Experimental Design For Injection Molding 1 Launsby Consulting Experimental Design For Injection...

Launsby Consulting14/2/2009

Experimental Design For Injection Molding

Experimental Design For Injection Molding

Launsby Consulting2009

Launsby Consulting2009

Launsby Consulting4/2/2009 2

Bob LaunsbyBob Launsby

• Taught experimental design to several thousand people

• Participated in numerous actual experiments

• Application is key• Co-developer of DOE Wisdom software• Co-Author of “DOE for Injection Molding”

• Taught experimental design to several thousand people

• Participated in numerous actual experiments

• Application is key• Co-developer of DOE Wisdom software• Co-Author of “DOE for Injection Molding”

[email protected]

www.launsby.com


IntroductionsIntroductions

• Name• Title• Background in Injection Molding

– Previous Courses– Cavity Pressure Control?

• Previous Experiences with Experimental Design and Statistics

• Name• Title• Background in Injection Molding

– Previous Courses– Cavity Pressure Control?

• Previous Experiences with Experimental Design and Statistics


Course GuidelinesCourse Guidelines

• Start and Stop Times• Breaks• Active Participation• You are Responsible for Learning• Importance of Applications

• Having Fun and Learning

• Start and Stop Times• Breaks• Active Participation• You are Responsible for Learning• Importance of Applications

• Having Fun and Learning


Module OneModule One

• Goals:– Understand the Building Blocks for a

Fundamentally Robust Molding Process– Understand the Need for Modern Design of

Experiments Techniques– Recognize the Power and Applicability of

These Approaches to Injection Molding– Understand the Basics

• Goals:– Understand the Building Blocks for a

Fundamentally Robust Molding Process– Understand the Need for Modern Design of

Experiments Techniques– Recognize the Power and Applicability of

These Approaches to Injection Molding– Understand the Basics


The Injection MoldingChallenge


The Challenge(Cont.)The Challenge(Cont.)• Complex Part Geometry,Many Finishes• Varying Wall Thickness• Snap Fits, Threads• No Secondary Operations• Consistency, High Prod. Rates• Regrind • Tight Tolerances, Cost Competition• QS 9000, Process Validation

• Complex Part Geometry,Many Finishes• Varying Wall Thickness• Snap Fits, Threads• No Secondary Operations• Consistency, High Prod. Rates• Regrind • Tight Tolerances, Cost Competition• QS 9000, Process Validation


The Process DiagramThe Process Diagram


PROCESS DIAGRAM FOR

INJECTION MOLDING

Some Potential FactorsMaterial Lot

Material Variation

% Regrind

Hold Pressure

Pellet Geometry

Plastic Temperature

Screw RPM

Injection Velocity

Potential ResponsesDimensions

Color

Black Specks

Warpage

Blisters

Blush

Knit Lines

Sinks

Process DiagramProcess Diagram


Basic Understandings Before DoeBasic Understandings Before Doe• Non-Newtonian Behavior of Plastic

– Static Pressure Loss– Relative Viscosity Curves

• Semi-Crystalline Vs. Amorphous Materials• Hygroscopic and non-hygroscopic

Materials• Shear Heating• Fountain Flow• Four Plastic Variables

• Non-Newtonian Behavior of Plastic– Static Pressure Loss– Relative Viscosity Curves

• Semi-Crystalline Vs. Amorphous Materials• Hygroscopic and non-hygroscopic

Materials• Shear Heating• Fountain Flow• Four Plastic Variables


Static Pressure LossStatic Pressure Loss

TRANSDUCERS

SPRUERUNNERSSCREWCAVITY

Where is Plastics Pressure Greatest?

Where is it the Least?

Source: RJG, Inc.


Relative ViscosityRelative Viscosity

VISC

OSI

TYTHICK

THIN

SLOW FASTFLOWRATE

High sensitivity tomachine fill speedfluctuation

Crossover point

Low sensitivity tomachine fill speedfluctuation

Source: RJG, Inc.


Crystalline Vs. AmorphousCrystalline Vs. Amorphous

• Crystalline (Semi-Crystalline)– Melt is Amorphous - Forms Crystals on Cooling– More Crystalline = More Shrinkage– Fast Cooling --> Less Time to Form Crystals --

> Less Crystallinity --> Less Shrinkage• Amorphous

– Both Melt and Solid are Amorphous– Cooling Rate Not Related to Shrinkage

• Crystalline (Semi-Crystalline)– Melt is Amorphous - Forms Crystals on Cooling– More Crystalline = More Shrinkage– Fast Cooling --> Less Time to Form Crystals --

> Less Crystallinity --> Less Shrinkage• Amorphous

– Both Melt and Solid are Amorphous– Cooling Rate Not Related to Shrinkage

Source: RJG, Inc.


Fountain FlowFountain Flow

• Fountain Flow, Skin Layer, and Alignment• Fountain Flow, Skin Layer, and Alignment

Source: RJG, Inc.


Four Plastic VariablesFour Plastic Variables

• Plastic Flow Rate• Plastic Temperature• Plastic Cooling• Plastic Pressure Gradient

• Plastic Flow Rate• Plastic Temperature• Plastic Cooling• Plastic Pressure Gradient


Before Attempting DOEBefore Attempting DOE

• Set Melt Temps at Nominal• Position Transfer• Fill Fast (But No Faster), Fill With Ample First

Stage Pressure– Relative viscosity curve

• Fill 95% to 99%, Then Transfer to Pack• Hold Plastic in Tool• Understand When Gate Seals (gate seal test)• Cool Efficiently• Demold Quickly and Consistently

• Set Melt Temps at Nominal• Position Transfer• Fill Fast (But No Faster), Fill With Ample First

Stage Pressure– Relative viscosity curve

• Fill 95% to 99%, Then Transfer to Pack• Hold Plastic in Tool• Understand When Gate Seals (gate seal test)• Cool Efficiently• Demold Quickly and Consistently

Check ring leakage?

Clogged cooling lines???

Is the materials dry?


What Is A Designed Experiment?What Is A Designed Experiment?• Systematic, Controlled Changes of the

Inputs (factors) to a Process in Order to Observe Corresponding Changes in the Outputs (responses).

• Systematic, Controlled Changes of the Inputs (factors) to a Process in Order to Observe Corresponding Changes in the Outputs (responses).


Types Of FactorsTypes Of Factors

• Constant Factors• Control Factors • Noise Factors (Robustness)

• Constant Factors• Control Factors • Noise Factors (Robustness)


What Do We Learn From Designed Experiments?What Do We Learn From Designed Experiments?

• Best Settings

• Sensitivity

• Best Settings

• Sensitivity


Why Do Designed Experiments?Why Do Designed Experiments?

• 50 Per Cent Improvement in Efficiency and Effectiveness

• 1 + 1 = 10

• 50 Per Cent Improvement in Efficiency and Effectiveness

• 1 + 1 = 10


How To Be Good At ItHow To Be Good At It

• Attend Training

• Read

• 510 Rule

• Attend Training

• Read

• 510 Rule


Engineering Experimental DesignEngineering Experimental Design• Not a Substitute For Knowledge of

Technology• Incorporates Current Understanding

• Physics First• If You Do Not Understand the Basics, You

Will Do EVIL Things With DOE

• Not a Substitute For Knowledge of Technology

• Incorporates Current Understanding

• Physics First• If You Do Not Understand the Basics, You

Will Do EVIL Things With DOE


Examples Of Poorly Done Doe’s Examples Of Poorly Done Doe’s • Quality Digest of 1999

– Injection Press– Gates– Barrel Temps– Moisture Content– Randomization, Replication

• Quality Digest of 1999– Injection Press– Gates– Barrel Temps– Moisture Content– Randomization, Replication


An ExampleAn Example

• Hinged Box, 100 ton Press• Thickness is .070 in• Length is response• Polypropylene• Single Cavity Mold• Set Transfer Point and Performed Gate

Seal Test• Fix Settings (except mtemp and hpress)

• Hinged Box, 100 ton Press• Thickness is .070 in• Length is response• Polypropylene• Single Cavity Mold• Set Transfer Point and Performed Gate

Seal Test• Fix Settings (except mtemp and hpress)


An ExampleAn Example

RUN Mtemp H Press Length

1 70 5000 15

2 70 7000 19

3 90 5000 12

4 90 7000 17


Pareto ChartPareto Chart

0

1

2

3

4

Hold press(B)

2.25

Mold temp(A)

-1.25

AB

0.25

Factors

Pareto ChartLength Avg Delta/2


Main Effects PlotMain Effects Plot

13

14.2

15.4

16.6

17.8

19

70(-) 90(+)Mold temp(A)

5000(-) 7000(+)Hold press(B)

Factors

Main Effects

Length


Transfer FunctionTransfer Function

• The equation (algebraic)

• It comes from MLR• Three important assumptions

– Two levels– O.A.– Variables are on orthogonal scale

• The equation (algebraic)

• It comes from MLR• Three important assumptions

– Two levels– O.A.– Variables are on orthogonal scale

Software packages use MLR to generate transfer function


MLR MathMLR Math

[ ] [ ]

=

=

++++=−

...

.........ˆ

12

2

1

0

1211222110

bbbb

YXXX

xxbxbxbbytt

β

β

=

ny

yyyy

Y

.

.4

3

2

1

−+++−+++−−−−

=1..1..1..11..1..1..11..1..1..11..1..1..1

X

includes factors (assumes 4 run previous example), and interaction effect

Note: the computer does the math, we just need to be able to interpret the output


Contour PlotContour Plot

70 74 78 82 86 90Mold temp

5000

5400

5800

6200

6600

7000

Hold press

Contour Plot

Length

15.2

14.4

16

16.8

17.618.4

13.6

12.81


RSM PlotRSM Plot

Length

Hold pressMold temp

Response Surface

7074

7882

86905000

54005800

62006600

7000

10

12.4

14.8

17.2

19.6

22


Example Using DOE WisdomExample Using DOE Wisdom

Click on new

Name example 1

click



Click on add

Enter info on first factor



Click to add additional factors



Add response



select

Click when done



Select data window

Enter data

Click save when done


Experimental ObjectivesExperimental Objectives

Launsby Consulting M12004 42

Where Can Molders Use Designed Experiments?Where Can Molders Use Designed Experiments?

• Problem solving

• Tool trials

• Establishment of process windows

• Problem solving

• Tool trials

• Establishment of process windows


Troubleshooting/screeningTroubleshooting/screening



FACTORS LOW HIGH Mold Temp 100 150 Barrel Temp Low High Cure Time 40 50 Back Press 50 150 Inj Velocity 1 3.1 Hold Press 200 1100



• Response– Appearance– Decreasing shape– Rate as 1, 2, 3 (3 is best)

• O.A.– L8 with 5 repetitions

• Response– Appearance– Decreasing shape– Rate as 1, 2, 3 (3 is best)

• O.A.– L8 with 5 repetitions


Main EffectsMain Effects

0

1

2

3

4

5

moldt barrelt injvel ctime holdp bckpreFactors

appear

Mold temp is big hitter, set at high for best appearance. Other factors appear to have little impact on appearance


Modeling DJ ExampleModeling DJ Example

Toshiba ink cartridge


DJ ExampleDJ Example

FACTOR LOW HIGH

Hold Pressure (psi) 5000 8500

Pack Speed (%) 15 30

Injection Vel. (%) 30 65Mold Temp (deg.) 100 150


Responses For DJResponses For DJ

RESPONSE LSL NOM. USL

SLOT1 31.90 31.95 32.0

SLOT2 56.68 56.83 56.98

SLOT3 38.62 38.72 38.8

SLOT4 33.60 33.65 33.70

SPLAY and FLOWLINES rated as Good, OK, Bad (3,2,1)


Runs For DJRuns For DJ

moldtemp injvel packspd holdpress

1 100 30 15 40002 100 30 30 80003 100 65 15 80004 100 30 30 40005 100 65 25 85006 100 65 15 40007 100 30 15 40008 150 65 30 40009 150 30 15 8500

10 150 65 15 850011 150 30 30 850012 150 30 15 4000

Note: here are the trials, 4 cavity tool, did 5 shots per run. Response values are not shown, only some of the simple analysis (follows)


Main Effects PlotSlot 1Main Effects PlotSlot 1

31.86

31.87

31.88

31.89

31.9

31.91

31.92

100(-) 150(+)moldtemp(A)

30(-) 65(+)injvel(B)

15(-) 30(+)packspd(C)

4000(-)8500(+)packpress(D)

Factors

Main Effects

slot 1


Main Effects Plot Slot 2Main Effects Plot Slot 2

56.76

56.77

56.78

56.79

56.8

56.81

56.82

100(-) 150(+)moldtemp(A)

30(-) 65(+)injvel(B)

15(-) 30(+)packspd(C)

4000(-)8500(+)packpress(D)

Factors

Main Effects

slot 2



38.6

38.62

38.64

38.66

38.68

38.7

38.72

100(-) 150(+)moldtemp(A)

30(-) 65(+)injvel(B)

15(-) 30(+)packspd(C)

4000(-)8500(+)packpress(D)

Factors

Main Effects

slot 3



33.57

33.58

33.59

33.6

33.61

33.62

33.63

100(-) 150(+)moldtemp(A)

30(-) 65(+)injvel(B)

15(-) 30(+)packspd(C)

4000(-)8500(+)packpress(D)

Factors

Main Effects

slot 4


Main Effects PlotSplayMain Effects PlotSplay

2.2

2.4

2.6

2.8

3

3.2

3.4

100(-) 150(+)moldtemp(A)

30(-) 65(+)injvel(B)

15(-) 30(+)packspd(C)

4000(-) 8500(+)packpress(D)

Factors

Main Effects

splay


Main Effects PlotFLOWLINESMain Effects PlotFLOWLINES

0

1

2

3

100(-) 150(+)moldtemp(A)

30(-) 65(+)injvel(B)

15(-) 30(+)packspd(C)

4000(-) 8500(+)packpress(D)

Factors

Main Effects

flowlines


What Is The Best Trade-off?What Is The Best Trade-off?

D(composite)

injvelmoldtemp

Response Surface**packspd(C)=15.0000,packpress(D)=7920.00

100

110

120

130

140

15030

37

44

51

58

65

0

0.1

0.2

0.3

0.4

Operate in this region


Slot 1 Slot 2 Slot 3 Slot 4

. . . .

PICTURAL View Of Trade-off (means)PICTURAL View Of Trade-off (means)

Note: slot 1 and slot 2 work the opposite of slots 3 and 4. Ifwe attempt to increase slot 1 and slot 2, slots 3 and slots 4 decrease. Good time to find this out is during tool trial

How About Variation?How About Variation?


Monte Carlo Simulation can be used to predict variation about a process meanDOE Wisdom Analysis of Variance

Dependent Variable: response 4Number Runs(N): 12Multiple R: 0.999807Squared Multiple R: 0.999614Adjusted Squared Multiple R: 0.995757Standard Error of Estimate: 0.000848528

Variable Coefficient best settingConstant 33.5985Mold Temp(A) 0.00506435 150Inj Vel(B) -0.00941707 47Pack Spd(C) -0.00507645 15Pack Prs(D) -0.00436898 7920AB 0.00572135AC 0.00363698AD -0.000393981BC -0.00360833BD -0.00193009CD -0.00225509

How closely can the factors be controlled in production?

Results of Monte Carlo SimulationResults of Monte Carlo Simulation



ROBUST DESIGNProduct LevelROBUST DESIGNProduct Level• What it Means

– Products Perform Intended Functions at Varying Usage Conditions

– Wide Range Customer Usage– Product Deterioration– Variation in Subsystems/Components

• What it Means– Products Perform Intended Functions at

Varying Usage Conditions– Wide Range Customer Usage– Product Deterioration– Variation in Subsystems/Components


Robustness At The Process LevelRobustness At The Process Level• Lot-to-Lot Variation in Resin• Regrind• Machine• Room Temperature• Moisture Content• Operator

• Lot-to-Lot Variation in Resin• Regrind• Machine• Room Temperature• Moisture Content• Operator


Robust Design(Cont.)Robust Design(Cont.)• Robust Design Recognizes That Variability

Exists and is the Enemy of High Quality Products and Processes

• Employs DOE as a Strategic Weapon• Accomplished by Selecting the Best Levels

for Control Factors so That Performance Insensitive to Noise Factors

• Robust Design Recognizes That Variability Exists and is the Enemy of High Quality Products and Processes

• Employs DOE as a Strategic Weapon• Accomplished by Selecting the Best Levels

for Control Factors so That Performance Insensitive to Noise Factors


Robust Design(Examples)Robust Design(Examples)• Caramel Candy Example

• Industry Examples (HP Ink Cartridge…see following slides)

• Caramel Candy Example

• Industry Examples (HP Ink Cartridge…see following slides)


HP weld exampleHP weld example


HP Weld Example, The PartHP Weld Example, The Part

Ink Cartridge

Energy director on base


Hp IrelandHp Ireland

EDH is energy director height, MFI is melt flow index. They are both noise factor in this example


Robust Design ExampleRobust Design Example

• HP Ireland– Review factors, levels, responses, Desirabilities– Any factor settings minimize variation?– What are optimal settings?

• HP Ireland– Review factors, levels, responses, Desirabilities– Any factor settings minimize variation?– What are optimal settings?

FACTORS C/N LOW HIGH

APRESS C 25 40

COL DIST C .004 .006

AMP C 65 85

DWN SPD C 2.6 4.0

MFI N LOW HIGH

EDH N LOW HIGH

Desirability functions allow us to trade-off multiple simultaneous responses (we will learn details later)


Run press dist amp spd1 25 0.004 65 2.62 25 0.004 85 43 25 0.006 65 44 25 0.006 85 2.65 40 0.004 65 46 40 0.004 85 2.67 40 0.006 65 2.68 40 0.006 85 4

high high low lowhigh low high lowstrength STD % strength STD % strength STD % strength STD %

0.0067 0.00148 0 0.00707 0.00088 0 0.00694 0.00116 0 0.00719 0.00111 00.00941 0.00056 100 0.00985 0.00079 100 0.00929 0.00044 100 0.00977 0.00088 980.00906 0.0006 87 0.00932 0.00101 74 0.00899 0.00068 80 0.00931 0.00112 740.01129 0.0005 100 0.01152 0.00086 99 0.01143 0.0004 100 0.01143 0.00077 1000.00703 0.00098 1 0.00703 0.00098 6 0.00697 0.00096 4 0.00718 0.0011 70.00941 0.00067 100 0.00991 0.00095 100 0.00932 0.00065 100 0.00953 0.00098 930.00911 0.00572 45 0.0085 0.00093 56 0.00862 0.00052 59 0.00859 0.00078 530.01136 0.00047 100 0.01177 0.0008 100 0.01121 0.00068 100 0.01182 0.00079 100

MFIEDH

The DataThe Data

File “hp robust 1”

Eight run inner OA


Robust Design, StrengthRobust Design, Strength

0.006

0.007

0.008

0.009

0.01

0.011

0.012

25(-) 40(+)press(A)

0.004(-) 0.006(+)dist(B)

65(-) 85(+)amp(C)

2.6(-) 4(+)spd(D)

Factors

Main Effects

strength

Average


Robust Design (Cont.)Robust Design (Cont.)

• Students: What is the best trade-off?• Students: What is the best trade-off?

Mean (Weld Str) Stand Dev (Weld Str) % Good Welds D(composite)0.0116059 0.00044375 122.25 1

95% CI: ± 0.000498452 ± 0.00193891 ± 39.7551Constant 0.00924781 0.000975 66.75Air Pressure(A) -3.78E-05 0.0001475 -2.75 25Collapse Distance(B) 0.000960313 6.44E-05 16.1875 0.006Amplitude(C) 0.00127219 -0.000275625 32.625 85Down Speed(D) 8.78E-05 -0.0001725 3.9375 4

Here are the predicted optimal setting for factors


RSM PlotRSM Plot

D(composite)

Collapse DistanceAmplitude

Response Surface**Air Pressure(A)=25.0000,Down Speed(D)=4.00000

6569

7377

81850.004

0.005

0.006

0

0.2

0.4

0.6

0.8

1


Knowledge Of The Technology To Enhance RobustnessKnowledge Of The Technology To Enhance Robustness

• Viscosity vs. Shear Curves

• Cavity Pressure Sensors

• Viscosity vs. Shear Curves

• Cavity Pressure Sensors

Cavity pressure changes are a major source of dimensional and appearance variation


Conventional MoldingConventional Molding

• Fill and Pack are Done on First Stage• Time is Usually Used to Transfer From

Boost to Hold

• Fill and Pack are Done on First Stage• Time is Usually Used to Transfer From

Boost to Hold


Typical Pressure ProfileTypical Pressure Profile

From “Plastic Part Design” by R.A. Malloy


Hydraulic Pressure Is MisleadingHydraulic Pressure Is Misleading

Source: RJG, Inc.

Hydraulic Injection Pressure

Mold Cavity Pressure


Decoupled MOLDINGTMDecoupled MOLDINGTM

DECOUPLED MOLDINGTM is a registered trademark of RJG, Inc.


Cavity Pressure ImpactCavity Pressure Impact

Source: RJG, Inc.


Cavity Control ImpactCavity Control Impact

MOLDINGTECHNIQUE

GATE ENDMOLDPRESS (s.d.)

EOF MOLDPRESS (s.d.)

Traditional 514 860

TotallyDecoupled

21.4 205

Source: RJG Associates, Decoupled Molding is a Trademark of RJG in Traverse City, MI


Box And Bubble ChartBox And Bubble Chart

• Planning• Select an Orthogonal Array• Conduct • Analysis• Confirmation

• Planning• Select an Orthogonal Array• Conduct • Analysis• Confirmation


PlanningPlanning

• Who Are the Customers?• How Will Customers Use Products?• What are the Functions?• Objectives?• Time Requirements• Responses, Factors, Money

• Who Are the Customers?• How Will Customers Use Products?• What are the Functions?• Objectives?• Time Requirements• Responses, Factors, Money


Orthogonal ArrayOrthogonal Array

• A Set of Experimental Conditions (runs) Where the Levels of Each Factors are Balanced Over the Levels of the Other Factors, Both Horizontally and Vertically

• A Balanced Family of Tests Which Allows For Fast, Efficient, Simple, and Powerful Analysis

• Example-----Golf

• A Set of Experimental Conditions (runs) Where the Levels of Each Factors are Balanced Over the Levels of the Other Factors, Both Horizontally and Vertically

• A Balanced Family of Tests Which Allows For Fast, Efficient, Simple, and Powerful Analysis

• Example-----Golf


Orthogonal Vs What? An ExampleOrthogonal Vs What? An Example


Factor AssignmentsFactor Assignments

FACTOR LEVELSCarbon Black (C) 1.2, 2.1Sulfur (S) 2, 2.5Filler (F) 30, 33Accelerator Type (A) Dupont, AlliedPolymer Type (P) 1, 2, 3, 4, 5


Full FactorialApproachFull FactorialApproach• Advantages

• Disadvantages

• Advantages

• Disadvantages


One-factor-atA TimeOne-factor-atA Time• Advantages

• Disadvantages

• Advantages

• Disadvantages


Best Guess ApproachBest Guess Approach

• Advantages

• Disadvantages

• Advantages

• Disadvantages


Experimentation InThe 00’sExperimentation InThe 00’s• Full Factorials, Taguchi O.A.’s• Fractional-Factorials• Plackett-Burman• Hadamard Matrices• Box-Behnken, Central Composite• D-optimal Designs

• Full Factorials, Taguchi O.A.’s• Fractional-Factorials• Plackett-Burman• Hadamard Matrices• Box-Behnken, Central Composite• D-optimal Designs


Module #2Module #2

• Goals– Understand the Steps Required for Success– Set-up and Analyze a Simple Design– Learn When Analysis is Unsuccessful and

Grasp How to Recover– Apply Desirability Functions (using software).

• Goals– Understand the Steps Required for Success– Set-up and Analyze a Simple Design– Learn When Analysis is Unsuccessful and

Grasp How to Recover– Apply Desirability Functions (using software).


The Box And Bubble DetailsThe Box And Bubble Details

• Who is the customer?• How will product be used?• Consider applicability of functional

analysis• What is the objective? What are the

detailed questions to be answered?• When can we start? When do we need an

answer?

• Who is the customer?• How will product be used?• Consider applicability of functional

analysis• What is the objective? What are the

detailed questions to be answered?• When can we start? When do we need an

answer?


The Box And Bubble Details (Cont)The Box And Bubble Details (Cont)• Responses

– Name, how measured?, MSA?, shape, critical values, weight

• Factors– Name, qualitative or quantitative? Range of

interest, levels, propensity for interactions• Costs

– Approximate cost per run, time per run

• Responses– Name, how measured?, MSA?, shape, critical

values, weight• Factors

– Name, qualitative or quantitative? Range of interest, levels, propensity for interactions

• Costs– Approximate cost per run, time per run


The Box And Bubble DetailsThe Box And Bubble Details• Select OA• Determine number of samples per run,

Discuss replication, randomization, and repetitions

• Conduct trials, record set points for constant factors

• Analysis• Confirm predictions

• Select OA• Determine number of samples per run,

Discuss replication, randomization, and repetitions

• Conduct trials, record set points for constant factors

• Analysis• Confirm predictions


Four Types Of FactorsFour Types Of Factors

• Effect Location

• Effect Variation

• Effect Both

• No Effect

• Effect Location

• Effect Variation

• Effect Both

• No Effect


Statistical AnalysisGolf Ball ExampleStatistical AnalysisGolf Ball Example


Introduction To Simple AnalysisIntroduction To Simple Analysis

Run TEMP PIN PACKT PACKP1 1 -20 5 6002 1 -20 15 9003 1 10 5 9004 1 10 15 6005 2 -20 5 9006 2 -20 15 6007 2 10 5 6008 2 10 15 900

DURA.4547646949496974

WT44.845.345.344.845.444.944.945.4



30

40

50

60

70

80

90

1(-) 2(+)TEMP(A)

-20(-) 10(+)PIN(B)

5(-) 15(+)PACKT(C)

600(-) 900(+)PACKP(D)

Factors

Main Effects

DURABILITY



44.8

44.9

45

45.1

45.2

45.3

45.4

1(-) 2(+)TEMP(A)

-20(-) 10(+)PIN(B)

5(-) 15(+)PACKT(C)

600(-) 900(+)PACKP(D)

Factors

Main Effects

WEIGHT


Stats AnalysisWeightStats AnalysisWeight

DOE Wisdom Analysis of Variance

Dependent Variable: WEIGHTNumber Runs(N): 128Multiple R: 0.963484Squared Multiple R: 0.928301Adjusted Squared Mu 0.925969Standard Error of Esti 0.067707

Variable Coefficient Std Error 95% CI Tolerance T P(2 Tail)

Constant 45.1056 0.005985 ± 0.0118460 7537.012 0TEMP(A) 0.048281 0.005985 ± 0.011846 1 8.068 0PIN(B) -0.0025 0.005985 ± 0.011846 1 -0.418 0.677PACKT(C) 0.007656 0.005985 ± 0.011846 1 1.279 0.203PACKP(D) 0.23375 0.005985 ± 0.011846 1 39.059 0


Stats AnalysisDurabilityStats AnalysisDurability


Dependent Variable: DURABILITYNumber Runs(N): 128Multiple R: 0.661862Squared Multiple R: 0.438061Adjusted Squared Mu 0.419787Standard Error of Esti 12.5573


Constant 58.4063 1.10992 ± 2.19701 52.622 0TEMP(A) 2 1.10992 ± 2.19701 1 1.802 0.074PIN(B) 10.5938 1.10992 ± 2.19701 1 9.545 0PACKT(C) 1.375 1.10992 ± 2.19701 1 1.239 0.218PACKP(D) 0.0625 1.10992 ± 2.19701 1 0.056 0.955

Source Sum of Sq DF Mean SquaF Ratio P

Regression 15119.63 4 3779.906 23.9713 0Residual 19395.25 123 157.685


Example Example

Run temp acid time time time time time time time1 1 0 67 79 71 73 69 65 702 1 1 66 71 81 67 68 73 613 2 0 17 22 18 19 17 17 174 2 1 26 26.5 25.5 27 28 27 26.6


Example (Cont.)Example (Cont.)

20

30

40

50

60

70

80

1(-) 2(+)temp(A)

0(-) 1(+)acid(B)

-1(-) 1(+)AB

Factors

Main Effects

ti

me



0

1

2

3

4

5

6

1(-) 2(+)temp(A)

0(-) 1(+)acid(B)

-1(-) 1(+)AB

Factors

Main Effects

S ti

me



R.O.T.: If absolute value of Ln S effect (Delta) is equal to or greater than 1.0, this is a strong reason to believe you have a factor which influences variation

0

1

2

3

4

temp(A)

-1.4787

AB

-0.58861

acid(B)

-0.25787

Factors

Pareto Chartti

me ln S Delta


Example #3Example #3

QUESTION: How The Tabled Taguchi Designs Differ From Fractional-Factorials?


Example # 4Example # 4

• Important terms– Interaction Columns– Aliasing– Resolution

• Important terms– Interaction Columns– Aliasing– Resolution


Tabled Taguchi DesignsTabled Taguchi Designs

See pages 52 thru 58 (Experimental Design for Injection Molding for L4, L8, L9, L16,…..)


D-optimal DesignsD-optimal Designs

• Advantages

• Disadvantages

• Advantages

• Disadvantages


How Many Samples?R.O.T.How Many Samples?R.O.T.

Response Type

Pass/Fail Visual (G,M,E) Quantitative

40 or More Per Experiment

10 to 20 Per Run

10≥′pN

Note: These are rules of thumb


How Many Samples?How Many Samples?

• Easy to provide if:– You have an estimate of the standard deviation

for response being studied– Know what is a practically significant difference

• Easy to provide if:– You have an estimate of the standard deviation

for response being studied– Know what is a practically significant difference


Statistical SignificanceStatistical Significance

• People talk a great deal about statistical significance; yet spend almost no time regarding practical significance

• Reality– Any effect (as long as it is not zero) will be shown as

statistically significant if enough samples are used– You can mathematically justify any sample size by

tweaking inputs to formula

• People talk a great deal about statistical significance; yet spend almost no time regarding practical significance

• Reality– Any effect (as long as it is not zero) will be shown as

statistically significant if enough samples are used– You can mathematically justify any sample size by

tweaking inputs to formula


Statistical/Practical SignificanceStatistical/Practical Significance


Constant 17.0505 0.201485 ± 0.464627 84.624 0 tech(A):A 1.06016 0.209227 ± 0.482480 5.067 0.001 tech(A):B -1.06016 0.209227 ± 0.482480 0.888 -5.067 0.001(B) 0.689843 0.209227 ± 0.482480 0.888 3.297 0.011(C) 0.796313 0.226216 ± 0.521657 0.908 3.52 0.008(D) -0.915697 0.249362 ± 0.575030 0.875 -3.672 0.006

All are statistically significant

If the difference is not greater than 4, it is not of practical importance

Not a big deal

Need both before you get very excited

14

15

16

17

18

19

20

A(-) B(+)(A)

1(-) 2(+)(B)

3(-) 5(+)(C)

2(-) 4(+)(D)

Factors

Main Effects

bump ht


Sample Size For Mean Shift (one approach)Sample Size For Mean Shift (one approach)

===

=

σλ

λσ

n

n

2

162

2

Total number of samples in experiment

Minimum practical difference we wish to find as significant

Error standard deviation

Example: We decide to conduct an L8. We decide that 4 and estimate the error standard deviation as 4. The number of samples for the experiment is 32. We need to run the L8 4 times.

=λ

222

222

/)22(302

/)(

λσ

βα

λσβα

+≈

≥==

+=

nn

ttn.02

.02


ConfirmationConfirmation

• Recommended # of Tests

• Graphical Approach

• Recommended # of Tests

• Graphical Approach


Why You May Not ConfirmWhy You May Not Confirm• Data Entry• Did Not Conduct Per Plan• Measurement System Not Reliable• Large Variation in the Response• Wrong About Interactions• Model is Inadequate• Something Changed (Viscosity)• “Computer On/Brain Off”

• Data Entry• Did Not Conduct Per Plan• Measurement System Not Reliable• Large Variation in the Response• Wrong About Interactions• Model is Inadequate• Something Changed (Viscosity)• “Computer On/Brain Off”


Golf ExampleAnalysis Of DiameterGolf ExampleAnalysis Of Diameter• Which Factors Appear to be Influencing the

Average?• Do Any Factors Appear to be Influencing

the Variation in the Diameter?• How Should We Set the Process to

Achieve a Target Response of 1.682?

• Which Factors Appear to be Influencing the Average?

• Do Any Factors Appear to be Influencing the Variation in the Diameter?

• How Should We Set the Process to Achieve a Target Response of 1.682?

Note: please use following graphs to answer above questions


Main EffectsDiameterMain EffectsDiameter

1.68

1.682

1.684

1.686

1.688

1.69

1.692

1(-) 2(+)TEMP(A)

-20(-) 10(+)PIN(B)

5(-) 15(+)PACKT(C)

600(-) 900(+)PACKP(D)

Factors

Main Effects

SIZE


Variance AnalysisDiameterVariance AnalysisDiameter

0

0.2

0.4

0.6

0.8

PACKP(D)

-0.54953

TEMP(A)

-0.28592

PIN(B)

0.061876

PACKT(C)

0.018528

Factors

Pareto ChartSIZE ln S Delta


Stats AnalysisDiameterStats AnalysisDiameter


Dependent Variable: SIZENumber Runs(N): 128Multiple R: 0.918717Squared Multiple R: 0.844041Adjusted Squared Mu 0.838969Standard Error of Esti 0.001534


Constant 1.68614 0.000136 ± 0.000268335 12438.2 0TEMP(A) 0.000874 0.000136 ± 0.000268 1 6.447 0PIN(B) -0.00023 0.000136 ± 0.000268 1 -1.709 0.09PACKT(C) 8.33E-05 0.000136 ± 0.000268 1 0.614 0.54PACKP(D) 0.003378 0.000136 ± 0.000268 1 24.916 0

Source Sum of Sq DF Mean SquaF Ratio P

Regression 0.001566 4 0.000391 166.417 0Residual 0.000289 123 2.35E-06


Contour PlotDiameterContour PlotDiameter

600 660 720 780 840 900PACKP

5

7

9

11

13

15

PACKT

Contour Plot**TEMP(A)=1.00000,PIN(B)=10.0000

SIZE

816

1.68241.6832 1.684 1.6848

1.68561.68641.68721.688


Residual AnalysisResidual Analysis

• What is it?– A method for evaluating errors in model

predictions• What are the benefits?

– Check of model assumptions– Evaluation of model adequacy– Increased understanding of technology

• What patterns should emerge?

• What is it?– A method for evaluating errors in model

predictions• What are the benefits?

– Check of model assumptions– Evaluation of model adequacy– Increased understanding of technology

• What patterns should emerge?


ExampleExample

• “Epsoon” (full-factorial, single cavity, 10 shots per run)

• “Epsoon” (full-factorial, single cavity, 10 shots per run)Factors LevelsMtemp 90, 130Injection Velocity 60, 80 %Pack Press 30, 60%

ResponsesDimension “E”Total run out


Dim “E”Dim “E”

13.01

13.02

13.03

13.04

13.05

13.06

13.07

90(-)130(+)mtemp(A)

60(-)80(+)vel(B)

-1(-) 1(+)-AB

30(-)60(+)pack(C)

-1(-) 1(+)-AC

-1(-) 1(+)-BC

-1(-) 1(+)ABC

Factors

Main Effects

dimension E


TIR TIR

0.046

0.047

0.048

0.049

0.05

0.051

0.052

90(-)130(+)mtemp(A)

60(-)80(+)vel(B)

-1(-) 1(+)-AB

30(-)60(+)pack(C)

-1(-) 1(+)-AC

-1(-) 1(+)-BC

-1(-) 1(+)ABC

Factors

Main Effects

Total run out


EPSOON Dim “E” Student ResidualEPSOON Dim “E” Student Residual


Dim “E” Student Residual PlotDim “E” Student Residual Plot

-4

-2

0

2

4

6

8

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980R u n O r d e r

d

i

m

E

s

t

u

d

r

e

s

R e s i d u a l S c a t t e r P l o t


TIR Student ResidualsTIR Student Residuals

0

2

4

6

8

10

-2.2

1

-2

0

-1.8

1

-1.6

2

-1.4

2

-1.2

9

-1

7

-0.8

4

-0.6

6

-0.4

2

-0.2

5

0

1

0.2

3

0.4

2

0.6

4

0.8

9

1

8

1.2

9

1.4

2

1.6

3

1.8

0

Total run out Studentized Residual

Count

Residual Histogram


TIR Student ResidualsTIR Student Residuals

-3

-2

-1

0

1

2

3

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980R u n O r d e r

r

u

n

o

u

t

s

t

u

d

r

e

s

l

R e s i d u a l S c a t t e r P l o t


Case Study “Hockey Sticks”Case Study “Hockey Sticks”

Responses of Interest:Length of the leftLength of the rightGap on leftGap on rightSinks on leftSinks on rightFactors Studied:Mold Temperature (150 and 190)Injection Velocity (2 and 4 in/sec.)Hold Pressure (5000 and 14000 psi plastic)

Trim part for saddle bags of motorcycle


Case Study (cont.)Case Study (cont.)

Two cavity tool for left and right part



SpeedRelative Visc.

0.5 18,720

1 10,070

1.5 7,225

2 5,715

3 4,270

4 3,540

5 2,950

0.5 1 1.5 2 3 4 5Rel. Visc.

0

5,000

10,000

15,000

20,000

speed

Decided to run DOE at 2 and 4 in/sec



Hold Time Part Weight

2 Less than .088

3 .088

4 .089

5 .089

6 .089

7 .089

A hold time of 6 seconds was selected. Appear to provide ample time for gate seal


Case Study (cont.)Case Study (cont.)Run mold temperature velocity hold pressure

1 150 2 5000

2 150 2 14000

3 150 4 5000

4 150 4 14000

5 190 2 5000

6 190 2 14000

7 190 4 5000

8 190 4 14000

Conducted five shots per run



-0.8

-0.56

-0.32

-0.08

0.16

0.4

150(-) 190(+)mold temp(A)

2(-) 4(+)velocity(B)

5000(-) 14000(+)hold press(C)

Factors

Main Effects

length right

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

150(-) 190(+)mold temp(A)


5000(-) 14000(+)hold press(C)

Factors

Main Effects

length left



2.4

2.6

2.8

3

3.2

3.4

3.6

150(-) 190(+)mold temp(A)


5000(-) 14000(+)hold press(C)

Factors

Main Effects

gap right

2

2.2

2.4

2.6

2.8

3

3.2

150(-) 190(+)mold temp(A)


5000(-) 14000(+)hold press(C)

Factors

Main Effects

gap left



1.6

1.8

2

2.2

2.4

2.6

2.8

150(-) 190(+)mold temp(A)


5000(-) 14000(+)hold press(C)

Factors

Main Effects

sink right

1.8

1.9

2

2.1

2.2

2.3

2.4

150(-) 190(+)mold temp(A)


5000(-) 14000(+)hold press(C)

Factors

Main Effects

sink left

Student question: does it make sense that these two responses display dramatically different main effects plots for Hold Press?

What could account for this

difference?




Dependent Variable: length rightNumber Runs(N): 40Multiple R: 0.977694Squared Multiple R: 0.955885Adjusted Squared Mu 0.946235Standard Error of Esti 0.078724


Constant -0.1625 0.012447 ± 0.0253545 -13.055 0mold temp -0.083 0.012447 ± 0.0253545 1 -6.668 0velocity(B) 0.006 0.012447 ± 0.0253545 1 0.482 0.633hold press( 0.3135 0.012447 ± 0.0253545 1 25.186 0AB -0.0045 0.012447 ± 0.0253545 1 -0.362 0.72AC -0.03 0.012447 ± 0.0253545 1 -2.41 0.022BC 0.029 0.012447 ± 0.0253545 1 2.33 0.026ABC 0.0215 0.012447 ± 0.0253545 1 1.727 0.094




Dependent Variable: length leftNumber Runs(N): 40Multiple R: 0.95219Squared Multiple R: 0.906665Adjusted Squared Mu 0.886248Standard Error of Esti 0.063236


Constant -0.13575 0.009998 ± 0.0203662 -13.577 0mold temp -0.03575 0.009998 ± 0.0203662 1 -3.576 0.001velocity(B) -0.00275 0.009998 ± 0.0203662 1 -0.275 0.785hold press( 0.17175 0.009998 ± 0.0203662 1 17.178 0AB -0.01175 0.009998 ± 0.0203662 1 -1.175 0.249AC -0.00325 0.009998 ± 0.0203662 1 -0.325 0.747BC 0.01075 0.009998 ± 0.0203662 1 1.075 0.29ABC -0.00525 0.009998 ± 0.0203662 1 -0.525 0.603




Dependent Variable: gap rightNumber Runs(N): 40Multiple R: 0.990342Squared Multiple R: 0.980778Adjusted Squared Mu 0.976573Standard Error of Esti 0.085878


Constant 2.9575 0.013579 ± 0.0276584 217.808 0mold temp -0.2575 0.013579 ± 0.0276584 1 -18.964 0velocity(B) -0.0225 0.013579 ± 0.0276584 1 -1.657 0.107hold press( 0.4825 0.013579 ± 0.0276584 1 35.534 0AB -0.0175 0.013579 ± 0.0276584 1 -1.289 0.207AC 0.0175 0.013579 ± 0.0276584 1 1.289 0.207BC 0.0225 0.013579 ± 0.0276584 1 1.657 0.107ABC 0.0175 0.013579 ± 0.0276584 1 1.289 0.207




Dependent Variable: gap leftNumber Runs(N): 40Multiple R: 0.994618Squared Multiple R: 0.989265Adjusted Squared Mu 0.986916Standard Error of Esti 0.053619


Constant 2.5975 0.008478 ± 0.0172689 306.384 0mold temp -0.0475 0.008478 ± 0.0172689 1 -5.603 0velocity(B) -0.0175 0.008478 ± 0.0172689 1 -2.064 0.047hold press( 0.4575 0.008478 ± 0.0172689 1 53.964 0AB -0.0025 0.008478 ± 0.0172689 1 -0.295 0.77AC -0.0075 0.008478 ± 0.0172689 1 -0.885 0.383BC 0.0025 0.008478 ± 0.0172689 1 0.295 0.77ABC -0.0025 0.008478 ± 0.0172689 1 -0.295 0.77




Dependent Variable: sink rightNumber Runs(N): 40Multiple R: 0.974639Squared Multiple R: 0.949922Adjusted Squared Mu 0.938967Standard Error of Esti 0.158114


Constant 2.275 0.025 ± 0.0509233 91 0mold temp -0.225 0.025 ± 0.050923 1 -9 0velocity(B) 0.225 0.025 ± 0.050923 1 9 0hold press( 0.475 0.025 ± 0.050923 1 19 0AB 0.225 0.025 ± 0.050923 1 9 0AC -0.025 0.025 ± 0.050923 1 -1 0.325BC 0.025 0.025 ± 0.050923 1 1 0.325ABC 0.025 0.025 ± 0.050923 1 1 0.325




Dependent Variable: sink leftNumber Runs(N): 40Multiple R: 0.725476Squared Multiple R: 0.526316Adjusted Squared Mu 0.422697Standard Error of Esti 0.33541


Constant 2.1 0.053033 ± 0.108025 39.598 0mold temp -0.15 0.053033 ± 0.108025 1 -2.828 0.008velocity(B) 0.05 0.053033 ± 0.108025 1 0.943 0.353hold press( 0 0.053033 ± 0.108025 1 0 1AB -0.2 0.053033 ± 0.108025 1 -3.771 0.001AC 0.15 0.053033 ± 0.108025 1 2.828 0.008BC -0.05 0.053033 ± 0.108025 1 -0.943 0.353ABC 0.1 0.053033 ± 0.108025 1 1.886 0.068



-6

-4

-2

0

2

4

6

1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334353637383940Run Order

left Studentized Resid

Residual Scatter Plot



D(composite)

mold temp

hold press

Response Surface**velocity(B)=2.00000

150

158

166

174

182

190

50006800

860010400

1220014000

0

0.2

0.4

0.6

0.8

1


Case Study Best Set PointsCase Study Best Set Points

Mold temperature = 173 degreesInjection velocity = 2 inches/secHold pressure = 14000 psi. plastic

(Note that this setting was not actually one of the eight trials conducted in the orthogonal array)

From these settings the following values were predicted:

Length right = .0965 +/- .1684Length left = .0247 +/- .1352Gap right = 3.404 +/- .183Gap left = 3.063 +/- .115Sink right = 2.43 +/- .34Sink left = 2.11 +/- .717

5 confirmation runs were conducted. All parts fell into above confidence Intervals


Desirability FunctionsDesirability Functions

• What are They?• Why are They Needed?• What are the Steps Required?

– For Each Response, Determine a Shape– For Each Response, Determine an Importance

Weight– Analyze Composite D

• What are They?• Why are They Needed?• What are the Steps Required?

– For Each Response, Determine a Shape– For Each Response, Determine an Importance

Weight– Analyze Composite D


Composite D ExampleComposite D Example

FACTOR LOW HIGH

A 1 2

B 1 2


Composite D ExampleComposite D Example

RESP TYPE MIN. NOM. MAX. WT.

Tensile Tent 1500 2000 2500 1

Hard. Decr. 20 50 2

Elong. Inc. 500 600 4


ExampleExample


Tensile ContourTensile Contour

1 1.2 1.4 1.6 1.8 2a

1

1.2

1.4

1.6

1.8

2

b

Contour Plot

Tensile

1750 17001800

1850

19001950

00

1650


Hardness ContourHardness Contour

1 1.2 1.4 1.6 1.8 2a

1

1.2

1.4

1.6

1.8

2

b

Contour Plot

Hardness

44 4240

3836

34

32


Elongation ContourElongation Contour

1 1.2 1.4 1.6 1.8 2a

1

1.2

1.4

1.6

1.8

2

b

Contour Plot

Elongation

540530

540550

560570

580

530

520510


Desirability ContourDesirability Contour

1 1.2 1.4 1.6 1.8 2a

1

1.2

1.4

1.6

1.8

2

b

Contour Plot

D(composite)

0.30.20.1

0.4

0.5

0.6

0


SummarySummary

• Understand the Technology of Molding

• Use the Four Plastic Variables as the Foundation for DOE

• Physics First

• 510 Rule

• Understand the Technology of Molding

• Use the Four Plastic Variables as the Foundation for DOE

• Physics First

• 510 Rule

Experimental Design For Injection Molding 1 Launsby Consulting Experimental Design For Injection...

Documents

Transcript of Experimental Design For Injection Molding 1 Launsby Consulting Experimental Design For Injection...