Evaluating the Contributions of Process Parameters in SLA Using Artificial Neural Network

Copyright 0 IFAC Inte lligent MaJlufaclUring Systems, Seoul, Korea, 1997

EVALUATING THE CONTRIBUTIONS OF PROCESS PARAMETERS IN SLA USING ARTIFICIAL NEURAL NETWORK ·W. S. Park. ·5. H. Lee. ··H. S . Cho. and ···M. C. Leu • : Graduate students, KAlST, Korea; .. : Professor, KAlST, Korea; ••• : Professor. NJn. USA Department ofMechanical Engineering KoreaAdvanced Institute ofScience and Technology Tel: +81-042-869-3153; Far: +81-41-869-3210; E-mail: [email protected] Department ofMechanical Engineering N€W Jusey Institute of Technology Tel: +1-101-596-3335; Far: + 1-101-596-5601; E-mail: mleu@nsjgov

Abstract: Though SLA(Stc:reolithograpby Apparatus) is being recognized as an innovative technology, it still can not be used to fully practical applications since it lacks of dimensional accuracy compared to conventional processes. In order to improve the acc:uracy of the SLA, this paper quantitatively evaluates bow largely eacb process parameter of the SLA contributes to the part acc:uracy. For this pupose, a multi-layered perceptroD is designed and uained by a set of sample patterns obtained via Taguchi's experiment planning. whicb estimates the dimensional errors of the test part, -letter-H- part from process parameters. Since the patterns are sparsely distributed. very careful design of the network is performed. Based upon the results obtained from the neural network estimator, a quality index of the part is evalu.atcd. through whicb contribution of eacb process parameter is evaluated and discussed in detail. Keywords: Rapid prototyping. Stereolithography, Process analysis, Diagnostic part

is being used only for a few applications since the accuracy of its products is still not high enough. Thus, many researcbers have tried 10 improve SLA accur.ICJ' through various approaches.

1. INTRODUCTION J. J Motivation RPD(rapid product development) is an emerging concept for global marketing and manufacturing. which can be constructed through effective organization of RPD network coosisting of solid modeling, CAE. CA reverse engineering. CA measurement and inspection. rapid machining. rapid prototyping. and so on. RP(Rapid Prototyping) is such technology that produces prototype parts in much shorter time than traditional machining This technology includes processes.

1.2 Related works on SLA part accuracy On the improvement of SLA part ac:curacy. there

have been several researches which can be classified into three categories as foUows: 1) Accuracy improvement by resin development: 1"""" (Jacobs, 1993) and Schulthess et al. (Schullhess, +) rq><>nee! that pans build from epoxy resin show rugher accwac:y than those from acrylate resin.

SLA(stA:reolithogr.lphy apparatus), LOM(laminaled object manufacturing), BPM(ballistic particle manufacturing), SLS(selective laser sintering), IDp(thn:e dimcnsiooaJ printing), FDM(fused deposition manufacturing), among which SLA sbows the best accur.ICJ' of the shapes ofpans[I,2).

2) Accvracy improvement by HIW or SIW development: Developments of higher performance servo controller and laser scanning system aided SLA 10 make more 3CC\1I1W: pans (lacobs, 1995). mien et al. (Ullett, 1994) proposed a new hatching

In spite of its potential usage to variety of areas.. SLA

189

L.....

scheme to reduce warpage in SLA.

m,,,... (X .Y .u""."

.~~

3) Accuracy improvement by SLA parameter tuning: Pahati and Dickens (Pahati and Dikens. 1995) found that there exits an optimal layer thickness for given hatch spacing. Cbanoff et al. (Cbanoff et al.) reported that sh.rinkage and warpage can be reduced by selecting appropriate scanniog speed of laser

", D"i/I

beam. hquld p holopotrm • •

In order to improve pan accuracy of SLA, here an approach that ana1yzes the contributions of process parameters to part ac:curacy is proposed, which can be classified to be one of the third approach described in section 1.2.

Fig. I

A schematic drawing of SLA

2.2 Process parameters ofSLA

In order to evaluate the contributions of SLA parameters to part accuracy, a multi-layered percepuon is utilizc:d. which models the relationships between the: dimensional errors of a standard pan and the: SLA parameters. To minimize the required volume of training patterns. Taguchi's experiment planning technique is used. By the experiment plan.niDg. the network can be trained by only 18 sets of patterns. which is quite notable.

There are three: kinds of parameters in SLA: pari parameters, support parameters, and reCOlJI paramelers, among which pan panmeterS arc: ~ most important ones that affect the accuracy of built partS in SL process. Thus, through the fine selection of part parameter, SLA can build parts more accurately, which is the point of this paper. Part parameters include IQ)If!r Ihickness. holch spacing. Ji/J spacing, border overcurt!, hatch overcure, and Jill cure depth. £oyer thickness is the depth of a layer, which is such region that is solidified at the same elevation. Spacing is the distance between a couple of adjacent strands which is the narrow region solidified by the laser scanning as shown in Fig. 2. If the stJand is located at the top or bottom surface of pan, spacing is called Jill spacing otherwise hatch spacing. Cure depth is the depth of strands. If the strand is located at the top or bottom surface of part, cure depth is calledJiIl curt! deplh. Overcure is the depth that a strand pierces into the lower adjacent layer. If it is located at the lateral boundaries, overcure is called border overcurt!, otherwise hotch ov(!/'CUr(!. In this paper, fill cure depth(DF) is selected to be 0.004 larger than fill cure deptb(UF) usually.

By aid of the generalizing perfOrtlWlce of ~ network, the contribution of each parameter IS determined by using a quality index which is defined iD this paper. Through the results of the analysis, layer thickness is found to be the major parameter that affects part accuracy more significantly than any other parameters.

2. STEREOLrIllOGRAPHY 2.1 Working principle ofSLA As shown in Fig. I, SL process utilizes visible or ultraviolet(UV) laser and scanning mechanism to selectively solidify liquid photo-curable resin and form a layer whose cross-sectional shape is previously prepared from CAD data of the product to be produced. Through repeating the forming layers in a specified direction, desired 3~nsiona1 shape is constructed layer by layer. This process solidifies the resin to 95% of full solidification. After building. the built part is put into an UV oven to be cured up

lis.,

focusing

"I"IS

solidl"ted ,.sin (str'nd)

.,.,,-~-

to 1000/0.. i.e. post-curing process.

1Ir-' 1 -"--~=:;1 Spicing

Fig. 2 Process parameters in SLA

190

3. PROCESS ANALYSIS USING 1.3 "utter-H" part : a standtvd geo~1ry

ARTIFICIAL NEURAL NETWORK

Genel3lly. in order to evaluate the acauacy of a 3dimensional shape. a lot of dimensional values _ l i n g the part geometry an: _ _ For example, wbcn the user-pan(GargiuJo aDd Ed. 1991) is under test. 110 dimensions should be measured. and aoalyzed, and six djmensions for a ..k:utr-H" pan(Pang et al .• 1995). This ·letter-II" part is a much more simple part than the former ODe as shown in Fig. 3. "Letter-H" part indicates reliably the distortion and shrinkage charaacristics of SLA with its simple shape and is easy to mcasurt. whose five dimensjoos are used for charac:terizing its dimensional aa:uracy. Thus, the "Ietter-H" part is chosen as a standardized test part. Its shape and characteristic dimensions are presented iD Fig. 3. 'The characteristic dimensions are denoted by H~op. B-IDP. Waist, AItkk, and lAteral, among which the A.1Ikk is utilized to replacc: the Foot, presented in Fig. 3, because of its poor repeatability.

3. J Training the neural network using Taguchi's experi~nt planning

For the relationship between process paramc:lerS and part dimensions, a neural network is to be constructed and trained by experimental data, which associates six categories of dimensional errors with the ....,... _ The type of DCUral network to be used here is a multi-layered pC:lceptron. A5 shown iD the Fig. 4, the network inputs., r=(Xt . xz .. ··.x.). are the process parameters and

=

the network outputs. Y (y> •y. ... '. )'S ) . "'" the dimensional errors of the "letter-H" pan described in sections 2.2 and 2.3. 1'hcre are six process pamoeters to be tested and five part dimensions to be measured. These large numbers of process parameters and part dimensions lead us to the necessity of great Dumbers of experiments and measurements. For a series of full factorial experiments., h~ experiments and 5·

~------<~------~

04

measu.rements should be performed.. where

~j

represents the number of levels of parameter i UDder test. If the numbers of levels, ~ , are set to be three

CAD dala(solid line) and built geometry(dotted line) ofa "Ietter-H"

equally for all parameters, it needs to perform 3' (729) experiments and 5'3' (= 3645). Therefore., it needs to reduce the number of experiments.

Fig. 3

Table I Trials

I 2 3 4 5 6 7 8 9 10

II 12 13 14 15 16 17 18

pan

Employed Orthogonal array:

layer

border

thickness

overcun:

hatch overam:

OJI04 0.008 0.012 0.004 0.008 0.012 0.004 0.008 0.012 0.004 0.008 0.012 0.004 0.008 0.012 0.004 0.008 0.012

0.005 0.009 0.013 0.005 0.009 0.013 0.009 0.013 0.005 0.013 0.005 0.009 0.009 0.01 3 0.005 0.013 0.005 0.009

.().004 .().001 0.003 .().001 0.003 .().004 .().004 .().001 0.003 0.003 .().004 .().001 0.003 .().004 .().001 .().001 0.003 .().004

Ll8

£unit : inch)

fill cure

fill cure

depth

depth

(UF)

(OF)

0.003 0.007 0.01l 0.007 0.01l 0.003 0.011 0.003 0.()()1 0.007 0.01l 0.003 0.003 0.007 0.01l 0.01l 0.003 0.007

0.007 0.01l 0.015 0.01l 0.015 0.007 0.015 0.007 0.01l 0.01l 0.015 0.007 0.007 0.01l 0.015 0.015 0.007 0.01l

191

fill spacing

baJch spacing

0.003 0.006 0.010 0.010 0 .003 0.006 0.006 0.010 0.003 0.006 0.010 0.003 0.010 0.003 0.006 0.003 0 .006 O.oIO

0.002 0.006 0.010 0.010 0.002 0.006 0.010 0.002 0.006 0.002 0.006 0.010 0.006 0.010 0.002 0.006 O.oIO 0.002

that can be previously determined based upon the magnitudcs of measurement error contained in training input patterns.

To set out an experiment plan reducing a number of experiments without the loss of pbysical characteristics of the process.. Taguchi's experiment planning metbod(Roy, 1992) is adopt
Fig. 5 presents the network errors evaluated by Eq. 2 while learning in case when the number of the nodes 11 of the hidden layer is varied from 3 10 7 . Fig. 5(a) denotes the case of r? "" 0 .3, a "" 0.3, whicb Fig.5(b)isthatfor " =0.1, a =0.3 . The mean magnitude of noises contained in the training patterns are formed to be .s J.UD which can be OODvertcd to be normalized error 0.015. From the figures.. it is easily seen that the network slightly UDderfits the training patterns in the case which n =< 3 and overfits in the cases which n =< 5,6,7. Thus, the optimal number of hidden nodes is selected to be 4, i.e ,,=< 4.

The neural network. estimator is trained by using 18 .... of input/OUIpUt pal1enIS. The system architcc\Ulc of the network. is shown in Fig.4. This network architecture known as multi~layered perc:eptron (MLP) is one of the most widely known networks. To tnlin this network, the bac:k~propagation (Haykin, 1994) learning rule with a momentum term is used in updading the weights as fOUOM: .6. m J/(n

i!E

+ 1) = -r?--(n) + a.6.w J/ (n)

om

wbere

E=L,.," i

=

(1)

)1

,

Ile'll

(2)

ji' - ji'" ,

(3)

....

Fig. 4 Newal network. estimating the dimensional errors of built pans

is the synaptic weight of synapse j belonging to , Amji(II}and Am jl( II + 1) are the incremental weight changes at step n and n+ 1 respectively, " is the learning rate, and a is the momentum rate. yl is the estimated output of pattern j and y/.' is the output pattern. t»

j/

neuron j

71 '" 03

•, •

.,-_.,..:,1_-,~ 1+ exp[ -(net + 8)}

,,,·3 ..

•

o ,E 0.01

p'

o

No.of.poch,

(al " '" 0.1

(4)

(r

'"

"i"

,., ,. , ",

•

°0.01 E

,

•

•

In order 10 prevent both of overfitting and underfitting. the numbers of hidden layers and hidden nodes "'" caruutJy selected(Hush, 1993). Since the number of levels of each parameter is three, which is quite small, the number of hidden layers is fixed to ODe. And various numbers of bidden nodes are tried and. checked to investigate if the energy represented as Eq. 2 converges to a specified value

03

'"

0.1

~

Mt j = ~ W Xj, Xi

is the inputs of neuron j and 8 is the &~t bias term. where

0.1

V

Through the tests on the proper number of hidden nodes. a single hidden layer and four bidden nodes are adopted. In learning of neural network estima1or, learning and momentum rate are selected as 0.1 and 0.3 respectively. The adopted sigmoid activation function is shown below:

f(net) =

a '" 03

o.oolL~_ _~,.-~.".,.-~,=_~~

o

10000

20000

30000

.0000

No. of epoch,

(b)

Fig. 5

192

Convergences of the tested neural networks

3.2 Evaluating contributions of process paramelers to the quality

In order to evaluate the quality of a built part. it oeeds to define a quality index that indic:ates bow ac:cura.tely or erromoously the part was builL To this eod, it is natural to ddiDe the quality index to be the sum of squares of the dimensional errors as foUows :

the standard H-part with respect to layer thickness and batcb overcure whicb are proved to be most importaDL As can be seen from the Figs.' (a) &-. (b), the dimensional erroI1 of the H·top and waist tend to decrease for smaller values of the two par.uoettrS. On the other band. the ankJe error sOOvr'S that there exists an optimal layer thickness for given range of the batch overcure, which gives the minimal error value.

(5) (x 10-6)

where y = (y ... ·oY ) is the dimensional errors of a pan. Once ~ network estimatioD is trained. it can be considered as a fuoction of process parameters ;

thi

,. 800 r - - - - - - - - - - - - , "C 600 o ] 400 '0

"u

o 200

y = NNE(i)

(6)

where the function NNE represents the relationship between the dimensional error and process parameters. Thus., the quality index can be rewritten as a com)X)Sition as foUows :

J(Y ). J (NNE(ii»

Fig. 6

,.

o

Contributions of the process parameters

(1)

The function representint the contribution of the ith parameter x, can be defined over a finite range

[x,aA ,

x,- ] by

(8)

(a)

H-top

(b)

Waist

In the above, the jth value of the x," xlj is defined by

. r.-ar - x~'"

x'..). =X~"+ • ,

m

' x j , j= 1.2,···,m

(9)

and i = (x,0 ,. . .• x6) are the nominal process parameters. wwch are recommended by resin suppliers and widely utilized by users., and m is the number of non-overlappiog partitions [XiJ-I, XIJ }, whose union becomes the whole range of parameter i,

[x,- , r;--] . Though evaluating the Eq. 8, the contribution of each parameter can be determined. Fig. 6 presents the contributions of parameters whicb are evaluated by the above Eqs. 8 and 9. The figure shows that the most important parameter is the layer thickness and hatcb overcure is the secondary. The rest of the parameters is found to be relatively less influential Figs. , present the estimated dimensional errors of

(c) Ankle Fig. , Error estimations with respect to layer thickness and batch overcure

RP&M technologies., ASME Press. !Gm, I., S. N. Hong, and I. H. Paik(1996), A study 00 algorithm developmeot of offset da1a

4 . CONCLUSION In order 10 evaluate the COOtn"butiODS of SLA parameters to part ac
generation in Stueolitbograpby, JOunlal of the Konan Society of Precision Engineering, 13, 9, SepIember. Lcslie, H., E. Gargrd>, and M Keefe(I995), An experimental study of the parameters affecting curl in pans created using Stereollthography,

process par.IlDCICrs. To minjmiu the required volume of training patterns., Taguchi's experimeot planning technique is used. Sioc:e the patterns are sparcely distributed, very card'ul design of the network is performed. which is for avoiding overfitting and UDder:6tting. For fitting the effects oC six parameters. only 1g sets of patterns are needed, which is quite DOtable.

The sixth international conferenc~ on Rapid Prototyping. Lcu, M C., D. H. Seba.dia o , and W. L. Yao(l996) Sreolithography rapid prototyping technology: characteristics, applications and R&D needs. Nguyea, H., J. Richter, and P. F. JacOOs(l992), Rapid prototyping and manufachlring: Jundam~ntals of SI~rt!olithography, SME. Dearborn. Ml.

By using the t.rainc:d network, a quality index is evaluated over the wbole domains of parameters. And the cootributions defined as a variation of the quality index over the whole domains of parameters.

Pahati,

5.,

and

P.

M

DickeDs(I995),

Stcreolithography process improvement, Fi,.st National Conf~rt!nc~ on Rapid Prototyping and Tooling R~search. Pang. T. H., M D. Guer1in, and H. D.

Through the evaluation processes, layer thickness is proved 10 be the most important one and hatch ovcrcure is the secondary. 1be dimensional errors of the H-top and Waist teDd to dc:crtase for smaller values of the two parameters. On the other band. the Ankle error shows that there exists an optimal layer thickness for given range of the hatch overcure, which gives the minimal error value.

Nguyen(I995), Acauacy of Sterecllthograhpy partS : mechanism and modes of distortion for a

-Letter·H- diagnostic part. Roy, R K..(l990), A prime,. on the taguchi method, Van NOSlr.Uld R<:inhold. Schulthc:ss, A., M. HWlZiker. and M. Hofmaoo, New

resins for Stercolithography applycat.ioDS, Rapid Prototyping Sys/~ms fast track 10 product.

The quality index is vel)' important, while it is not sufficiently refined in this paper. Thus, it needs to work more on this, and for the fine tuning of SLA., it also occds more training patterns planned by higher

Ulle.. J. 5., R. R. Cbanoff(l994.), Reducing warpage in Stereolithography through novel draw style., Solid Freefonn Fabrication System. Yao, W. L., H. Won&. M. C. Lcu, and D . H. Sebastian(1996.), An analytic study of

level orthogooal array ofTaguchi's method.

investment casting with webbed epoxy pancrns.. Conftrenc~ and Rapid R~sponse Manufacturing Symposium,

ASME 1996 Winte,. Annual

REFERENCES

Atlanta, GA, Nov.

Cbanoff, RP., L. Flach, and P. Weissman(I995), Material and process prameters that affect accuracy in Stereolitbography, The sixth international conference on Rapid Prototyping Cben, C. C., and P. le Sullivan(I995), Solving the mystery - The problem oC Z·beigbt inac:auac:y of the Stcreolithography parts, Th~ Sixth Int~rnationaJ Conftnnc~

on Rapid Prototyping.

GargiuJo and Ed(l991), Proc. of the 1991 North

American Stcrcograpbiy User Group Meeting, Or1ando, Florida, Mal