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
GroundStandard Deviation: 839 lbsAverage Pressure: 3463 lbsPressure Uniformity: 0.24
Un-groundStandard Deviation: 1124 lbsAverage Pressure: 3733 lbsPressure Uniformity: 0.30
U172.4° skew angle, 270 lb/in compliance, 130
lb load, portrait orientation, Parallel
16
GroundStandard Deviation: 717 lbsAverage Pressure: 3554 lbsPressure Uniformity: 0.20
Un-groundStandard Deviation: 1662 lbsAverage Pressure: 4056 lbsPressure Uniformity: 0.41
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
22
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
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
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
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
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
35
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
36
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
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
Orientation Compliance
Main Effects Plot for Average PressureData Means
39
Interaction Plot of Average Pressures
170130 LandscapePortrait 5602705600
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
44
Representative 1.9° skew angle pressure pattern (U16)
1.9° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape
45
Representative 2.4° skew angle pressure pattern (U24)
1.9° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape
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
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
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)
52
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
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
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 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
Main Effects Plot for Standard Deviation
59
Interaction Plot for Standard Deviation
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.
75
76