j ournal of mater ials process ing technology 2 0 6 ( 2 0 0 8 ) 7882

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

The o in

T. Wanga School of Eb Departmen 2 1Rc Departmen al UnXian 71007

a r t i c

Article histor

Received 11

Received in

2 November 2007

Accepted 2 December 2007

Keywords:

Shot peenin

(Shot) peen

Optimisatio

Process mod

Finite eleme

on an

lates

ing p

found byminimising the deviation of the computed deformed shape from the desired shape

subject to certain constraints. This optimal solution of peening parameters can be directly

used for practical operations. An optimisation example for forming a cylindrical shape on

a 76mm76mm3mm sample is provided. The experimental results demonstrate theapplicability of the present optimisation method.

1. In

Bombardinhard shotshape. Thisbeen espepanels.

The keydeterminedesired shbeen throupeen formtance of eheavily depple, VanLumethod for

CorresponE-mail a

0924-0136/$doi:10.1016/g

forming

n

el

nt analysis (FEA)

2007 Elsevier B.V. All rights reserved.

troduction

g the surface of a metal sheet by a stream of smallwith sufcient kinetic energy can form a specicprocess is called (shot) peen forming, which has

cially used for contouring integral aircraft skin

problem for peen forming processes is how toan optimal design of peening parameters for theape. However, in practical applications this hasgh trial and error. Tatton (1986) described shoting in production and emphasized the impor-xperience. Some numerical methods that areendent upon tests were also developed. For exam-chene and Cramer (1996) presented a numericalpredicting peening intensity patterns by assum-

ding author.ddress: tao.wang@brunel.ac.uk (T. Wang).

ing the peen forming process as a linear nite elementsystem responding to the peening induced stresses. Empiri-cal equations determined by physical experiments in BoeingCommercial Airplane Group were relied upon to set up therelationship between the induced stresses and the peen-ing intensity. As recognized in their paper, Homer andVanLuchene (1991) stated that the experimental data arebased on peening of unconstrained specimens but assumedto be applicable for constrained specimens, which may intro-duce error because in reality various constraints, such asgeometry, jigs (pre-stresses), and peening sequences, arepossible.

Wang (2003) and Wang et al. (2006) presented a processmodel and veried it in various experimental conditions withdifferent constraints. This model has also been discussed andfurther developed by Blackwell et al. (2004) of QinetiQ. Usingthe calibrated and veried process model, a non-linear rela-

see front matter 2007 Elsevier B.V. All rights reserved.j.jmatprotec.2007.12.019ptimisation of shot peen form

a,, M.J. Plattsb, J. Wuc

ngineering and Design, Brunel University, Uxbridge UB8 3PH, UKt of Engineering, University of Cambridge, Mill Lane, Cambridge CBt of Aircraft Manufacturing Engineering, Northwestern Polytechnic2, China

l e i n f o

y:

August 2006

revised form

a b s t r a c t

An optimisation method based

and veried process model simu

linear relationship between peeng processes

X, UKiversity,

effective process model is presented. The calibrated

peening on realistic components and provides a non-

arameters and deections. An optimal solution can be

j ournal of mater ials process ing technology 2 0 6 ( 2 0 0 8 ) 7882 79

tionship between the peening parameters and deection ofspecied points can be set up. A constrained optimisation pro-cedure canaccording twill be disc

2. Th

Up to a ceimpacts caof discreteneously anlayer. Basedto model tloading uning paramepressure. Rby multipleloading cycwhich makEach loadinperature prthickness onodal degreperature cathus mimicthis equivais realised bThis leavesdetails of thal. (2006).

3. Th

Three milimin the presYoungs mtension testionship forin an air-blastant 13.67at a distanc

Unconstsamples wa19mm19ing, becausbe approximachine bAlmen gau

As a pacal shape oradius of 60tions. The cchallenge, anormally pwas used toface. As the

measurement was also conducted before peening. The deec-tion was nally taken as the subtraction of the initial reading

he nal one.

The optimisation method

The assumption

ne-dimensional problem (one peening area and oneion as the calibration test), it is found that a non-linearnship

t

+ t (1)

n the peen-formed arc height w and exposure time tboth the experimental results and nite element anal-shown in Fig. 1.a multidimensional problem as shown in Fig. 2, a sim-ationship can be assumed as follows

Aijtj

ij + tj

tj istionion oefcith nd bybecaecti

peenich icon

rices

Them.consequently be used to nd an optimal solutiono specied deection. This optimisation methodussed in this paper.

e process model

rtain intensity of coverage the individual peenn be regarded as acting independently. A numberimpacts can therefore be assumed to act simulta-d their effects are distributed in a specic plasticon this assumption, a static loading unit is found

he macroscopic effect of this shot peening. Theit can be conveniently calibrated from the peen-ters, such as shot radius, mass ow rate and airealistic peening intensities can then be simulatedapplication of this loading unit. The number ofles is in direct proportion to the peening time,es the model applicable to practical applications.g cycle includes two steps. In the rst step, a tem-ole is applied to the section points through thef composite shell elements in ABAQUS when alles of freedom are xed. This application of tem-uses the surface layer to be stretched beyond yield,king the effect of peening. After the application oflent load to induce a plastic layer, the second stepy simply releasing the extra boundary conditions.the material in a deformed conguration. Moree model can be found in Wang (2003) and Wang et

e experimental approach

etre thick aluminium 5251-H22 sheet was usedent study. Its proportional limit is about 103MPa,odulus 69GPa and Poissons ratio 0.33. Uniaxialts were conducted to provide the stressstrain rela-the analysis. Cast steel S660 peenswere employedst machine. The mass ow rate was kept as a con-g/s. The nozzle was kept vertical to the worktablee of 300mm.rained 20psi peening on 76mm19mm3mms used for calibration tests. Only the central areamm was peened, with the rest protected by mask-e the distribution of peens within this area canmated as a uniform distribution for the peeningeing used. Arc height was measured by a digitalge like the normal Almen test.rticular example for the optimisation, a cylindri-n 76mm76mm3mmsampleswith a curvature0mm was desired under the experimental condi-ylindrical shape was chosen because it provides as it is known that uniform unconstrained peening

roduces a double-curved shape. A digital dial gaugemeasure the deformed shape on the peened sur-sample was not absolutely at before peening, the

from t

4.

4.1.

In a odeectrelatio

w = ab

betweecan tyses as

Forilar rel

wi = B

wherepropordeectting coat thetributeerrorsthedesively5% wh

As aof mat

Kt = w

Fig. 1 proble(i = 1,2, . . . , n and j = 1,2, . . . , m) (2)

the exposure time (or a variable which is in directto it) on the jth peening element only, wi is thef the ith node, and Aij and Bij are the non-linear t-ients. This assumption implies that the deectionode can be simply added by the components con-each peening element. This might involve certainuse it is known that the peening sequence affectson.However, as shown inWanget al. (2006), succes-ing on two adjacent areas has a variation of abouts neglectable.venient means, Eq. (2) can be written in the format

(3a)

deection development of a one-dimensional

80 j ournal of mater ials process ing technology 2 0 6 ( 2 0 0 8 ) 7882

Fig. 2 Th

or

K11 K12

K21 K22

. . . . . .

. . . . . .

Kn1 Kn2

where Kij =In the physthe jth elem

4.2. Th

For a givenunique becof w mightprocedure iprocess, thformed shand an opt

f (t) = Kt

subject to s

{tl t

Kt w

where tl anthe maximbe describe

The conguration for an optimisation example.

cretise the 2D blank to peening elements and locate theecic nodes for assessing the deformed shape.termine the shot size and air pressure for the peeningchine being used.nduct FE analysis on each of the peening elements totermine the individual Kij.semble the overall matrix K.termine the optimal t subject to Eqs. (4) and (5).

tep 5 to determine the optimal t, a sequential quadraticmming algorithm is used. Gill et al. (1981) pointed oute conguration for a multidimensional problem.

. . . K1m

. . . K2m

. . . . . .

. . . . . .

. . . Knm

t1

t2

. . .

tm

=

w1

w2

. . .

. . .

wn

(3b)

Fig. 3

(1) Dissp

(2) Dema

(3) Code

(4) As(5) De

In Sprogra(wi/tj) = (Aij/(Bij + tj)) (i=1,2,. . ., n and j=1,2,. . ., m).ical aspects, it means peening to one unit of tj onent can produce a deection of Kij at the ith node.

e optimisation procedure

desired w, the solution to Eq. (3a) is generally notause nmight not be equal tom and the componentsnot be independent. Therefore, an optimisation

s needed to nd an optimal solution t. As a forminge most important concern is the accuracy of thepe. The optimisation problem can be given as toimal t which minimises the target function

w (4)

pecic constraints, for example,

tu

inf (5)

d tu are lower and upper bounds, respectively, isum allowed error. The optimisation procedure cand as follows,

Fig. 4 Thon a centrae computation result for modelling shot peeningl area.

j ournal of mater ials process ing technology 2 0 6 ( 2 0 0 8 ) 7882 81

Fig. 5 The comparison of the desired shape and theexperimental results.

that optimisation methods have progressed tremendously inall problem categories and commented that these develop-ments meaoptimisatiostart fromwrite his oof view, itselected frpractical prforming proemployed.algorithm iminimumFor details

5. Re

For the p76mm76of 600mm,16 peeningelement wThe wholeareas. The

Processquarter ofcomputatioshown in Fto all FEA r

Referrinradius of 60and E is 0mas shown intu are set ttion t is shoto this optialong Sectition of theSections 2relatively laeffects.

It is worthat the opcase. If is scannot be sresult cannpre-stressesingle-curv

6. Co

As demonmethod bavide a prelithe desiredon realisticsimulationa non-linean that the typical person who wishes to solve ann problem would not (and, in our view, should not)scratch to devise his own optimisation method orwn implementation. Therefore, from this pointwas suggested that available routines should beom high quality mathematical software to solveoblems. In the current optimisation work for peencesses, the optimisation functions in MATLAB areParticularly, a sequential quadratic programmingmplemented in a function, constr, is used to nd theof a constrained non-linear multivariate function.of this algorithm, see MathWorks (1997).

sults and discussion

urpose of forming a cylindrical shape onmm3mm samples with a curvature radiusthe 2D shape as shown in Fig. 3 is divided intoelements and 25 nodal points. Only one peening

as peened by masking others in each increment.process was done by incrementally peening all 16shot size and air pressure were set as stated above.modelling was correspondingly conducted for athe model because the sample is symmetric. Then result for modelling peening on a central area isig. 4. The overall matrix K is assembled accordingesults.g to Fig. 3, for a cylindrical shape with a curvature0mm, the component of the desired w at point Am, point B and D is 0.9mm, and point C is 1.2mmsolid lines of Fig. 5(a)(e) for Sections 15. If tl and

o 0 and 60 s and is 0.47mm, the optimal solu-wn in Fig. 3 for each peening element. Accordingmal solution, the experimental results measuredons 15 at 25 points are shown in Fig. 5. The devia-experimental results from the desired shape along4 is a few percent, while Sections 1 and 5 have arger deviation. This could be attributed to the edge

th noting that 0.47mm of is the minimum errortimisation procedure can achieve for this testedet to a smaller value, the constraints givenbyEq. (5)atised. This indicates that a slight double-curvedot be avoided by this unconstrained peening andd peening could be further used to shape a moreed shape.

nclusion

strated in the present work, the optimisationsed on the effective process model is able to pro-minary optimal design of peening parameters forshape. The process model serves like virtual testscomponents and can produce a more accurate

than previous models. From the modelling results,r relationship between peening parameters spec-

82 j ournal of mater ials process ing technology 2 0 6 ( 2 0 0 8 ) 7882

ied for discrete peening areas and deections specied fornodal points can be set up. On the basis of this relationship,a constrained optimisation procedure can be used to ndan optimal solution which can be directly used for practicaloperations.

Acknowledgements

This paper is based on a project initially carried out inCambridge University Engineering Department, which wassupported by Airbus UK, Cambridge Overseas Trust, and Uni-versities UK. The authors would like to thank Andy Levers andDavid Gardiner for their useful discussion during the project.

r e f e r enc e s

Blackwell, P.L., Grifths, M.D., Ward, T., Gardiner, S., 2004. Acomputer modelling capability for shot peen forming. MetalFinishing News 5 (3), 1214.

Gill, P.E., Murray, W., Wright, M.H., 1981. Practical Optimization.Academic Press, London.

Homer, S.E., VanLuchene, R.D., 1991. Aircraft wing skincontouring by shot peening. Journal of Material ShapingTechnology 9 (2), 89101.

MathWorks, MATLAB Optimisation Toolbox. Users Guide Version5, 1997.

Tatton, R.J.D., 1986. Shot peen forming. In: Meguid, S.A. (Ed.),Impact Surface Treatment (The Second InternationalConference on Impact Treatment Processes, CraneldInstitute of Technology, Bedford, UK). Elsevier, London, pp.134143.

VanLuchene, R.D., Cramer, E.J., 1996. Numerical modelling of awing skin peen forming process. Journal of MaterialsEngineering and Performance 5 (6), 753760.

Wang, T., 2003. Numerical simulation and optimisation of shotpeen forming processes. PhD Thesis. University ofCambridge.

Wang, T., Platts, M.J., Levers, A., 2006. A process model for shotpeen forming. Journal of Materials Processing Technology 172(2), 159162.

The optimisation of shot peen forming processesIntroductionThe process modelThe experimental approachThe optimisation methodThe assumptionThe optimisation procedure

Results and discussionConclusionAcknowledgementsReferences