1. P10505 – Cold Pressure Fusing II Performance Review Team Fusion 14 May 2010 1

2. 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

3. 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

4. Electronic Control System LabView Interface Transducer Box Motor Controller 4

5. System Architecture 5

6. Design Schematics of Fuser High Low High Parallel Splayed 6

7. Project Development Process Planning Defined Goals Defined Customer Needs Defined Engineering Metrics Concept Selection 5 Individual PUGH Concept Selections Product Design Feasibility Analysis and Calculations Final Design Detailed CAD Drawings Finalized BOM Manufacture Purchased Materials Machined Parts Assembly Debugging Testing Full Factorial DOE Test with replicates Tested Parallel and Splayed Rollers MSD IMSD II 7

8. 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

9. Comparison of Average Pressure and Standard Deviation across Skew Angles – Parallel Configuration 9

10. Optimizing Skew Angle 10

11. Expected variation @1.9 angle, loads between 130-270, 50/50 landscape/portrait, compliance set to 270 Running 10,000 pages at the above conditions yields pressure uniformity at the histogram on the right with a mean pressure above. Uniformity goal was 390 psi at mean of 3900 psi. Current actual is ~2000 psi 11

12. 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)

13. Comparison of Average Pressure and Standard Deviation across Skew Angles – Splayed Configuration 13

14. U2 1.4° skew angle, 270 lb/in compliance, 130 lb load, portrait orientation, Parallel 14 Ground Standard Deviation: 1722 lbs Average Pressure: 3287 lbs Pressure Uniformity: 0.52 Un-ground Standard Deviation: 1638 lbs Average Pressure: 3979 lbs Pressure Uniformity: 0.41

15. U14 1.9° skew angle, 270 lb/in compliance, 130 lb load, portrait orientation, Parallel 15 Ground Standard Deviation: 839 lbs Average Pressure: 3463 lbs Pressure Uniformity: 0.24 Un-ground Standard Deviation: 1124 lbs Average Pressure: 3733 lbs Pressure Uniformity: 0.30

16. U17 2.4° skew angle, 270 lb/in compliance, 130 lb load, portrait orientation, Parallel 16 Ground Standard Deviation: 717 lbs Average Pressure: 3554 lbs Pressure Uniformity: 0.20 Un-ground Standard Deviation: 1662 lbs Average Pressure: 4056 lbs Pressure Uniformity: 0.41

17. Usp 2 1.9° skew angle, 270 lb/in compliance, 130 lb load, portrait orientation, Splayed 17

18. Project Metrics Customer NeedsSpecificationsAchievementsSuccess Customer wants to determine the capabilities of the P09505 prototype. N/A Focus moved from testing of P09505 prototype to remanufacturing No Customer wants a user friendly data capture system that can be re-used to determine the capabilities of future prototypes N/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 CMM Yes 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 configuration Yes 18

19. 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

20. Questions? 20

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23. Comparison of Average Pressure and Standard Deviation across Skew Angles – Parallel Configuration 23

24. Signal to Noise Ratios S/N = µ/σ = Std Dev/Mean 1.41.92.4 Standard Deviation 1926.5 1634.1 9 1900.8 1 Average Pressure 4161.6 3 5011.9 44631.5 S/N 2.163.072.44 N/S 0.460.330.41 24

25. 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

26. Standard Deviation vs. Skew Angle 26

27. Main Effects Plot for Standard Deviation 27

28. Skew Angle Curve Fit 28

29. ANOVA Assumptions These assumptions must be justified to perform an Analysis of Variance. – Normal distribution – Constant variance – Constant mean – Independent data 29

30. Justification of ANOVA Assumptions 30

31. Justification of ANOVA Assumptions 31

32. ANOVA Table for Standard Deviation Analysis of Variance for Average Pressure, using Adjusted SS for Tests SourceDFSeq SSAdj SSAdj MSFP Skew Angle25805582.000 2902791.00018.1800.000 Load19135948.000 57.2100.000 Orientation13083067.000 19.3100.000 Compliance11827931.000 11.4500.002 Skew Angle*Load21170453.000 585226.0003.6600.041 Skew Angle*Orientation21709290.000 854645.0005.3500.012 Skew Angle*Compliance2772812.000 386406.0002.4200.110 Load*Orientation1444098.000 2.7800.108 Load*Compliance1276185.000 1.7300.201 Orientation*Compliance1439110.000 2.7500.110 Skew Angle*Load*Orientation142443.000 21222.0000.1300.876 Skew Angle*Load*Compliance21153858.000 576929.0003.6100.042 Skew Angle*Orientation*Compliance2573191.000 286596.0001.7900.188 Load*Orientation*Compliance155013.000 0.3400.563 Skew Angle*Load*Orientation*Compliance2479479.000 239740.0001.5000.243 Error243832342.000 159681.000 Total4730800800.000 Legend Green: P-value < 0.005 Orange: P-value < 0.015 White: P-value > 0.010 32

33. Main Effects Plot for Standard Deviation 33

34. Interaction Plot for Standard Deviation 34

35. Interaction Plot for Standard Deviation 35

36. Interaction Plot for Standard Deviation 36

37. Interaction Plot for Standard Deviation 37

38. ANOVA Table for Average Pressure Analysis of Variance for Standard Deviation, using Adjusted SS for Tests SourceDFSeq SSAdj SSAdj MSFP Skew Angle2838375.000 419188.0004.3800.024 Load1944724.000 9.8700.004 Orientation1271502.000 2.8400.105 Compliance11387.000 0.0100.905 Skew Angle*Load22274411.000 1137205.00011.8800.000 Skew Angle*Orientation2573000.000 286500.0002.9900.069 Skew Angle*Compliance258055.000 29028.0000.3000.741 Load*Orientation1184016.000 1.9200.178 Load*Compliance1182533.000 1.9100.180 Orientation*Compliance160492.000 0.6300.434 Skew Angle*Load*Orientation2222213.000 111106.0001.1600.330 Skew Angle*Load*Compliance238580.000 19290.0000.2000.819 Skew Angle*Orientation*Compliance212875.000 6437.0000.0700.935 Load*Orientation*Compliance165860.000 0.6900.415 Skew Angle*Load*Orientation*Compliance2109942.000 54971.0000.5700.571 Error242297803.000 95742.000 Total478135768.000 Legend Green: P-value < 0.005 Yellow: P-value < 0.010 Orange: P-value < 0.015 White: P-value > 0.010 38

39. Main Effects for Average Pressure 39

40. Interaction Plot of Average Pressures 40

41. 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

42. Optimal Design Standard Deviation – Main Effects: 1.9 deg, portrait, 130 lbs, k=270 – 2 nd Order Effects: 1.9 deg, portrait, 170 lbs, k = 270 42

43. 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

44. Representative 1.4° skew angle pressure pattern (U4) 1.4 ° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape 44

45. Representative 1.9° skew angle pressure pattern (U16) 1.9 ° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape 45

46. Representative 2.4° skew angle pressure pattern (U24) 1.9 ° skew angle, k = 270 lb/in (gray), 170 lbs load, landscape 46

47. Average Pressure vs. Test Configuration 47

48. Standard Deviation vs. Test Configuration 48

49. Probability Plot of Average Pressure 49

50. Probability Plot of Standard Deviation 50

51. Standard Deviation vs. Test Configuration 51

52. Residuals vs. Test Configuration 52

53. Standard Deviation vs. Test Configuration 53

54. Splayed DOE 54

55. 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 Deviation1151 Average of the Average Pressures4052.125 S/N2.61 N/S0.38 55

56. Comparison to Signal to Noise Ratio for Parallel Configuration Parallel 1.4 Parallel 1.9 Parallel 2.4 Parallel Mean of Standard Deviation1926.51634.191900.81 Mean of Average Pressure4161.635011.944631.5 S/N2.163.072.44 N/S0.460.330.41 Splayed 1.9 Splayed Mean of Standard Deviation1151 Mean of Average Pressures4052.125 S/N2.61 N/S0.38 56

57. Average Pressure ANOVA Table Analysis of Variance for Average Pressure, using Adjusted SS for Tests SourceDFSeq SSAdj SSAdj MSFP Compliance1228826 5.540.1 Load11937496 46.910.006 Paper Orientation1943251 22.840.017 Compliance*Load152326 1.270.342 Error3123917 41306 Total73285817 S = 203.238R-Sq = 96.23%R-Sq(adj) = 91.2% TermCoefSE CoefTP Constant4052.1371.8656.390 Compliance 270-169.1271.86-2.350.1 Load 130-492.1271.86-6.850.006 Paper Orient Landscape-343.3771.86-4.780.017 Compliance*Load 270130-80.8771.86-1.130.342 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

58. Standard Deviation ANOVA Table Analysis of Variance for Standard Deviation, using Adjusted SS for Tests SourceDFSeq SSAdj SSAdj MSFP Compliance13458434585 1.40.322 Load1276024 11.150.044 Paper Orientation1142044 5.740.096 Compliance*Load13698 0.150.725 Error374242 24747 Total7530594 S =157.313R-Sq = 86.01%R-Sq(adj) = 67.35% TermCoefSE CoefTP Constant155155.6227.890 Compliance 270-65.7555.62-1.180.322 Load 130-185.7555.62-3.340.044 Paper Orient Landscape133.2555.622.40.096 Compliance*Load 270 130-21.555.62-0.390.725 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. Main Effects Plot for Standard Deviation 59

60. Interaction Plot for Standard Deviation 60

61. Main Effects Plot for Average Pressure 61

62. Interaction Plot for Average Pressure 62

63. ANOVA Assumptions These assumptions must be justified to perform an Analysis of Variance. – Normal distribution – Constant variance – Constant mean – Independent data 63

64. Justifying ANOVA Assumptions, Standard Deviation 64

65. Central Limit Theorem If y 1, y 2,…y n is a sequence of n independent and identically distributed random variables with E(y i )=μ and V(y i ) = σ 2 (both finite) and x = y 1 + y 2 + … +y n, then the limiting form of the distribution…as n → ∞, is the standard normal distribution. – Design and Analysis of Experiments. Dr. Douglas Montgomery 2 65

66. 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 website 1 66

67. Test Matrix Compliance (lb/in) Load (lb)Paper Orientation Usp1270 (gray)130Landscape Usp2271 (gray)130Portrait Usp3272 (gray)170Landscape Usp4273 (gray)170Portrait Usp5560 (purple)130Landscape Usp6561 (purple)130Portrait Usp7562 (purple)170Landscape Usp8563 (purple)170Portrait 67

68. Scatter Plot of Average Pressures 68

69. Justifying ANOVA Assumptions, Average Pressure 69

70. Scatter Plot of Standard Deviation 70

71. Usp 2 k=270 lb/in, Load = 130 lbs, Portrait Average Pressure: 3640 lbs Standard Deviation: 1222 71

72. Usp 7 k=560 lb/in, Load = 170 lbs, Landscape Average Pressure: 4437 lbs Standard Deviation: 2060 72

73. Probability Plot of Standard Deviation 73

74. Probability Plot of Average Pressure 74

75. Bibliography 1 Awasthi, Sanjay. University of Texas Arlington.. 5 May 2010. Montgomery, Douglas. Design and Analysis of Experiments. 7 th Ed. John Wiley and Sons Inc. 2009. 75

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