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DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
DOE- Injection Molding
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DOE- Injection Molding

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  • 1. DOE - Injection Molding ExperimentCreated by Stergios Taris
  • 2. Contents• Executive Summary…………………………………………………………………………………………..... 3• Introduction………………………………………………………………………………………………………. 4• Injection Molding Experiment…………………………………………………………………………….. 6• Practical Analysis……………………………………………………………………………………………….. 9• Graphical Analysis……………………………………………………………………………………………… 10• Response Optimization………………………………………………………………………………………. 17• Multiple Regression…………………………………………………………………………………………… 18• Resolving the Ambiguity AE+BF+CH+DG ………………………………………………………….… 19• Results of Replicated Factorial………………………………………………………………………….… 21• Conclusions……………………………………………………………………………………………………..… 22• References…………………………………………………………………………………………………............ 232DOE – Injection Molding
  • 3. Executive SummaryDesign of Experiments (DOE) techniques enables designers to determinesimultaneously the individual and interactive effects of many factors thatcould affect the output results in any design. DOE also provides a fullinsight of interaction between design elements. Therefore, it helps turnany standard design into a robust one.In this project is examined how the outcome y “shrinkage” is affected by 8factors. It is used 2IV8-4 Fractional Factorial. So 16runs are used instead of28 =256 runs that would be used with a Full Factorial and would be veryexpensive to implement.3DOE – Injection Molding
  • 4. Introduction• Objective▫ Identify important factors effecting part shrinkage.▫ Less shrinkage is better.• Design to be used▫ 2IV8-4 Fractional Factorial▫ Design of resolution IV No main effects I confounded with any 2-factor interaction. 2- factor interactions are confounded with each other• Factors and levels4Factor Low (-1) High (+1)A. Mold Temperature Low HighB. Moisture Content Low HighC. Holding Pressure Low HighD. Cavity Thickness Low HighE. Booster Pressure Low HighF. Cycle time Low HighG. Gate Time Low HighH. Screw Speed Low HighDOE – Injection Molding
  • 5. Introduction - Why Fractional Factorial?• Large number of factors▫ large number of experiments▫ full factorial design too expensive▫ Use a fractional factorial design• 2k-p design allows analyzing k factors with only 2k-p experiments.▫ 2k-1 design requires only half as many experiments▫ 2k-2 design requires only one quarter of the experimentsKey Points about Fractional Factorial :• Many effects and interactions are confounded• The resolution of a design is the sum of the order of confounded effects• A design with higher resolution is considered better5DOE – Injection Molding
  • 6. Injection Molding ExperimentFactors: 8 Base Design: 8, 16 Resolution: IVRuns: 16 Replicates: 1 Fraction: 1/16Blocks: 1 Center pts (total): 0Design Generators: E = BCD, F = ACD, G = ABC, H = ABDDefining Relation: I = BCDE = ACDF = ABCG = ABDH = ABEF = ADEG = ACEH = BDFG = BCFH = CDGH = CEFG = DEFH = BEGH = AFGH =ABCDEFGHAlias Structure (up to order 4)I + ABCG + ABDH + ABEF + ACDF + ACEH + ADEG + AFGH + BCDE + BCFH + BDFG + BEGH + CDGH + CEFG + DEFHA + BCG + BDH + BEF + CDF + CEH + DEG + FGHB + ACG + ADH + AEF + CDE + CFH + DFG + EGHC + ABG + ADF + AEH + BDE + BFH + DGH + EFGD + ABH + ACF + AEG + BCE + BFG + CGH + EFHE + ABF + ACH + ADG + BCD + BGH + CFG + DFHF + ABE + ACD + AGH + BCH + BDG + CEG + DEHG + ABC + ADE + AFH + BDF + BEH + CDH + CEFH + ABD + ACE + AFG + BCF + BEG + CDG + DEFAB + CG + DH + EF + ACDE + ACFH + ADFG + AEGH + BCDF + BCEH + BDEG + BFGHAC + BG + DF + EH + ABDE + ABFH + ADGH + AEFG + BCDH + BCEF + CDEG + CFGHAD + BH + CF + EG + ABCE + ABFG + ACGH + AEFH + BCDG + BDEF + CDEH + DFGHAE + BF + CH + DG + ABCD + ABGH + ACFG + ADFH + BCEG + BDEH + CDEF + EFGHAF + BE + CD + GH + ABCH + ABDG + ACEG + ADEH + BCFG + BDFH + CEFH + DEFGAG + BC + DE + FH + ABDF + ABEH + ACDH + ACEF + BDGH + BEFG + CDFG + CEGHAH + BD + CE + FG + ABCF + ABEG + ACDG + ADEF + BCGH + BEFH + CDFH + DEGH6DOE – Injection Molding
  • 7. Injection Molding Experiment - Design MatrixStdOrder RunOrder CenterPt Blocks A B C D E F G H y1 1 1 1 - - - - - - - - 20.32 2 1 1 + - - - - + + + 16.83 3 1 1 - + - - + - + + 154 4 1 1 + + - - + + - - 15.95 5 1 1 - - + - + + + - 17.56 6 1 1 + - + - + - - + 247 7 1 1 - + + - - + - + 27.48 8 1 1 + + + - - - + - 22.39 9 1 1 - - - + + + - + 1410 10 1 1 + - - + + - + - 16.711 11 1 1 - + - + - + + - 21.912 12 1 1 + + - + - - - + 15.413 13 1 1 - - + + - - + + 27.614 14 1 1 + - + + - + - - 21.515 15 1 1 - + + + + - - - 17.116 16 1 1 + + + + + + + + 22.57DOE – Injection Molding
  • 8. • Factors C, E and interaction AE have significant effects.• The confounding pattern assumes negligible interaction between 3 or moreeffects.• The AE=4.6 in not easily explained. But it estimates the sum of effectsAE+BF+CH+DG .▫ So we need 4 additional runs to resolve the ambiguity.Injection Molding Experiment-Terms-Effects-Coef.Term Effect CoefConstant - 19.744A -0.7125 -1.90625B -0.1125 -0.05625C 5.4875 0.29375D -0.3125 0.59375E -3.8125 -0.30625F -0.1125 0.44375G 0.5875 -0.20625Term Effect CoefH 1.1875 2.29375AB -0.6125 -0.15625AC 0.8875 -0.10625AD -0.4125 -0.30625AE 4.5875 -1.90625AF -0.3125 -0.05625AG -0.2125 0.29375AH -0.6125 0.593758DOE – Injection Molding
  • 9. Practical Analysis of runsRun A B C D E F G H y1 - - - + + + - +142 - + - - + - + +153 + + - + - - - +15.44 + + - - + + - -15.95 + - - + + - + -16.76 + - - - - + + +16.87 - + + + + - - -17.18 - - + - + + + -17.59 - - - - - - - -20.310 + - + + - + - -21.511 - + - + - + + -21.912 + + + - - - + -22.313 + + + + + + + +22.514 + - + - + - - +2415 - + + - - + - +27.416 - - + + - - + +27.6# of -1 = #of+1 / whenA<medianthen +1# of -1 =#of+1C<medianthen -1, else+1# of -1 =#of+1E<medianthen 1, else -1# of -1 =#of+1# of -1 =#of+1H close tomedian then-1, else +19DOE – Injection Molding
  • 10. Graphical Analysis - y10DOE – Injection Molding
  • 11. Graphical Analysis - Residual Plots for y• Here is the residual Plots for y▫ P>0.05, all point within control limits11DOE – Injection Molding
  • 12. Graphical Analysis - Effects• It can be seen that factors A, E and interaction AE have significanteffects to y.12DOE – Injection Molding
  • 13. Graphical Analysis - Effects• The factors C and E have steeper slopes▫ So bigger impacts on the outcome13DOE – Injection Molding
  • 14. Graphical Analysis - Effects• Non parallelism indicates an interaction▫ AE-BF-DG-CH14DOE – Injection Molding
  • 15. Graphical Analysis - Effects• Contour Plots for y versus▫ AE-BF-DG-CH15DOE – Injection Molding
  • 16. Graphical Analysis - Effects• Contour Plots for y versus▫ AE-BF-DG-CH16DOE – Injection Molding
  • 17. Response Optimization17ParametersGoal Lower TargetY 15 16Upper Weight Import18 1 1Global SolutionA = -0.0805435B = 0.926920C = -0.344855D = -0.968586E = 0.946994F = 1G = -1H = -1DOE – Injection Molding
  • 18. Multiple Regression to the OutcomeRegression Analysis: y versus C, E, AEThe regression equation is y = 19.7 + 2.74 C - 1.91 E + 2.29 AEPredictor Coef SE Coef T PConstant 19.7438 0.2971 66.45 0.000C 2.7438 0.2971 9.24 0.000E -1.9062 0.2971 -6.42 0.000AE 2.2938 0.2971 7.72 0.000S = 1.18840 R-Sq = 93.9% R-Sq(adj) = 92.4%Analysis of VarianceSource DF SS MS F PRegression 3 262.772 87.591 62.02 0.000Residual Error 12 16.948 1.412Total 15 279.719Source DF Seq SSC 1 120.451E 1 58.141AE 1 84.18118We can see that p=0 sothey are significantcorrelated. R=92.4%, sothe results are explainedvery well with that modelDOE – Injection Molding
  • 19. Resolving the Ambiguity AE+BF+CH+DGRun A B C D E F G H Y17 - + + + - - - + 29.418 - + - - - + + + 19.719 + + - - + - - + 13.620 + + + + + + + + 24.7AE BF DG CH+ - - ++ + - -+ - + -+ + + +19Here is a combinations of +1 and -1 that canallow separate estimation of their true values.These 4 runs can create the above combinations.• Now we should incorporate the above 4 runs to the 16 runs.• The original data can explained by▫ a mean level▫ main effects of C,E ,H▫ effects of AE, BF, CH, DGDOE – Injection Molding
  • 20. Resolving the Ambiguity AE+BF+CH+DGRun M 0.5C 0.5E 0.5H 0.5AE 0.5BF 0.5DG 0.5CH Y17 + + - + + - - + 29.418 + - - + + + - - 19.719 + - + + + - + - 13.620 + + + + + + + + 24.7(this row comes from the first16 interactions)+ + + + 0.5(AE+BF+CH+DG)=2.30.5AE 0.5BF 0.5DG 0.5CH Y+ - - + 3.2+ + - - -1.0+ - + - -3.3+ + + + 2.320• By solving the above equations we get M and the new reduced table ofinteractions is:• By solving the above equations we get:0.6->AE 0.7->BF -1.6->DG 4.9->CHDOE – Injection Molding
  • 21. The Replicated Factorial21Whereas at low holding pressure (C) increasing screw speed (H) reducesshrinkage(y) from 19 to 15 units, at high holding pressure (C) increasingscrew speed (H) increases shrinkage (y) from 20 to 25 units.DOE – Injection Molding
  • 22. Conclusions22• We used a 2IV8-4 Fractional Factorial for the first 16 Runs and we madesome of the conclusions in a 23 replicated factorial.• In general, Factors C, E and interaction AE have significant effects.• AE estimates the sums of AE+BF+CH+DG, so additional 4 more runsused to identify the relationship of these interactions and y and see ifanother factor except from C and E are important.• From the latter 2 points seems that C E and H are the importantfactors.• Regression Analysis made to verify that C ,E and AE are important to y.DOE – Injection Molding

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