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, '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

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 Tested by varying internal pressure 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

FactorLabelLow (-1)High (+1) Carbon Fibre UTSUTS5.4 Gpa5.85 Gpa Resin Tack LevelRTLowHigh Winding TensionWF3.6 kg4.5 kg Auto-Frettage pressureAF580 bar600 bar Experimental 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

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

TWO-LEVEL DESIGNS

ANALYSIS MATRIX

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 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

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

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

2 3 full factorial design

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 with Results

Calculated Effects

Half-Normal plot of Permanent Expansion effects

Permanent Expansion Predicted by all the Main-effects alone Cycle Life Effected by ‘Interactions’

Predictive Equation Permanent Expansion = (UTS) + 2.7(RT) (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

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.