P10505 – Cold Pressure Fusing II Performance Review Team Fusion 14 May 2010

P10505 – Cold Pressure Fusing IIPerformance Review

Team Fusion14 May 2010

1

Project Review Agenda• Presentation Outline

– Design Summary– Evaluation of Project Goals– System Architecture– Design Schematics of Fuser– Project Development Process– Budget– Summary of Results– Project Wrap Up– Recommendations

2

Design Summary

Motor

Skewed rollers

Springs for compliance

Fusing roller

End blocks

Load cells

Main roller

Motor Mounting Brackets

Gear Box (6:1)

Dowel pins

3

Electronic Control System

LabView Interface

Transducer Box

Motor Controller 4

System Architecture

5

Design Schematics of Fuser

High

High

Low

Low

LowLow

High High

Parallel Splayed

6

Project Development ProcessPlanning• Defin

ed Goals

• Defined Customer Needs

• Defined Engineering Metrics

Concept Selection• 5

Individual PUGH Concept Selections

Product Design• Feasi

bility Analysis and Calculations

Final Design• Detai

led CAD Drawings

• Finalized BOM

Manufacture• Purc

hased Materials

• Machined Parts

• Assembly

• Debugging

Testing• Full

Factorial DOE Test with replicates

• Tested Parallel and Splayed Rollers

MSD I MSD II

7

Budget

• $3000 initial budget– Mechanical Expenses: $933.87– Electrical Expenses: $750.00– Total Spent: $1683.87– Total Saved: $1316.13

• Gifted Items $ 3,487.00 • Total $5170.87

8

Skew AngleStandard DeviationAverage Pressure

2.41.91.42.41.91.4

7000

6000

5000

4000

3000

2000

1000

0

Data

Boxplot of Average Pressure, Standard Deviation

Comparison of Average Pressure and Standard Deviation across Skew Angles – Parallel Configuration

9

Optimizing Skew Angle

10

Expected variation @1.9 angle, loads between 130-270, 50/50 landscape/portrait, compliance set to 270

Pressure StDev Histogram

0

1000

2000

3000

4000

5000

0 500 1000 1500 2000

Running 10,000 pages at the above conditions yields pressure uniformity at the histogram on the right with a mean pressure above.

Average Pressur Histogram

0

50

100

150

200

250

300

2994 3194 3394 3594 3794 3994 4194 4394 4594 4794

Uniformity goal was 390 psi at mean of 3900 psi. Current actual is ~2000 psi

11

Best Configuration

12

• The DOE analysis points to a 1.9° skew angle, 130 lb per bolt load, 270 lb/in compliance, and portrait orientation as the best configuration for achieving pressure uniformity

• The parallel and splayed configurations produced almost identical pressure uniformity• Best case for the parallel agreed with the above configuration,

producing a standard deviation of 1125 lbs and an average pressure of 3733 lbs for a ratio of 0.30

• Best case for the splayed produced a standard deviation of 1502 lbs and an average pressure of 4828 lbs producing a ratio of 0.31

• This is the same as the above configuration, except with 560 lb/in compliance. The standard deviation to pressure ratio with the 270 lb/in compliance is 0.33 (StDev: 1655 lbs, Pressure: 4996 lbs)

Comparison of Average Pressure and Standard Deviation across Skew Angles – Splayed

Configuration

13

U21.4° skew angle, 270 lb/in compliance, 130 lb

load, portrait orientation, Parallel

14

GroundStandard Deviation: 1722 lbsAverage Pressure: 3287 lbsPressure Uniformity: 0.52

Un-groundStandard Deviation: 1638 lbsAverage Pressure: 3979 lbsPressure Uniformity: 0.41

U141.9° skew angle, 270 lb/in compliance, 130

lb load, portrait orientation, Parallel

15



U172.4° skew angle, 270 lb/in compliance, 130

lb load, portrait orientation, Parallel

16



Usp 21.9° skew angle, 270 lb/in compliance, 130

lb load, portrait orientation, Splayed

17

Project MetricsCustomer Needs Specifications Achievements Success

Customer wants to determine the capabilities of the P09505 prototype. N/A

Focus moved from testing of P09505 prototype to

remanufacturingNo

Customer wants a user friendly data capture system that can be re-used to determine the capabilities of future

prototypesN/A

LabView interface giving read out of load, torque, and motor

RPM was created.Yes

Customer wants to be able to fuse a print image within acceptable limits

Prototype will fuse print across 100% of the page

Customer specifed that testing fusing was not useful with the

known pressure non-uniformity

No

Customer wants a design for a fuser that is optimal for uniform fusing

Prototype will vary in nip pressure less than 10%

The standard deviation of the nip pressure at the best

configuration is 30% of the average pressure

No

Prototype will minimally calendar print No visible calendaring Yes

Customer wants the ability to vary parameters to determine effect on fusing.

Prototype must be capable of adjusting to three skew angles

All three skew angles have been manufactured and

verified by CMMYes

Prototype must be able to reach a 1.9° skew angle

1.9° skew angle end block has been manufactured Yes

Prototype must accommodate both 20 and 24 lb paper while meeting all other

specifications

Prototype is capable of adjusting to any paper weight

but was only tested using 20gsm (80# text) Digital Color

Elite Gloss Coated Media

Yes

Customer wants to spend the minimum required to achieve their goals Prototype must cost less than $3000 Actual cost: $1683.83 Yes

Customer wants a multi-level factorial experiment testing key parameters N/A

DOE testing has been completed with two replicates

for every configurationYes

18

Recommendations

• Mount the motor on a solid, machined, right-angle bracket

• Manufacture each skew angle as a complete unit to remove errors during assembly

• Tolerances on rollers to 0.0000x”, per consult with Rob Kraynik

• Thrust bearings to prevent rollers from traveling when rolling under load

19

Questions?

20

21

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2.41.91.42.41.91.4

7000

6000

5000

4000

3000

2000

1000

0

Data

Boxplot of Average Pressure, Standard Deviation

Comparison of Average Pressure and Standard Deviation across Skew Angles – Parallel Configuration

23

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 Pressure4161.6

35011.9

4 4631.5

S/N 2.16 3.07 2.44N/S 0.46 0.33 0.41

24

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. 25

Standard Deviation vs. Skew Angle

2.502.252.001.751.50

2500

2000

1500

1000

500

Skew Angle

Stan

dard

Dev

iatio

n

Scatterplot of Standard Deviation vs Skew Angle

26

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

27

Skew Angle Curve Fit

28

ANOVA Assumptions

• These assumptions must be justified to perform an Analysis of Variance.– Normal distribution– Constant variance– Constant mean– Independent data

29

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

30

10005000-500-1000

99

90

50

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

31

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 32


2.41.91.4

2000

1900

1800

1700

1600170130

LandscapePortrait

2000

1900

1800

1700

1600560270

Skew Angle

Mea

n

Load


Main Effects Plot for Standard DeviationData Means

33

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

34



2000

15002500

2000

15002500

2000

1500

Skew Angle

Load

Orientation

Compliance

1.41.92.4

AngleSkew

130170

Load

PortraitLandscape

Orientation


35



2000

15002500

2000

15002500

2000

1500

Skew Angle

Load

Orientation

Compliance

1.41.92.4

AngleSkew

130170

Load

PortraitLandscape

Orientation


36



2000

15002500

2000

15002500

2000

1500

Skew Angle

Load

Orientation

Compliance

1.41.92.4

AngleSkew

130170

Load

PortraitLandscape

Orientation


37

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 38

Main Effects for Average Pressure

2.41.91.4

50004800460044004200

170130

LandscapePortrait

50004800460044004200

560270

Skew Angle

Mea

n

Load


Main Effects Plot for Average PressureData Means

39

Interaction Plot of Average Pressures


4800

40005600

4800

40005600

4800

4000

Skew Angle

Load

Orientation

Compliance

1.41.92.4

AngleSkew

130170

Load

PortraitLandscape

Orientation

Interaction Plot for Average PressureData Means

40

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

41

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

42

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

43

Representative 1.4° skew angle pressure pattern (U4)

1.4° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape

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45



46

Average Pressure vs. Test Configuration

2520151050

6500

6000

5500

5000

4500

4000

3500

3000

U Number

Aver

age

Pres

sure

Scatterplot of Average Pressure vs U Number

47

Standard Deviation vs. Test Configuration

2520151050

2500

2000

1500

1000

500

U Number

Stan

dard

Dev

iatio

n

Scatterplot of Standard Deviation vs U Number

48

700060005000400030002000

99

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

49

30002500200015001000500

99

9590

80706050403020

105

1

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

50


2520151050

2500

2000

1500

1000

500

U Number

Stan

dard

Dev

iatio

n


51

Residuals vs. Test Configuration

2520151050

800

600

400

200

0

-200

-400

-600

-800

U Number

Resid

ual

Residuals Versus U Number(response is Standard Deviation)

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2520151050

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2000

1500

1000

500

U Number

Stan

dard

Dev

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53

Splayed DOE

54

Signal To Noise Ratio for 1.9 Splayed

• Standard deviation is used as a metric of pressure uniformity. The ratio of standard deviation to average pressure is the percent change in pressure.

1.9 Splayed

Average Standard Deviation 1151

Average of the Average Pressures 4052.125

S/N 2.61

N/S 0.38

55

Comparison to Signal to Noise Ratio for Parallel Configuration


2.41.91.42.41.91.4

7000

6000

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2000

1000

0

Data

Boxplot of Average Pressure, Standard Deviation Parallel 1.4 Parallel

1.9 Parallel

2.4 Parallel

Mean of Standard Deviation 1926.5 1634.19 1900.81

Mean of Average Pressure 4161.63 5011.94 4631.5

S/N 2.16 3.07 2.44N/S 0.46 0.33 0.41

Splayed 1.9 Splayed

Mean of Standard Deviation 1151

Mean of Average Pressures 4052.125

S/N 2.61

N/S 0.38

56

Average Pressure ANOVA TableAnalysis of Variance for Average Pressure, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PCompliance 1 228826 228826 228826 5.54 0.1Load 1 1937496 1937496 1937496 46.91 0.006Paper Orientation 1 943251 943251 943251 22.84 0.017Compliance*Load 1 52326 52326 52326 1.27 0.342Error 3 123917 123917 41306Total 7 3285817

S = 203.238 R-Sq = 96.23% R-Sq(adj) = 91.2%

Term Coef SE Coef T PConstant 4052.13 71.86 56.39 0Compliance270 -169.12 71.86 -2.35 0.1Load130 -492.12 71.86 -6.85 0.006Paper OrientLandscape -343.37 71.86 -4.78 0.017Compliance*Load270 130 -80.87 71.86 -1.13 0.342

Only one replicate has been tested so far, so all the interaction effects except Compliance*Load were used as estimators of MSE. All interactions except this one were assumed to be statistically insignificant based off the analysis of the 1.9 parallel configurations. 57

Standard Deviation ANOVA TableAnalysis of Variance for Standard Deviation, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PCompliance 1 34584 34585 34585 1.4 0.322Load 1 276024 276024 276024 11.15 0.044Paper Orientation 1 142044 142044 142044 5.74 0.096Compliance*Load 1 3698 3698 3698 0.15 0.725Error 3 74242 74242 24747Total 7 530594

S =157.313 R-Sq = 86.01% R-Sq(adj) = 67.35%

Term Coef SE Coef T PConstant 1551 55.62 27.89 0Compliance270 -65.75 55.62 -1.18 0.322Load130 -185.75 55.62 -3.34 0.044Paper OrientLandscape 133.25 55.62 2.4 0.096Compliance*Load270 130 -21.5 55.62 -0.39 0.725

Only one replicate has been tested so far, so all the interaction effects except Compliance*Load were used as estimators of MSE. All interactions except this one were assumed to be statistically insignificant based off the analysis of the 1.9 parallel configurations. 58


59


60

Main Effects Plot for Average Pressure

61

Interaction Plot for Average Pressure

62

ANOVA Assumptions

• These assumptions must be justified to perform an Analysis of Variance.– Normal distribution– Constant variance– Constant mean– Independent data

63

Justifying ANOVA Assumptions, Standard Deviation

64

Central Limit Theorem

• If y1, y2,…yn is a sequence of n independent and identically distributed random variables with E(yi)=μ and V(yi) = σ2 (both finite) and x = y1 + y2 + … +yn, then the limiting form of the distribution…as n → ∞, is the standard normal distribution.

– Design and Analysis of Experiments. Dr. Douglas Montgomery2

65

Bimodal Distributions

• “Bimodality of the distribution in a sample is often a strong indication that the distribution of the variable in population is not normal…. the bimodality may indicate that the sample is not homogenous and the observations come in fact from two or more ‘overlapping’ distributions.”

– University of Texas website1

66

Test Matrix

Compliance (lb/in)

Load (lb) Paper Orientation

Usp1 270 (gray) 130Landscape

Usp2 271 (gray) 130Portrait

Usp3 272 (gray) 170Landscape

Usp4 273 (gray) 170Portrait

Usp5 560 (purple) 130Landscape

Usp6 561 (purple) 130Portrait

Usp7 562 (purple) 170Landscape

Usp8 563 (purple) 170Portrait

67

Scatter Plot of Average Pressures

68

Justifying ANOVA Assumptions,Average Pressure

69

Scatter Plot of Standard Deviation

70

Usp 2 k=270 lb/in, Load = 130 lbs, Portrait

Average Pressure: 3640 lbsStandard Deviation: 1222

71

Usp 7 k=560 lb/in, Load = 170 lbs, Landscape

Average Pressure: 4437 lbsStandard Deviation: 2060

72

Probability Plot of Standard Deviation

73

Probability Plot of Average Pressure

74

Bibliography• 1Awasthi, Sanjay. University of Texas Arlington. <http://www.uta.edu/faculty/sawasthi/Statistics/glosb.html>. 5 May 2010.• Montgomery, Douglas. Design and Analysis of Experiments. 7th Ed. John Wiley and Sons Inc. 2009.

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Documents

P10505 – Cold Pressure Fusing II Performance Review Team Fusion 14 May 2010