Optimising Manufacture of Optimising Manufacture of Pressure Cylinders via DoEPressure Cylinders via DoE

Dave Stewardson, Shirley ColemanDave Stewardson, Shirley Coleman

ISRUISRU

Vessela StoimenovaVessela Stoimenova

SU “St. Kliment Ohridski”SU “St. Kliment Ohridski”

This presentation was partly supported with This presentation was partly supported with

funding funding

from thefrom the

'Growth' programme of the European 'Growth' programme of the European

Community, Community,

and was and was

prepared in collaboration byprepared in collaboration by

member organisations of the Thematic Network - member organisations of the Thematic Network -

Pro-Enbis - EC Pro-Enbis - EC

contract number G6RT-CT-2001-05059.contract number G6RT-CT-2001-05059.

BackgroundBackground

•German Company with site in Northumberland UK

•Major producer of safety and breathing equipment

•Fire-fighters a major customer

Main ObjectivesMain 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 CylindersCompleted Cylinders

•Systematic Investigation To find optimum settings

•Cylinders normally tested to Destruction

•Second objective:

Find a non-destructive test!

Main Rationale of Designed ExperimentsMain 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 machineTesting machine

New Test

Permanent Expansion after Auto-Frettage

Via

Water displacement test

Auto-Frettage ProcedureAuto-Frettage Procedure

•Fill cylinder with water

•Now Pressurise

•This deforms the liner

•Stresses Carbon fibre

•Improves cylinder resistance

Four factorsFour factors

•Carbon Fibre

•Winding Tension

•Auto-Frettage Pressure

•Resin Tack ‘Advancement’ Level

Factor Label Low (-1) High (+1)Carbon Fibre UTS UTS 5.4 Gpa 5.85 GpaResin Tack Level RT Low HighWinding Tension WF 3.6 kg 4.5 kg

Auto-Frettage pressure AF 580 bar 600 bar

Experimental factors and their settingsExperimental factors and their settings

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

DoEDoE

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

STEPSSTEPS

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=B0+B1*A+B2*B+B12*A+error

Factors and responses

TWO-LEVEL DESIGNSTWO-LEVEL DESIGNS

run A B C D

1 -1 -1 -1 -1

2 1 -1 -1 -1

3 -1 1 -1 -1

4 1 1 -1 -1

5 -1 -1 1 -1

6 1 -1 1 -1

7 -1 1 1 -1

8 1 1 1 -1

9 -1 -1 -1 1

10 1 -1 -1 1

11 -1 1 -1 1

12 1 1 -1 1

13 -1 -1 1 1

14 1 -1 1 1

15 -1 1 1 1

16 1 1 1 1

ANALYSIS MATRIXANALYSIS MATRIXrun I A B C D AB AC AD BC BD CD ABC ABD ACD BCD ABCD

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

2 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1

3 1 -1 1 -1 -1 -1 1 1 -1 -1 1 1 1 -1 1 -1

4 1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 1

5 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1

6 1 1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 1

7 1 -1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 -1 1

8 1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 -1 -1

9 1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 1 1 -1

10 1 1 -1 -1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1

11 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1

12 1 1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1

13 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 1

14 1 1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 -1 -1

15 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1

16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

THE MODEL OF THE THE MODEL OF THE EXPERIMENTEXPERIMENT

Y = X*B + experimental errorX16x16 - design matrix

B - vector of unknown model coefficients

Y - vector consisting of the 16 trial response observations

XtX = I - orthogonal coding

Full factorial designsFull 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 2k runs

we can estimate all k main effects, h-factor interactions and one k-factor interaction

cannot estimate the experimental error if we do not have replications

kh

Fractional Factorial DesignsFractional 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

224-14-1fractional factorial designfractional factorial design

run A=BCD B=ACD C=ABD D=ABC AB=CD AC=BD AD=BC I=ABCD1 -1 -1 -1 -1 1 1 1 14 1 1 -1 -1 1 -1 -1 16 1 -1 1 -1 -1 1 -1 17 -1 1 1 -1 -1 -1 1 110 1 -1 -1 1 -1 -1 1 111 -1 1 -1 1 -1 1 -1 113 -1 -1 1 1 1 -1 -1 116 1 1 1 1 1 1 1 1

ConfoundingConfounding

I = ABCD : generating / defining relation

Set of aliases:

{ A=A2BCD=BCD;

B=AB2CD=ACD; C=ABC2D=ABD; D=ABCD2=ABC}

AB=CD; AC=BD; BC=AD

223 3 full factorial designfull factorial design

run I B C D CD BD BC BCD

1 1 -1 -1 -1 1 1 1 -12 1 1 -1 -1 1 -1 -1 13 1 -1 1 -1 -1 1 -1 14 1 1 1 -1 -1 -1 1 -15 1 -1 -1 1 -1 -1 1 16 1 1 -1 1 -1 1 -1 -17 1 -1 1 1 1 -1 -1 -18 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!

Run UTS RT WT AF1 5.4 Gpa Low 3.6 kg 580 bar

2 5.85 Gpa Low 3.6 kg 600 bar

3 5.4 Gpa High 3.6 kg 600 bar

4 5.85 Gpa High 3.6 kg 580 bar

5 5.4 Gpa Low 4.5 kg 600 bar

6 5.85 Gpa Low 4.5 kg 580 bar

7 5.4 Gpa High 4.5 kg 580 bar

8 5.85 Gpa High 4.5 kg 600 bar

Real Factor settings

Orthogonal Array

Orthogonal Array with ResultsOrthogonal Array with Results

Run UTS RT WT AFUTSxRT WTxAF

UTSxWT RTxAF

RTxWT UTSxAF

Cycle Life Exp’n

1 -1 -1 -1 -1 1 1 1 5595 54.7

2 1 -1 -1 1 -1 -1 1 6200 55.3

3 -1 1 -1 1 -1 1 -1 6517 64.3

4 1 1 -1 -1 1 -1 -1 6210 54.9

5 -1 -1 1 1 1 -1 -1 6334 51.5

6 1 -1 1 -1 -1 1 -1 4935 41.5

7 -1 1 1 -1 -1 -1 1 8004 50.7

8 1 1 1 1 1 1 1 5528 54.7

InteractionsCoded Factor settings

Orthogonal ArrayResults

Factor Expansion Cycle LifeUTS -3.7 -894RT 5.4 799WT -7.7 70AF 6 -41

UTSxRT WTxAF 1 -497

UTSxWT RTxAF 0.7 -1043

RTxWT UTSxAF 0.8 333

Effect

Calculated EffectsCalculated Effects

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2

Normal Scores

Eff

ect

in g

ram

mes

WT

AFRT

UTS

Half-Normal plot of Permanent Expansion Half-Normal plot of Permanent Expansion effectseffects

Permanent ExpansionPermanent Expansion

•Predicted by all the Main-effects alone

Cycle LifeCycle Life

• Effected by ‘Interactions’

Predictive EquationPredictive 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 LifeCycle 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

4500

5000

5500

6000

6500

7000

7500

0

Eff

ec

t in

Cy

cle

s

WT High WT Low

UTS High UTS LOW

Interaction PlotInteraction Plot

FindingsFindings

•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 isminimised, hence giving speedier andcheaper results.

The results can be used to predictoutcomes within the entire experimentalrange.

We can identify the most importantfactors influencing outcomes over a rangeof conditions.

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

The effect of changing one parameter inrelation to the setting of another can beestimated.

We can estimate levels of backgrounduncertainty (experimental error).

We can often estimate effects of factors notincluded in the design, provided they are alsomonitored and measured.

Where there are multiple responses, we donot need to know which measured outcome iscritical at the outset.

We can overcome human errors such as theincorrect setting of parameters.

The method is ‘robust’ in the sense that lackof control over the parameters beinginvestigated is not fatal.

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