p10505 – cold pressure fusing ii performance review team fusion 5/7/2010

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

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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

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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

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Scatterplot of Standard Deviation vs Skew Angle

Main Effects Plot for Standard Deviation

2.41.91.4

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LandscapePortrait

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Skew Angle

Mean

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

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Observation Order

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Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Standard Deviation

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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

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LandscapePortrait

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Mean

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Main Effects Plot for Standard DeviationData Means

Interaction Plot for Standard Deviation

170130 LandscapePortrait 5602702500

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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

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Mean

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Main Effects Plot for Average PressureData Means

Interaction Plot of Average Pressures

170130 LandscapePortrait 560270

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Skew Angle

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Orientation

Compliance

1.41.92.4

AngleSkew

130170

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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

Average Pressure vs. Test Configuration

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U Number

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Scatterplot of Average Pressure vs U Number

Standard Deviation vs. Test Configuration

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Scatterplot of Standard Deviation vs U Number

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Average Pressure

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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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Standard Deviation

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Mean 1821StDev 416.1N 48AD 0.324P-Value 0.515

Probability Plot of Standard DeviationNormal - 95% CI

Probability Plot of Standard Deviation


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Residuals vs. Test Configuration

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Residuals Versus U Number(response is Standard Deviation)


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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

p10505 – cold pressure fusing ii performance review team fusion 5/7/2010

Documents

standard deviation anova

standard deviation1926

orien angle

skew angle main effects

pressure uniformity

skew anglessignal

skew anglenote

average pressure data