p10505 – cold pressure fusing ii performance review team fusion 5/7/2010
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P10505 – Cold Pressure Fusing IIPerformance Review
Team Fusion5/7/2010
Introduction
• Two results are analyzed, standard deviation to indicate pressure uniformity and average pressure
• Presentation Outline– Present data– Justify ANOVA assumptions– Analyze significant factors– Analyze interactions– Conclusions
Skew AngleStandard DeviationAverage Pressure
2.41.91.42.41.91.4
7000
6000
5000
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1000
0
Data
Boxplot of Average Pressure, Standard Deviation
Comparison of Average Pressure and Standard Deviation across Skew Angles
Signal to Noise Ratios
• S/N = µ/σ = Std Dev/Mean
1.4 1.9 2.4Standard Deviation 1926.5 1634.19 1900.81
Average Pressure 4161.63 5011.94 4631.5
S/N 2.16 3.07 2.44
N/S 0.46 0.33 0.41
2.502.252.001.751.50
6500
6000
5500
5000
4500
4000
3500
3000
Skew Angle
Aver
age
Pres
sure
Scatterplot of Average Pressure vs Skew Angle
Average Pressure vs. Skew Angle
Note: Standard deviation is not the analysis of variance between these average pressure data points. It is the analysis of pressure
variations across the entire scan.
Standard Deviation vs. Skew Angle
2.502.252.001.751.50
2500
2000
1500
1000
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Skew Angle
Stan
dard
Dev
iatio
n
Scatterplot of Standard Deviation vs Skew Angle
Main Effects Plot for Standard Deviation
2.41.91.4
2000
1900
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1700
1600170130
LandscapePortrait
2000
1900
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1700
1600560270
Skew Angle
Mea
n
Load
Orientation Compliance
Main Effects Plot for Standard DeviationData Means
Skew Angle Curve Fit
ANOVA Assumptions
• These assumptions must be justified to perform an Analysis of Variance.– Normal distribution– Constant variance– Constant mean– Independent data
Justification of ANOVA Assumptions
8004000-400-800
99
90
50
10
1
Residual
Perc
ent
2500200015001000
800
400
0
-400
-800
Fitted Value
Resid
ual
6004002000-200-400-600
20
15
10
5
0
Residual
Freq
uenc
y
454035302520151051
800
400
0
-400
-800
Observation Order
Resi
dual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Standard Deviation
10005000-500-1000
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90
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10
1
Residual
Perc
ent
60005500500045004000
1000
500
0
-500
-1000
Fitted Value
Resi
dual
8004000-400-800
24
18
12
6
0
Residual
Freq
uenc
y
454035302520151051
1000
500
0
-500
-1000
Observation Order
Resi
dual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Average Pressure
Justification of ANOVA Assumptions
ANOVA Table for Standard DeviationAnalysis of Variance for Average Pressure, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F PSkew Angle 2 5805582.000 5805582.000 2902791.000 18.180 0.000Load 1 9135948.000 9135948.000 9135948.000 57.210 0.000Orientation 1 3083067.000 3083067.000 3083067.000 19.310 0.000Compliance 1 1827931.000 1827931.000 1827931.000 11.450 0.002Skew Angle*Load 2 1170453.000 1170453.000 585226.000 3.660 0.041Skew Angle*Orientation 2 1709290.000 1709290.000 854645.000 5.350 0.012Skew Angle*Compliance 2 772812.000 772812.000 386406.000 2.420 0.110Load*Orientation 1 444098.000 444098.000 444098.000 2.780 0.108Load*Compliance 1 276185.000 276185.000 276185.000 1.730 0.201Orientation*Compliance 1 439110.000 439110.000 439110.000 2.750 0.110Skew Angle*Load*Orientation 1 42443.000 42443.000 21222.000 0.130 0.876Skew Angle*Load*Compliance 2 1153858.000 1153858.000 576929.000 3.610 0.042Skew Angle*Orientation*Compliance 2 573191.000 573191.000 286596.000 1.790 0.188Load*Orientation*Compliance 1 55013.000 55013.000 55013.000 0.340 0.563Skew Angle*Load*Orientation*Compliance 2 479479.000 479479.000 239740.000 1.500 0.243Error 24 3832342.000 3832342.000 159681.000 Total 47 30800800.000
LegendGreen: P-value < 0.005Orange: P-value < 0.015White: P-value > 0.010
Main Effects Plot for Standard Deviation
2.41.91.4
2000
1900
1800
1700
1600170130
LandscapePortrait
2000
1900
1800
1700
1600560270
Skew Angle
Mea
n
Load
Orientation Compliance
Main Effects Plot for Standard DeviationData Means
Interaction Plot for Standard Deviation
170130 LandscapePortrait 5602702500
2000
15002500
2000
15002500
2000
1500
Skew Angle
Load
Orientation
Compliance
1.41.92.4
AngleSkew
130170
Load
PortraitLandscape
Orientation
Interaction Plot for Standard DeviationData Means
Interaction Plot for Standard Deviation
170130 LandscapePortrait 5602702500
2000
15002500
2000
15002500
2000
1500
Skew Angle
Load
Orientation
Compliance
1.41.92.4
AngleSkew
130170
Load
PortraitLandscape
Orientation
Interaction Plot for Standard DeviationData Means
Interaction Plot for Standard Deviation
170130 LandscapePortrait 5602702500
2000
15002500
2000
15002500
2000
1500
Skew Angle
Load
Orientation
Compliance
1.41.92.4
AngleSkew
130170
Load
PortraitLandscape
Orientation
Interaction Plot for Standard DeviationData Means
Interaction Plot for Standard Deviation
170130 LandscapePortrait 5602702500
2000
15002500
2000
15002500
2000
1500
Skew Angle
Load
Orientation
Compliance
1.41.92.4
AngleSkew
130170
Load
PortraitLandscape
Orientation
Interaction Plot for Standard DeviationData Means
ANOVA Table for Average Pressure
Analysis of Variance for Standard Deviation, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F P
Skew Angle 2 838375.000 838375.000 419188.000 4.380 0.024Load 1 944724.000 944724.000 944724.000 9.870 0.004Orientation 1 271502.000 271502.000 271502.000 2.840 0.105Compliance 1 1387.000 1387.000 1387.000 0.010 0.905Skew Angle*Load 2 2274411.000 2274411.000 1137205.000 11.880 0.000Skew Angle*Orientation 2 573000.000 573000.000 286500.000 2.990 0.069Skew Angle*Compliance 2 58055.000 58055.000 29028.000 0.300 0.741Load*Orientation 1 184016.000 184016.000 184016.000 1.920 0.178Load*Compliance 1 182533.000 182533.000 182533.000 1.910 0.180Orientation*Compliance 1 60492.000 60492.000 60492.000 0.630 0.434Skew Angle*Load*Orientation 2 222213.000 222213.000 111106.000 1.160 0.330Skew Angle*Load*Compliance 2 38580.000 38580.000 19290.000 0.200 0.819Skew Angle*Orientation*Compliance 2 12875.000 12875.000 6437.000 0.070 0.935Load*Orientation*Compliance 1 65860.000 65860.000 65860.000 0.690 0.415Skew Angle*Load*Orientation*Compliance 2 109942.000 109942.000 54971.000 0.570 0.571Error 24 2297803.000 2297803.000 95742.000 Total 47 8135768.000
LegendGreen: P-value < 0.005Yellow: P-value < 0.010Orange: P-value < 0.015White: P-value > 0.010
Main Effects for Average Pressure
2.41.91.4
50004800460044004200
170130
LandscapePortrait
50004800460044004200
560270
Skew Angle
Mea
n
Load
Orientation Compliance
Main Effects Plot for Average PressureData Means
Interaction Plot of Average Pressures
170130 LandscapePortrait 5602705600
4800
40005600
4800
40005600
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4000
Skew Angle
Load
Orientation
Compliance
1.41.92.4
AngleSkew
130170
Load
PortraitLandscape
Orientation
Interaction Plot for Average PressureData Means
Conclusions
• Abaqus model was on target– Experimental results point to 1.91° as the optimal
skew angle to maximize pressure uniformity• The average pressure value changes based on
the configuration, but several configurations fell in the acceptable pressure range
Optimal Design
• Standard Deviation– Main Effects: 1.9 deg, portrait, 130 lbs, k=270– 2nd Order Effects: 1.9 deg, portrait, 170 lbs, k =
270
Optimal Design
• Average Pressure– Main Effects:
• Load is variable but ~140 lbs,• Orientation is variable, no specified preference• Compliance is variable but ~415 lbs/in, by interpolation
– Interaction effects agree with main effects, except landscape orientation is preferred• P-value for the average pressure DOE is 0.105• P-value for the standard deviation DOE is 0.000
Representative 1.4° skew angle pressure pattern (U4)
1.4° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape
Representative 1.9° skew angle pressure pattern (U16)
1.9° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape
Representative 2.4° skew angle pressure pattern (U24)
1.9° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape
Average Pressure vs. Test Configuration
2520151050
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U Number
Aver
age
Pres
sure
Scatterplot of Average Pressure vs U Number
Standard Deviation vs. Test Configuration
2520151050
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U Number
Stan
dard
Dev
iatio
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Scatterplot of Standard Deviation vs U Number
700060005000400030002000
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9590
80706050403020
105
1
Average Pressure
Perc
ent
Mean 4602StDev 809.5N 48AD 0.990P-Value 0.012
Probability Plot of Average PressureNormal - 95% CI
Probability Plot of Average Pressure
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9590
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Standard Deviation
Perc
ent
Mean 1821StDev 416.1N 48AD 0.324P-Value 0.515
Probability Plot of Standard DeviationNormal - 95% CI
Probability Plot of Standard Deviation
Standard Deviation vs. Test Configuration
2520151050
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U Number
Stan
dard
Dev
iatio
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Scatterplot of Standard Deviation vs U Number
Residuals vs. Test Configuration
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U Number
Resid
ual
Residuals Versus U Number(response is Standard Deviation)
Standard Deviation vs. Test Configuration
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U Number
Stan
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Scatterplot of Standard Deviation vs U Number
Customer Needs
Customer Needs
Engineering SpecificationsEngr.
Spec. # Importance Source Specification (description) Unit of Measure Marginal Value Ideal Value
ES4 1 Customer Need Prototype will fuse print across 95% of the pagePercentage fused, Width of unfused, 90% fusing 95% fusing
ES6 1 Customer Need Prototype will vary in nip pressure less than 10%
Width of Pressure Indication, Xerox
Metric 10% variation 5% variation
ES8 1 Customer NeedPrototype must be capable of adjusting to three skew angles Number of Settings 2 angles Analog
ES10 1 Customer NeedPrototype must adhere to Abaqus model created by Xerox Yes/No N/A Yes
ES12 1 Customer Need Prototype must be able to reach a 1.9° skew angle Degrees 1.8°-2.0° 1.9°
ES14 1 Customer NeedPrototype must be adjustable to the same skew angle to a 1/10th degree for ~25 runs Standard Deviation
1/5th degree variation
1/10th degree variation
ES3 2 Customer Need Prototype will minimally calendar print Qualitative Moderate None
ES5 2 Customer NeedPrototype will produce trailing edge wrinkles less than once every twenty prints Number
1 wrinkle every 10 prints No wrinkles ever
ES11 3 Customer Need Feed rate must not decrease by more than 15% Torque15% reduction of
speed5% reduction of
speed
ES13 1 ImpliedPrototype must be dimensionally stable for a load of 4000 psi Force Vibration Stationary
1 Customer NeedPrototype vibration will be less than 3 lbs as measured by the load cells. Force 5 lbs 0 lbs
ES9 4 ImpliedPrototype will take less than 60 secs of user time to set up print Time Required 120 sec 0 secs
ES1 3 Implied Prototype must be manufacturable within ~2 week Time Required, Y/N 4 weeks 2 week
ES7 1 Customer NeedPrototype must accommodate both 20 and 24 lb paper while meeting all other specifications Yes/No
Accomodates 20 and 24 lb paper
Accomodates all paper weights
ES15 3 ImpliedPrototype must be able to print >1000 copies without failure
Life Cycle (Number of Prints) 500 copies 1000
ES2 4 Customer Need Prototype must cost less than $3000 Dollars $3,000 $1,500Importance Scale: 1-Highest, 4-Lowest
Final Design
Recommendations
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