Optimising Manufacture of Pressure Cylinders via DoE

Dave Stewardson, Shirley Coleman ISRU Vessela Stoimenova SU “St. Kliment Ohridski”

This presentation was partly supported with funding from the 'Growth' programme of the European Community, and was prepared in collaboration by member organisations of the Thematic Network Pro-Enbis - EC contract number G6RT-CT-2001-05059.

Background

•German Company with site in Northumberland UK •Major producer of safety and breathing equipment •Fire-fighters a major customer

Main Objectives

•Product Improvement •Compressed Air Cylinders •Carbon Fibre - Resin matrix is used to wrap Seamless Aluminium liner •‘Wrapping’ process

critical

for producing Strong cylinders

Completed Cylinders

•Systematic Investigation To find optimum settings •Cylinders normally tested to Destruction •Second objective: Find a non-destructive test!

Main Rationale of Designed Experiments

•Experiment over a small balanced sub set of the total number of possible combinations of factor settings •Minimum effort - Maximum Information

•Sub-sets called Orthogonal Designs •Means ‘balanced’ •All combinations of factors investigated over an equal number of all the others •Known since 1920s after Fisher (UK) •Made Popular by Taguchi, a Japanese Engineer

•Idea here to get a good mathematical model that predicts effect on cylinder of changing various factors •We can then find the optimum in terms of safety Vs profit Vs ability to make it •Minimum number of trials to do this

•Want to Maximise life of cylinder •European Standard = prEN 12245 •Tested by varying internal pressure 0 - 450 Bar up to 15 cycles per minute up to total of 7500 cycles •MUST pass 3750 cycles or Fail test

Testing machine

New Test

Permanent Expansion after Auto-Frettage Via Water displacement test

Auto-Frettage Procedure

•Fill cylinder with water •Now Pressurise •This deforms the liner •Stresses Carbon fibre •Improves cylinder resistance

Four factors

•Carbon Fibre •Winding Tension •Auto-Frettage Pressure •Resin Tack ‘Advancement’ Level

Experimental factors and their settings

Factor

Carbon Fibre UTS Resin Tack Level Winding Tension Auto-Frettage pressure

Label

UTS RT WF AF

Low (-1)

5.4 Gpa Low 3.6 kg 580 bar

High (+1)

5.85 Gpa High 4.5 kg 600 bar

If we choose only 2 levels of each Factor the total possible combinations is 16 We will run half of these, a balanced sub set of the ‘full factorial’ 8

DoE

 The statistical design of experiments is an efficient procedure for planning experiments so that the data obtained can be analyzed to yield valid and objective conclusions

STEPS

   Determine the objectives Select the process factors Well chosen experimental designs maximize the amount of information that can be obtained for a given amount of experimental effort   The statistical theory underlying DOE generally begins with the concept of process models   Linear models, for instance: Y=B 0 +B 1* A+B 2* B+B 12* A+error Factors and responses

run 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9

16

A

TWO-LEVEL DESIGNS

-1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 B -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 C -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 D -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1

ANALYSIS MATRIX

run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

16

I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1

A -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 B -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 C -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 D 1 1 1 1 1 1 1 1 -1 AB 1 AC 1 AD 1 BC 1 BD 1 CD 1 ABC ABD ACD BCD ABCD -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 1 1 -1 1 1 -1 1 -1 -1 1

THE MODEL OF THE EXPERIMENT

   Y = X*B + experimental error X 16x16 - design matrix B - vector of unknown model coefficients  Y - vector consisting of the 16 trial response observations  X t X = I - orthogonal coding

Full factorial designs

 A design with all possible high /low combinations of all the input factors is called full factorial design in two levels   If there are

k

factors, each at 2 levels, a full factorial design has 2

k

we can estimate all

k

runs

k

main effects,

h

factor interactions and one

k-

factor interaction  cannot estimate the experimental error if we do not have replications

Fractional Factorial Designs

 A factorial experiment in which only an adequately chosen fraction of the treatment combination required for the complete factorial experiment is selected to be run  balanced and orthogonal

2

4-1

fractional factorial design

run 10 6 7 11 13 16 1 4 A=BCD B=ACD C=ABD D=ABC AB=CD AC=BD AD=BC I=ABCD

-1 -1 -1 -1 1 1 1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1 1 1 1 1 1 1

Confounding

 I = ABCD : generating / defining relation  Set of aliases: { A=A 2 BCD=BCD; B=AB 2 CD=ACD; C=ABC 2 D=ABD; D=ABCD 2 =ABC}  AB=CD; AC=BD; BC=AD

run 1 2 3 7 8 6 4 5 I

2

3

full factorial design

1 1 1 1 1 1 1 1

B

-1 1 -1 1 -1 1 -1 1

C

-1 -1 -1 -1 1 1 1 1

D

-1 -1 -1 -1 1 1 1 1

CD

-1 -1 -1 -1 1 1 1 1

BD

-1 1 -1 1 -1 1 -1 1

BC

-1 1 -1 1 -1 1 -1 1

BCD

-1 1 -1 1 -1 1 -1 1

Effects are calculated by taking the average of the results at one level from the average at the other It is all very simple!

Orthogonal Array

Real Factor settings Run 6 7 8 1 2 3 4 5

UTS

5.4 Gpa 5.85 Gpa 5.4 Gpa 5.85 Gpa 5.4 Gpa 5.85 Gpa 5.4 Gpa 5.85 Gpa

RT

Low Low High High Low Low High High

WT

3.6 kg 3.6 kg 3.6 kg 3.6 kg 4.5 kg 4.5 kg 4.5 kg 4.5 kg

AF

580 bar 600 bar 600 bar 580 bar 600 bar 580 bar 580 bar 600 bar

Orthogonal Array with Results

Run 1 2 3 4 5 6 7 8 UTS -1 1 -1 1 -1 1 -1 1

Orthogonal Array

Coded Factor settings Interactions RT -1 -1 1 1 -1 -1 1 1 WT -1 -1 -1 -1 1 1 1 1

Results

AF -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1

UTSxRT WTxAF UTSxWT RTxAF RTxWT UTSxAF

1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 1

Cycle Life

5595 6200 6517 6210 6334 4935 8004 5528

Exp’n

54.7

55.3

64.3

54.9

51.5

41.5

50.7

54.7

Factor UTS RT WT AF

Calculated Effects

Expansion Effect Cycle Life

-3.7

5.4

-7.7

6 -894 799 70 -41 UTSxRT WTxAF UTSxWT RTxAF RTxWT UTSxAF 1 0.7

0.8

-497 -1043 333

Half-Normal plot of Permanent Expansion effects

6 5 8 7 2 1 4 3 0 0 0.5

UTS RT AF 1

Normal Scores

1.5

WT 2

Permanent Expansion

•Predicted by all the Main-effects alone

Cycle Life

• Effected by ‘Interactions’

Predictive Equation

Permanent Expansion = 53.54

-

1.85(UTS)

+

2.7(RT)

-

3.85(WT)

+

3(AF) + e UTS, RT, WT, AF = 1 or -1

Cycle Life

•Need to do four further tests to ‘untangle’ the interactions •However a plot of the UTS x WT interaction is given next – this assumes that the RT x AF interaction doe not exist

Interaction Plot

7500 7000 6500 6000 5500 5000 4500 0 UTS High W T High UTS LOW W T Low

Findings

•We can link the tests completely once the interactions are untangled •We can already predict how the factors effect Permanent Expansion •So we will be able to use the new test as a substitute for the destructive test

•By choosing the ‘best’ settings for the manufacturing process, maximising Cycle life against cost, we can then use the new test.

•For example: we know that if we choose mid levels for WT and AF then we can already predict Cycle life directly from the Permanent expansion alone.

•In that case we know that as Permanent Expansion goes up by 1 unit then: •Cycle life goes up by at least 195 cycles, and by as much as 250 cycles, on average.

Benefits The number of trials or experiments is minimised, hence giving speedier and cheaper results.

The results can be used to predict outcomes within the entire experimental range.

We can identify the most important factors influencing outcomes over a range of conditions.

The effect of changing several parameters at the same time can be estimated.

The effect of changing one parameter in relation to the setting of another can be estimated.

We can estimate levels of background uncertainty (experimental error).

We can often estimate effects of factors not included in the design, provided they are also monitored and measured.

Where there are multiple responses, we do not need to know which measured outcome is critical at the outset.

We can overcome human errors such as the incorrect setting of parameters.

The method is ‘robust’ in the sense that lack of control over the parameters being investigated is not fatal.

We can accurately estimate the cost of the experimental programme in advance.