optimising manufacture of pressure cylinders via doe
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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.