ee-590 foundations of projectsapte/ee590/ee590_lect1c_notes.pdf · " electric discharge...

20 Jan 2012 P.R. Apte : EE-590: Lect 1c Various Case Studies Case Studies - 1

EEEE--590590

Foundations of ProjectsFoundations of Projects

Design and Analysis of Experiments Design and Analysis of Experiments

usingusing Taguchi MethodTaguchi Method

By

Prakash R. ApteEE Department

IIT Bombay


Taguchi Method CaseTaguchi Method Case--StudyStudy

OPTIMIZATIONOPTIMIZATION

of of

ELECTRIC DISCHARGE MACHINE (EDM)ELECTRIC DISCHARGE MACHINE (EDM)

COMPANY : ELECTRONICA MACHINE TOOLS, PUNE, INDIA


8 STEPS IN TAGUCHI METHODOLOGYCOMPANY : ELECTRONICA MACHINE TOOLS, PUNE" ELECTRIC DISCHARGE MACHINE (EDM) OPTIMIZATION AND STABILIZATION "

1. IDENTIFY THE MAIN FUNCTION,SIDE EFFECTS, AND FAILURE MODE

2. IDENTIFY THE NOISE FACTORS,TESTING CONDITIONS, AND QUALITY CHARACTERISTICS

3. IDENTIFY THE OBJECTIVE FUNCTION TO BE OPTIMIZED

4. IDENTIFY THE CONTROL FACTORS AND THEIR LEVELS

5. SELECT THE ORTHOGONAL ARRAY MATRIX EXPERIMENT

6. CONDUCT THE MATRIX EXPERIMENT

7. ANALYZE THE DATA,PREDICT THE OPTIMUM LEVELS AND PERFORMANCE

8. PERFORM THE VERIFICATION EXPERIMENTAND PLAN THE FUTURE ACTION


STEPS IN TAGUCHI METHODOLOGYCOMPANY : ELECTRONICA MACHINE TOOLS, PUNE" ELECTRIC DISCHARGE MACHINE (EDM) OPTIMIZATION AND STABILIZATION "


MAIN FUNCTION : (1) Optimize and Stabilize the EDM

Performance Characteristics namely

a. Material Removal Rate ( MRR )

b. Percent Electrode Wear ( EW )

SIDE EFFECTS : Since this first trial application no other

Quality Characteristics will be observed

FAILURE MODE : Control Factor Levels are selected so that there will not be any failure during

experimentation leading to aborting an

experiment



1. IDENTIFY THE MAIN FUNCTION,

SIDE EFFECTS, AND FAILURE MODE


NOISE FACTORS : (1) Variations in Hardness of material

(2) Variation in Dielectric Bath temperature

TESTING CONDITIONS : Keep sparking time constant

for all experiments

NOISE CAPTURING TEST CONDITIONS :

For each experiment make

4 work pieces under the

following noise conditions






Work piece

No.

Noise Factors

Material Bath Temp.

1

2

3

4

Hard

Hard

Soft

Soft

Room Temp.

Room Temp.

High Temp.

High Temp.

NOISE CAPTURING TEST CONDITIONS :

For each experiment make

4 work pieces under the

following noise conditions

Measure MRR and EW

on these 4 work pieces

QUALITY CHARACTERISTICS : (1) MRR (2) EW







i = 1

MRR= – 10 Log

10

1n---

1

y2---

i = 1

n

= – 10 Log 10

1n--- y2

n

EW

OBJECTIVE FUNCTION :

(1) MRR ---> LARGER - THE - BETTER

(2) EW ---> SMALLER - THE - BETTER








CONTROL FACTORS LEVELS

1 2 3

A. PULSE ON TIME (µSec) 150 200 500

B. GAP CURRENT (Amps) 30 34 50

C. BI-PULSE CURRENT (Amps) 0 1 3









DEGREES OF FREEDOM =1 FOR MEAN AND 2 EACH FOR 3 FACTORS = 7

ORTHOGONAL ARRAYS WITH 3 - LEVEL FACTORS :

NO. OF FACTORS

ORTHOGONAL ARRAY

2-4 5-7 8-13

L9 L18 L27L9




L9 ORTHOGONAL ARRAY

EXPT. NO. A1

B2

C3 4

1 A1 B1 C1 -

2 A1 B2 C2 -

3 A1 B3 C3 -

4 A2 B1 C2 -

5 A2

A2

B2 C3 -

6 B3 C1 -

7 A3 B1 C3 -

8 A3 B2 C1 -

9 A3 B3 C2 -










---> CONDUCT THE 9 EXPTS. OF L9 ARRAY

---> IN EACH EXPT. MEASURE THE MRR AND %EWFOR THE 4 NOISE CONDITIONS OF HARDNESSAND BATH TEMPERATURE




L9 ORTHOGONAL ARRAY AND EXPERIMENTER'S LOG

EXPT. NO.PULSE ON TIME

AGAP CURRENT

BBIPULSE CURRENT

CEmpty

D

30

3450

150150150

200200200

500500500

303450

303450

013

130

301

---

---

---

123

456

789

S / N RATIOn nMRR EW


EXPERIMENTER'S LOG FOR MRR AND %EW

EXPT. NO.ON TIME

ACURRENT

BCURRENT

Cempty

D MRR %EW

1 150 30 0 - 44.34 -22.93

2 150 34 1 - 46.76 -16.78

3 150 50 3 - 49.96 -20.83

4 200 30 1 - 45.57 -7.96

5 200 34 3 - 47.45 -12.05

6 200 50 0 - 49.82 -23.53

7 500 30 3 - 45.80 4.43

8 500 34 0 - 45.10 -16.91

9 500 50 1 - 50.13 -4.61

PULSE GAP BIPULSE S / N RATIO











ASSUMING ADDITIVITY

FACTOR EFFECTS PLOTS

PREDICTOPTIMUM FACTOR LEVELS

PREDICTED IMPROVEMENT


Plots of Factor Effects S/N Analysis of MRR for EDM M/C

CONTROL FACTORS AND THEIR LEVELS

n' M

RR

(d

B)

A1 A2 A3 B1 B2 B3 C1 C2 C344(dB)

45(dB)

46(dB)

47(dB)

48(dB)

49(dB)

50(dB)

51(dB)

52(dB)Average PULSE ON TIME

GAP CURRENT BIPULSE CURRENT


Plots of Factor Effects S/N Analysis of %EW for EDM M/C

CONTROL FACTORS AND THEIR LEVELS

n' %

EW

(d

B)

A1 A2 A3 B1 B2 B3 C1 C2 C3

0(dB)0(dB)

-5(dB)

-10(dB)

-15(dB)

-20(dB)

-25(dB)

Average PULSE ON TIME

GAP CURRENT BIPULSE CURRENT


PREDICTION AND VERIFICATIONMRR AND %EW for EDM Machine

FACTOR

SETTINGS PREDICTED OBSERVED PREDICTED OBSERVED

NOMINAL A2 B2 C2 233 236 4.13 4.0

OPTIMUM A3 B3 C2 319 321 1.75 1.7

% IMPROVEMENT 39% 36% 57% 57%

CONTROL MRR ( ccm / min ) %EW










8. PERFORM THE VERIFICATION EXPERIMENTAND PLAN THE FUTURE ACTION

RESULTS MATCH WELL WITH PREDICTION

ADOPTNEWSETTINGS


STEPS IN TAGUCHI METHODFOR POLYSILICON DEPOSITION IN VLSI



2. IDENTIFY THE NOISE FACTORS,

TESTING CONDITIONS, AND QUALITY CHARACTERISTICS





7. ANALYZE THE DATA, PREDICT THE OPTIMUM CONTROL

FACTOR LEVELS AND PERFORMANCE

8. CONDUCT THE VERIFICATION EXPERIMENT


GasInlet

3-Zone Furnace

Wafers

ToPump

PressureGauge

Schematic Diagram of a low pressure reactor


X

X

X

X

X

X

X

X

X

END 1 CENTRE END 2

Testing conditions -- 3-points on 3-wafers


Control Factors and Their Levels

Starting levels are indicated in italics

CONTROL FACTORSLEVELS

1 2 3

A. Temperature To-25 To To+25

B. Pressure Po-200 Po Po+200

C. Nitrogen No No-150 No-75

D. Silane So-100 So-50 So

E. Settling time to to+8 to+16

F. Cleaning None CM2 CM3


L18 ORTHOGONAL ARRAY

EXPT. NO. 1. A .

2. B .

3. C .

4. D .

5. E .

6. F .

7. G .

8. H .

#1 1 1 1 1 1 1 1 1

#2 1 1 2 2 2 2 2 2

#3 1 1 3 3 3 3 3 3

#4 1 2 1 1 2 2 3 3

#5 1 2 2 2 3 3 1 1

#6 1 2 3 3 1 1 2 2

#7 1 3 1 2 1 3 2 3

#8 1 3 2 3 2 1 3 1

#9 1 3 3 1 3 2 1 2

#10 2 1 1 3 3 2 2 1

#11 2 1 2 1 1 3 3 2

#12 2 1 3 2 2 1 1 3

#13 2 2 1 2 2 1 3 2

#14 2 2 2 3 3 2 1 3

#15 2 2 3 1 1 3 2 1

#16 2 3 1 3 3 3 1 2

#17 2 3 2 1 1 1 2 3

#18 2 3 3 2 2 2 3 1


MATRIX EXPERIMENT

MATRIX EXPERIMENT IS A

– SET OF EXPERIMENTS WHERE SETTINGS ARECHANGED FROM ONE EXPERIMENT TO ANOTHER

MATRIX EXPERIMENT IS USED TO

– STUDY EFFECTS OF CONTROL FACTORS AND NOISE– EVALUATE QUALITY THROUGH S / N RATIOS– DETERMINE BEST S/N RATIO AND PARAMETER SETTINGS

VERIFICATION EXPERIMENT

– CONFIRMS THE ADDITIVITY MODEL– GIVES " GREEN SIGNAL " TO MANUFACTURE


L18 ORTHOGONAL ARRAY AND EXPERIMENTER'S LOGTEMPERATURE COLUMN VARIABLE SHOWS HOW TO ENTER THE EXPT. LOG

EXPT #7 AND #8 SHOW THE EXPERIMENTER'S LOG

EXPT. NO. TEMPERATUREA

PRESSUREB

NITROGENC

SILANED

SETTLING TIMEE

CLEANING METHODF

#1 1-->T0-25 1 - 1 - 1 - 1 - 1 -

#2 1-->T0-25 2 - 2 - 2 - 2 - 2 -

#3 1-->T0-25 3 - 3 - 3 - 3 - 3 -

#4 2-->T0 1 - 1 - 2 - 2 - 3 -

#5 2-->T0 2 - 2 - 3 - 3 - 1 -

#6 2-->T0 3 - 3 - 1 - 1 - 2 -

#7 3-->T0+25 1-->P0-200 2-->N0-150 1-->S0-100 3-->t0+16 3-->CM3

#8 3-->T0+25 2-->P0 3-->N0-75 2-->S0-50 1-->t0 1-->NONE#9 3-->T0+25 3 - 1 - 3 - 2 - 2 -

#10 1-->T0-25 1 - 3 - 3 - 2 - 1 -

#11 1-->T0-25 2 - 1 - 1 - 3 - 2 -

#12 1-->T0-25 3 - 2 - 2 - 1 - 3 -

#13 2-->T0 1 - 2 - 3 - 1 - 2 -

#14 2-->T0 2 - 3 - 1 - 2 - 3 -

#15 2-->T0 3 - 1 - 2 - 3 - 1 -

#16 3-->T0+25 1 - 3 - 2 - 3 - 2 -

#17 3-->T0+25 2 - 1 - 3 - 1 - 3 -

#18 3-->T0+25 3 - 2 - 1 - 2 - 1 -


ADDITIVE MODEL

AN ADDITIVE MODEL ( ALSO CALLED SUPERPOSITION MODEL )

– RELATIONSHIP BETWEEN RESPONSE VARIABLE AND CONTROL FACTORS

– EFFECTS OF CONTROL FACTOR LEVELS IS ESTIMATED SEPARATELY

– PREDICTION BY SIMPLY ADDING INDIVIDUAL FACTOR EFFECTS

THE ADDITIVITY IS INFLUENCED BY THE CHOICE OF

– QUALITY CHARACTERISTICS, S/N RATIO, CONTROL FACTORS / LEVELS

BENEFITS OF ACHIEVING ADDITIVITY :

– PREDICTIONS VALID FOR LAB AND MANUFACTURING CONDITIONS


Plots of Factor EffectsAnalysis of Thickness Data

20.00(dB)

25.00(dB)

30.00(dB)

35.00(dB)

40.00(dB)

A1A2A3 B1B2B3 C2C3C1 D1D2D3 E1E2 E3 F1 F2 F3

Temperature Pressure Nitrogen Silane Settling Cleaning

n'(

dB

)

Average Temperature Pressure

Nitrogen Silane Settling Time

Cleaning Method


Plots of Factor EffectsAnalysis of Surface Defects Data

70.00-(dB)

60.00-(dB)

50.00-(dB)

40.00-(dB)

30.00-(dB)

20.00-(dB)

A1A2A3 B1B2B3 C2C3C1 D1D2D3 E1 E2E3 F1 F2 F3

Temperature Pressure Nitrogen Silane Settling Cleaning

n'(d

B)

Average Temperature Pressure

Nitrogen Silane Settling Time

Cleaning Method


PREDICTION AND VERIFICATION

STARTING CONDITIONS : ( A2 B2 C2 D2 E2 F2 )

SURFACE DEFECTS = 600 / Sq. cm.

THICKNESS VARIATION = 2.8 % (OF MEAN)

OPTIMUM CONDITIONS : (PREDICTION) [ A1 B1 C1 {D2 E2 F2} ]

SURFACE DEFECTS = 7 / Sq. cm.

THICKNESS VARIATION = 1.3 %

(VERIFICATION) UNDER OPTIMUM CONDITIONS :

SURFACE DEFECTS = 1 TO 10 / Sq. cm.

THICKNESS VARIATION = 1.2 - 1.5 %

PREDICTED AND MEASURED RESULTS MATCH WELL.


Case-Study for Robust Circuit Design

# 3 Schmitt Trigger

(Insensitivity to Temperature)


Schmitt Trigger Circuit

Vout



� A typical Schmitt Trigger circuit gives

� Lower Trigger Voltage Vlow

� Upper Trigger Voltage Vhigh

� Design a circuit to give

� Very low temperature sensitivity to temperature

variation between 0 C – 100 C

� Adjust the low threshold trigger voltage to 3.0

(while maintaining the insensitivity to temperature)



Vout


L9 expt. with 1 Noise Factors

Expt.No.

1

2

3

4

5

6

7

8

9

1

1

1

2

2

2

3

3

3

1

2

3

1

2

3

1

2

3

1

2

3

3

1

2

2

3

1

1

2

3

2

3

1

3

1

2

R1 R2 β1 β2

Control Factors Measurements to Capture Noise

Y11 Y12 Y13

Y21 Y22 Y23

Y31 Y32 Y33

Y41 Y42 Y43

Y51 Y52 Y53

Y61 Y62 Y63

Y71 Y72 Y73

Y81 Y82 Y83

Y91 Y92 Y93

T1 T2 T3

Y14

Y24

Y34

Y44

Y54

Y64

Y74

Y84

Y94

T4

Y15

Y25

Y35

Y45

Y55

Y65

Y75

Y85

Y95

T5


L9 expt. with 1 Noise Factors

Expt.No.

1

2

3

4

5

6

7

8

9

470K

1M

220K 150

300

600

R1 R2 β1 β2

Control Factors

220K

220K

470K

470K

1M

1M

220K

220K

220K

470K

470K

470K

1M

1M

1M

150

150

150

150

150

300

300

300

300

300

600

600

600

600

600

“Trigger Voltage (Low)” at

Different Temperatures

0°C

Vlow11

Vlow21

Vlow31

Vlow41

Vlow51

Vlow61

Vlow71

Vlow81

Vlow91

Vlow12

Vlow22

Vlow32

Vlow42

Vlow52

Vlow62

Vlow72

Vlow82

Vlow92

Vlow13

Vlow23

Vlow33

Vlow43

Vlow53

Vlow63

Vlow73

Vlow83

Vlow93

Vlow14

Vlow24

Vlow34

Vlow44

Vlow54

Vlow64

Vlow74

Vlow84

Vlow94

Vlow15

Vlow25

Vlow35

Vlow45

Vlow55

Vlow65

Vlow75

Vlow85

Vlow95

25°C 50°C 75°C 100°C


Circuit Simulation using PSPICE

� Use PSPICE simulator� Each row is one simulation

� In each simulation use 5 different values of temperature

� Collect data for ALL simulations� 9 groups of data (one for each row)

� Do the data analysis – find S/N ratio (Nominal-The-Best type)η = 10 Log10 {µ2/σ2}

� Plot Vout vs- Vin� To show the trigger voltage

� at different temperatures


Schmitt Trigger WorstWorst--CaseCase

Input ramp

Trigger Voltage (Low) at



OptimizedOptimized Schmitt Trigger Circuit

Input ramp

Trigger Voltage (Low) at



Factor Effect Plots for S/N Ratio

R1 R2 β1 β2


Factor Effect Plots for Mean

R1 R2 β1 β2


Taguchi Method Prediction based on Simulations using PSPICE

� Plot Vout vs- Vin� To show the trigger voltage

� at different temperatures

� Find

� Dominant Factors and their Levels

� Predict the best result (at the best settings)

� Adjustment factor

� That affects the mean but not the variance


Optimum Settings

A1 or A2

R1 = 220K or 470K

B2

Beta 2 = 300

Dominant Factors

Adjustment

R2

R2 = 220K to 1M

R1 R2 β1 β2

R1 R2 β1 β2

A R1

B β2


Schmitt Trigger Voltage

� Confirmation Simulations and Results

� Use adjustment parameter “R2” to adjust the Schmitt Trigger Voltage to the desired value of 3.0 volts


Conclusions

�� Taguchi MethodTaguchi Method is the only method that ‘encourages’ noisy inputs during

experimentation

�� ROBUST processes/products


Thank You

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