Optimal Design: 38 Total Trials Run
Curing Agent 1
MOD 1 MOD 2 MOD 3 AP 1 AP 2
1 0.00 0.0 15 0 0.5 02 1.00 0.0 30 0 0 0.53 1.00 0.0 0 0 0.5 04 1.00 0.0 30 0 0.25 05 0.00 0.0 0 30 0 0.56 0.50 0.0 0 0 0 0.57 0.00 0.0 30 0 0.5 0.58 1.00 30.0 0 0 0 09 0.00 30.0 0 0 0.5 0.2510 0.00 0.0 0 0 0 011 1.00 0.0 0 30 0 0.2512 0.00 0.0 15 15 0 013 0.25 3.8 3.75 18.75 0.25 0.12514 0.00 0.0 0 30 0.5 015 0.00 0.0 0 0 0 016 1.00 0.0 15 0 0 017 1.00 15.0 0 15 0.5 018 0.00 15.0 15 0 0.5 019 1.00 15.0 0 0 0.5 020 0.00 0.0 15 15 0 021 0.00 30.0 0 0 0 022 0.00 0.0 30 0 0 0.523 1.00 30.0 0 0 0.5 0.524 0.00 0.0 0 30 0.5 0.525 1.00 0.0 0 15 0 0.526 0.50 10.0 10 0 0.25 0.2527 1.00 0.0 0 0 0.5 028 1.00 0.0 0 0 0.25 0.529 0.00 0.0 0 0 0.5 0.530 1.00 0.0 30 0 0.5 0.2531 1.00 15.0 0 15 0 0.532 0.00 0.0 0 0 0.5 0.533 0.50 0.0 0 30 0 034 1.00 0.0 0 15 0 0.535 0.00 30.0 0 0 0 0.536 1.00 0.0 0 30 0.5 037 0.00 0.0 30 0 0 038 1.00 0.0 0 30 0.5 0.5
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Component Polyamine Curing Agent
1
Polyamine Curing Agent
2
MODIFIER 1
MODIFIER 2
MODIFIER 3
ADHESION PROMOTER
1
ADHESION PROMOTER
2
Resin (grams)
Total Mixture (grams)
Fraction of Available Epoxide Equivalents
0.00 1.00 0.00 15.00 0.00 0.50 0.00 100 200.00
Equivalents 0.00 0.44 0.00 0.06 0.00 0.0021 0.50 200.00grams 0.00 52.83 0.00 15.00 0.00 0.50 0.00 100 168.33
% Total 0.00 0.31 0.00 0.09 0.00 0.00 0.00 0.59 1.00
Conversions
Trial #1
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Experimental Design Run
Curing Agent 1 (grams)
Curing Agent 2
(grams)
MOD 1 (grams)
MOD 2 (grams)
MOD 3 (grams)
AP 1 (grams)
AP 2 (grams)
Resin (grams)
Total Mixture (grams)
1 0.00 52.83 0.00 15.00 0.00 0.50 0.00 100.00 168.332 66.19 0.00 0.00 30.00 0.00 0.00 0.50 100.00 196.693 86.62 0.00 0.00 0.00 0.00 0.50 0.00 100.00 187.124 66.37 0.00 0.00 30.00 0.00 0.25 0.00 100.00 196.625 0.00 67.43 0.00 0.00 30.00 0.00 0.50 100.00 197.936 43.13 29.75 0.00 0.00 0.00 0.00 0.50 100.00 173.387 0.00 45.91 0.00 30.00 0.00 0.50 0.50 100.00 176.918 65.63 0.00 30.00 0.00 0.00 0.00 0.00 100.00 195.639 0.00 45.53 30.00 0.00 0.00 0.50 0.25 100.00 176.2810 0.00 59.50 0.00 0.00 0.00 0.00 0.00 100.00 159.5011 97.75 0.00 0.00 0.00 30.00 0.00 0.25 100.00 228.0012 0.00 56.55 0.00 15.00 15.00 0.00 0.00 100.00 186.5513 22.13 45.81 3.75 3.75 18.75 0.25 0.13 100.00 194.5714 0.00 67.69 0.00 0.00 30.00 0.50 0.00 100.00 198.1915 0.00 59.50 0.00 0.00 0.00 0.00 0.00 100.00 159.5016 76.22 0.00 0.00 15.00 0.00 0.00 0.00 100.00 191.2217 82.06 0.00 15.00 0.00 15.00 0.50 0.00 100.00 212.5618 0.00 45.72 15.00 15.00 0.00 0.50 0.00 100.00 176.2219 76.31 0.00 15.00 0.00 0.00 0.50 0.00 100.00 191.8120 0.00 56.55 0.00 15.00 15.00 0.00 0.00 100.00 186.5521 0.00 45.28 30.00 0.00 0.00 0.00 0.00 100.00 175.2822 0.00 45.66 0.00 30.00 0.00 0.00 0.50 100.00 176.1623 66.00 0.00 30.00 0.00 0.00 0.50 0.50 100.00 197.0024 0.00 67.69 0.00 0.00 30.00 0.50 0.50 100.00 198.6925 92.00 0.00 0.00 0.00 15.00 0.00 0.50 100.00 207.5026 36.44 25.14 10.00 10.00 0.00 0.25 0.25 100.00 182.0727 86.62 0.00 0.00 0.00 0.00 0.50 0.00 100.00 187.1228 86.43 0.00 0.00 0.00 0.00 0.25 0.50 100.00 187.1829 0.00 59.75 0.00 0.00 0.00 0.50 0.50 100.00 160.7530 66.56 0.00 0.00 30.00 0.00 0.50 0.25 100.00 197.3131 81.69 0.00 15.00 0.00 15.00 0.00 0.50 100.00 212.1932 0.00 59.75 0.00 0.00 0.00 0.50 0.50 100.00 160.7533 48.88 33.72 0.00 0.00 30.00 0.00 0.00 100.00 212.5934 92.00 0.00 0.00 0.00 15.00 0.00 0.50 100.00 207.5035 0.00 45.28 30.00 0.00 0.00 0.00 0.50 100.00 175.7836 98.12 0.00 0.00 0.00 30.00 0.50 0.00 100.00 228.6237 0.00 45.66 0.00 30.00 0.00 0.00 0.00 100.00 175.6638 98.12 0.00 0.00 0.00 30.00 0.50 0.50 100.00 229.12
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ANOVA TableLow-Energy Blunt Impact
Response: LE Blunt Transform: Natural log Constant: 1.99
Sum of Mean FSource Squares DF Square Value Prob > FModel 90.25 4 22.56 13.24 < 0.0001 significantA 25.75 1 25.75 15.11 0.0004B 5.05 1 5.05 2.96 0.0943D 1.25 1 1.25 0.74 0.3972BD 10.13 1 10.13 5.94 0.0201
Residual 57.93 34 1.70Lack of Fit 44.96 28 1.61 0.74 0.7297 not
significantPure Error 12.97 6 2.16Cor Total 148.18 38
The Model F-value of 13.24 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise.
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Low-Energy Blunt Impact
DESIGN-EXPERT Plot
Ln(LE Blunt + 1.99)X = B: ATUY = D: GTS
Actual FactorsA: A2 = 0.38C: OP = 7.50E: GTMS = 0.25F: OS = 0.28
0.54
8.03
15.52
23.01
30.50
LE
Blun
t
0.0
7.5
15.0
22.5
30.0
0.0
7.5
15.0
22.5
30.0
B: ATU D: GTS
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ANOVA TableHigh-Energy Blunt Impact
Response: HE Blunt Transform: Inverse sqrt Constant: 2.24
Sum of Mean FSource Squares DF Square Value Prob > FModel 1.56 8 0.19 4.52 0.0011 significantA 0.28 1 0.28 6.52 0.0160B 0.12 1 0.12 2.87 0.1007C 0.090 1 0.090 2.09 0.1588D 0.19 1 0.19 4.39 0.0448E 0.17 1 0.17 3.92 0.0570F 0.037 1 0.037 0.86 0.3606BD 0.30 1 0.30 6.87 0.0136CF 0.43 1 0.43 10.09 0.0034
Residual 1.29 30 0.043Lack of Fit 0.91 24 0.038 0.59 0.8333 not
significantPure Error 0.38 6 0.064Cor Total 2.85 38
The Model F-value of 4.52 implies the model is significant. There is only a 0.11% chance that a "Model F-Value" this large could occur due to noise.
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DESIGN-EXPERT Plot
1.0/Sqrt(HE Blunt + 2.24)X = B: ATUY = D: GTS
Actual FactorsA: A2 = 0.38C: OP = 7.50E: GTMS = 0.25F: OS = 0.28
0
3
6
8
11
HE
Blun
t
0.00
7.50
15.00
22.50
30.00
0.00
7.50
15.00
22.50
30.00
B: ATU D: GTS
High-Energy Blunt Impact
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Response: HE Sharp Transform: Square rootConstant: 7.84
Sum of Mean FSource Squares DF Square Value Prob > FModel 1342.46 8 167.81 24.41 < 0.0001
significantA 1004.82 1 1004.82 146.19 < 0.0001B 71.07 1 71.07 10.34 0.0031D 19.44 1 19.44 2.83 0.1030E 15.29 1 15.29 2.23 0.1462F 0.22 1 0.22 0.032 0.8590E2 50.30 1 50.30 7.32 0.0111AD 85.92 1 85.92 12.50 0.0013EF 174.46 1 174.46 25.38 < 0.0001
Residual 206.20 30 6.87Lack of Fit 171.12 24 7.13 1.22 0.4346 not
significantPure Error 35.08 6 5.85Cor Total 1548.66 38
The Model F-value of 24.41 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise.
ANOVA TableHigh-Energy Sharp Impact
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Tail-Hook Impact ResistanceHigh-Energy Sharp
DESIGN-EXPERT Plot
X = Polyamine Curing Agent 2Y = Modifier 3
Actual FactorsB: Modifier 1 = 0.00C: Modifier 2 = 0.00E: A.P. 1 = 0.50F: A.P. 2 = 0.00
6
112
217
323
429
H
E S
har
p
0.00
0.25
0.50
0.75
1.00
0.00
7.50
15.00
22.50
30.00
Polyamine Curing Agent 2 Mod 3
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DESIGN-EXPERT Plot
X = AP 1Y = AP 2
Actual FactorsCuring Agent 2 = 0.00Modifier 1 = 23.11Modifier 2 = 0.00Modifier 3 = 0.00
0
26
52
78
103
HE
Sha
rp
0.00
0.13
0.25
0.38
0.50
0.00
0.13
0.25
0.38
0.50
AP 1 AP 2
Tail-Hook Impact ResistanceHigh-Energy Sharp
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ConstraintsLower Upper Lower Upper
Name Goal Limit Limit Weight Weight ImportanceA2 is in range 0 1 1 1 3ATU is in range 0 30 1 1 3OP is in range 0 30 1 1 3GTS is in range 0 30 1 1 3GTMS is in range 0 0.5 1 1 3OS is in range 0 0.5 1 1 3HE Sharp minimize 0 784 1 1 5
Solutions
ID A2 ATU OP* GTS GTMS OS HE SharpDesirability1 0.00 20.25 0.00 0.86 0.50 0.00 3 0.983
2 0.00 11.65 9.18 9.17 0.50 0.00 6 0.9633 0.00 23.17 3.98 2.65 0.00 0.50 9 0.9464 0.00 17.54 2.80 3.37 0.00 0.50 16 0.9185 0.00 17.26 2.74 0.00 0.00 0.50 20 0.9036 0.00 20.96 0.00 0.12 0.50 0.22 22 0.8967 0.02 13.35 0.00 16.65 0.00 0.36 29 0.8728 0.00 0.88 9.67 19.03 0.00 0.50 30 0.8699 0.00 2.65 0.00 7.15 0.50 0.15 36 0.84810 0.00 10.02 0.00 0.00 0.49 0.30 56 0.794
OptimizationHigh-Energy Sharp
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Results
Based on the results of this study, two candidate formulations have been identified which provide improved performance in blunt and sharp impact resistance. These formulations are unique blends which did not appear in the original DOE.
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Team Participants
Applied Research LaboratoryEpoxy Chemicals, Inc.Pratt & Whitney AutomationSt. Gobain Mineral Abrasives