Experimental real time linear shrinkage rate measurements simulating stereolithography
are used in an analysis of shrinkage during line drawing in stereolithography. While the amount of
shrinkage depends on the polymerization kinetics, shrinkage kinetics and overall degree of cure, it
also depends on the length of time to draw a line of plastic. A line drawn slowly will exhibit less
apparent shrinkage than one drawn very quickly because much of the shrinkage is compensated
for as the line is drawn. The data also indicates that a typical stereolithography resin in the green
state may shrink to only 65% of its maximum, thus retaining considerable potential for shrinkage
during post-cure. This infonnation can be used to predict the amount of shrinkage to be expected
under certain exposure conditions and to fonnulate overall strategies to reduce shrinkage and
subsequent warpage that causes shape distortion.Mechanical Engineerin

Chartoff, Richard P.

Flach, Lawrance

Weissman, Peter

English

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MATERIAL AND PROCESS PARAMETERSTHAT AFFECT ACCURACY IN STEREOLITHOGRAPHYRichard P. Chartoff, Lawrance Flach,and Peter Weissman*University of DaytonRapid Prototype Development Laboratory andCenter for Basic and Applied Polymer ResearchDayton, Ohio 45469-0130ABSTRACTExperimental real time linear shrinkage rate measurements simulating stereolithographyare used in an analysis of shrinkage during line drawing in stereolithography. While the amount ofshrinkage depends on the polymerization kinetics, shrinkage kinetics and overall degree of cure, italso depends on the length of time to draw a line of plastic. A line drawn slowly will exhibit lessapparent shrinkage than one drawn very quickly because much of the shrinkage is compensatedfor as the line is drawn. The data also indicates that a typical stereolithography resin in the greenstate may shrink to only 65% of its maximum, thus retaining considerable potential for shrinkageduring post-cure. This infonnation can be used to predict the amount of shrinkage to be expectedunder certain exposure conditions and to fonnulate overall strategies to reduce shrinkage andsubsequent warpage that causes shape distortion.INTRODUCTIONIn order to better understand the shrinkage-related problems associated withstereolithography, and to minimize their effect, it is essential to understand the relationshipbetween the polymerization kinetics, shrinkage kinetics, total shrinkage, and the laser scan rate.These variables directly affect the amount of shrinkage that will occur in a line of plastic drawn bythe stereolithography apparatus (SLA) and ultimately in the warpage and shape distortion of thefinal part. In this paper we discuss the results of a series of real time shrinkage rate measurements(in an apparatus that simulates stereolithography) and use the rate data in an analysis of theshrinkage that occurs when a single strand of material is fonned. The analysis indicates that therate of shlinkage rather than shrinkage itself is the key parameter for controlling shrinkage-relateddimensional effects.EXPERIMENTALReal time shrinkage measurements were perfonned on "full line" exposures of threephotopolymers: Ciba XB5081-1, UD experimental fonnulas 60.1 and 61.1. The so-called "fullline" exposure is performed by exposing an approximately 7 mm long by 0.2 rom wide line to afocused Argon-Ion UV laser beam. The apparatus and procedures for making thesemeasurements have been described elsewhere [1,2]. The current experiments were designed to* Current Address: UCB Radcure, Inc., 200 Lake Park Drive, Smyrna, GA 30080-7611.245compare the shrinkage rates as well as the shrinkage occurring under both short term and longterm laser illumination. This was accomplished by exposing a line of polymer to a single 40 m secpulse (short term exposure) and subsequently a series of successive 40 m sec pulses untilmaximum shrinkage was achieved.Real time shrinkage measurements were made, in duplicate, for the three polymers. Thelaser power was varied for each so that a cure depth (C.D.) of 0.85 mm was obtained. Theenergy densities 76.9, 65.2, and 66.5 mJ/cm2 were used to obtain a uniform specified cure depthfor XB5081-1, 60.1, and 61.1, respectively. The total shrinkage was noted five minutes after thefirst exposure. Each sample was then exposed again the standard amount and the additionalshrinkage noted after five minutes. This procedure was repeated to obtain the desired number ofexposures. Each material was subjected to five consecutive exposures with a five minute pausebetween each. XB5081-1 was tested using eight consecutive exposures.DISCUSSION OF EXPERIMENTAL RESULTSThe real time shrinkage data for the six samples (three polymers in duplicate) that wereexposed once are shown in Figure 1. Resins 60.1 and 61.1 show a shorter induction time, steeperslope, and higher shrinkage than XB5081-1.The data of Figure 2 indicate that 60.1 and 61.1 complete a greater percentage of theirultimate shrinkage after the first exposure than does the XB5081-1. Table I tabulates thepercentage of maximum shrinkage that has occurred after each individual exposure. The changein shrinkage due to additional exposures became very small after the fifth exposure for 60.1 and61.1. However, for XB5081-1 the change in shrinkage with continued exposures does notdecrease significantly until the eighth exposure. Therefore, the maximum shrinkage for 60.1 and61.1 was taken as that which had occurred after the fifth exposure, while for XB5081-1 it wastaken as that which had occurred after the eighth exposure.Additional data on the density changes for the three photopolymers measured after longterm cure under Hg vapor lamp exposure indicates that approximately 15-25% of the totalshrinkage that occurs is missed by the real time shrinkage apparatus. This is the amount thatoccurs before gelation and does not affect the dimensions of a line actually drawn by a laser.Further density characterization of full line specimens after long term laser exposure is now beingcalTied out to determine more exactly the amount of initial shrinkage not detected in the real timeshrinkage measurements.SHRINKAGE ANALYSISThe amount of shrinkage observed when a line of plastic is drawn by the SLA isdetermined by the polymerization kinetics, the shrinkage kinetics, and the laser scan rate. Adetailed analysis is required in order to determine the inter-relationships between the appropriatevariables. There are two shrinkage components that must be considered. These are: (1) curerelated shrinkage arising due to a change in chemical bond distances in the unpolymerizedmonomer relative to the polymer, and (2) thermal expansion/contraction due to temperature246changes in the resin on polymerization. The latter is assumed negligible as discussed elsewhere[2]. The analysis incorporates the experimental shrinkage rate data described previously.The basis for the analysis is that any shrinkage that occursbeforecompletillg the laser scanfor a particular line of plastic will be compensated for at least partially by the fact that the laserstill scans a line of the correct length. The actual shrinkage that will be observed should be basedon the amount of shrinkage that will occur at each point along the line at the time the line iscompleted. At that time the line is the correct length (due to a scan of the correct length) and anychange in length is a result of polymerization and shrinkage occurring after completion ofexposure.If L is the desired length of a line of plastic drawn by the SLA, then the overall linearshrinkage (fraction) due to cure for the line of plastic will be given by:IlLFe = - f/x)dxL 0 (1)where fr(x) is the residual shrinkage (fraction) at position x along the line, i.e. the amount ofshrinkage that will occur at that point after completion of the line as indicated in Figure 3.The residual shrinkage, fr(x), can be obtained from experimentally determined shrinkagevs. time data, or can be estimated from model~basedpredictions of the degree of cure along theline of plastic. If ts is the time taken for the laser to scan from position x to the end of the line L,and fts(x) the fractional shrinkage that has occurred up to time ts at position x, then the residualshrinkage is just(2)where foo is the maximum fractional shrinkage that occurs at t~oo (see Figure 4).Using the fact thatandfoo = f(t)fts (x) =f(t)as t~ooL-xat t=--s(3)(4)where s is the laser scan (draw) rate and f(t) the shrinkage vs. time curve, eqn. (2) can betransformed to a time integral as follows:sILlSF = f - - f(t)dtc ... L 0247(5)this expression LIs is just time required for the laser to scan (draw) the line of plastic oflength so eqn. (5) can be written as:= __l_fscan f(t)dttscan0(6)is the scan time LIs).SCAN RATES, SCAN TIMES ANDModification of the scan (draw) rate typically requires that laser power be adjusted inorder to maintain the same actinic exposure levels. This is necessary if use is to be made of asingle curve valid at a particular exposure level only. In all further discussions thus,when is made to scan rate adjustment, it should be understood that this is accompaniedby appropriate laser power level adjustments.computer program was developed to investigate the relationship between the shrinkagelaser scan (for a line of plastic of constant length), and between shrinkage and line length(for a constant scan rate). The shrinkage data used for the investigation are those shown in1 for Cibatool XB5081-1 stereolithography resin and the faster curing experimentalformulation 1. program utilizes eqn. (6) to estimate the shrinkage that will occur whendrawing a line plastic of a specified length at a specified scan rate. Results were computed fortwo test cases. the first, the scan rate was varied for a line of plastic of length 10 cm, and inthe second, the line length was varied for a scan rate of 10 cm sec-I. Typical operating laser scanrates for 1 are in the range 10-200 cm sec-I. Results for the two tests can be found in5 and 6. As can be seen the shrinkage increases with increasing scan rate and decreasingline length. both cases the maximum shrinkage value of foo is attained when the scan iscOlnpleted during the shrinkage induction time, i.e. before any measurable shrinkage occurs. Notethat the does not depend independently on the two parameters, scan rate and linesingle parameter tscan (as revealed by eqn. (6)) which is a combination of thetwo (eqn. (4)).aJL."'U .... V'V.l. of interesting facts are revealed when considering the results of this analysis for()lU..111AUF,V data set:1. will always be equal to or less thanthe scan is very rapid or the line of plastic is very short (tscan--70), thenthe scan is very slow or the line of plastic is very long (tscan--7oo), then Fc--70.is a particular set data.(6) is simply the cumulative shrinkage that occurs during thelaser scan and as such is subtracted from the maximum shrinkage that could occur.248Inspection of eqn. (6) reveals that for any particular shrinkage curve (resin, exposurecombination), the measured shrinkage that occurs during the drawing of a line ofplastic depends on the scan time only, Le. on the combination of line length and scanrate, and not on the individuaLparameters.It is an important consideration that experimentally measured shrinkage data, such as that inFigure 1, represent the composite effect of polymerization kinetics and shrinkage kinetics relativeto conversion.When comparing results different resins which exhibit different shrinkage rates anddifferent final amounts of shrinkage, foo, some interesting observations can be made. F61.1resin shrinks considerably faster than XB508 and exhibits a higher final shrinkage.Figures 5 and 6, however, that the shrinkage expected to occur when drawing a ofplastic is less for the faster curing and higher shrinking resin for certain scan rates and lengths.This is a result the compensating effect of shrinkage that occurs during the drawing process.of a measured shrinkage curve, the mathematical process modelsstereolithography together with a shrinkage model such as that proposed byand Peppas [4], would allow estimation of the shrinkage that might be expected to occur whendrawing a line of plastic. Eqn. (6) would still be required to compute the overall shrinkage. Aprocedure for such an "a priori" approach will be discussed in a future report.CONCLUSIONSThe conclusions that can drawn from the above experiments and analysis is thefollowing:1. A significant amount of shrinkage occurs during cure prior to gelation that is notmeasured linear shrinkage experiments that simulate stereolithography.amounts to around 20% (or more) of total volume shrinkage and does not impactstereolithography process. Thus volume shrinkage data will overestimate the actualSLA shrinkage.The amount of shrinkage, warpage, and dimensional inaccuracies for stereolithographyproduced parts may be reduced by using very low scan rates (and low laser power) or,alternatively, developing a resin that shrinks rapidly compared to typical scan rates.The of these two conclusions appears contrary to the concept of a rapidprototype technique, but should be considered when, for example, a high precisionpart is required. Selection of an optimum scan rate would be based on a compromisebetween the dimensional accuracy required and the speed of prototype production.second conclusion is one that has influence on resin formulation. A fast .........Jl ..... A'...fast shrinking resin would be desirable for stereolithography use. A resin with agreater final shrinkage (foo) could be tolerated if the shrinkage occurred rapidlycompared to the scan rate.2493. During the SLA part drawing process hatch vectors should not be attached untilshrinkage is largely completed, i.e. for a fixed length vector, the scan rate should beadjusted to minimize Fc (use low scan rates).4. Another aspect of the shrinkage/warpage problem that might be addressed byimplementation of a fast curing, fast shrinking resin is residual post cure shrinkage.Resins such as F60.1 and F61.1 that shrink and cure more fully during the initial laserexposure will lead to less residual shrinkage and warpage during post cure.NOMENCLATUREf(t) shrinkage function (fractional linear shrinkage vs. time)fr(x) residual shrinkage at position xfts(x) at position x at time tsfoo maximum shrinkage expected (t-7oo)fractional shrinkage in a line of plasticL length of line of plastic (cm)s scan rate (cm sec-I)ts for to scan from position x to L (sec)tscan laser scan time, L/s (sec)x position along line of plastic (cm)ACKNOWLEDGEMENTSauthors gratefully acknowledge the financial support of the State of Ohio EdisonMaterials Technology Center (EMTEC), the United States Air Force and an industrial consortiumof companies. contributions of Stanley Rodrigues who assisted with shrinkage measurementsand Shwn-Meei Linden who helped with resin preparation are acknowledged.REFERENCES1. Weissman, Bolan, and Chartoff, "Measurements of Linear Shrinkage andResidual Stresses Developed During Laser Photopolymerization," Proc. 3rd lnt. Conf.Prototyping, Dayton, OH, June 7-10, 1992.Weissman, P.T., Chartoff, S.J. Rodrigues, and S.-M. Linden, "Real TimeMeasurements of Linear Shrinkage During Laser Photopolymerization: ImplicationsConcerning Post Cure Shrinkage," Proc. 4th lnt. Conf. Rapid Prototyping, Dayton, OH,14-17, 1993.Chartoff, "Laser Photopolymerization in the Stereolithography Process:J. Rad. CurihgjRad. Curing, No.4, 4-9, 1992; also paperaccepted for publication in Polymer Eng. and Sci.4. Bowman, C.N. and N.A. Peppas, "Coupling of Kinetics and Volume Relaxation DuringPolymerizations of Multiacrylates and Multimethacrylates," Macromolecules, 24, 1914-1991.250TABLE 1SHRINKAGE AFTER MULTIPLE 0.040 SECONDEXPOSURES (DATA ARE NORMALIZED BY THEMAXIMUM SHRINKAGE FOR EACH POLYMER)60.1 61.1W W89.5 88.893.6 94.696.3 97.799.5 98.8100 100XB5081·1Exposure W1 64.42 81.43 86.64 90.75 94.36 97.47 99.48 100Ultimate6.0VolumetricShrinkage6.4 7.5Full Line Exposure(0.04 sec. e:x:pClsure. C.D,"O.S6)3.0a • XB5081.1 76.9 ml/ em28.·F60.1 85.2 mll em22.5 20 • F61.1 66.5 mIl em ... 7•;...!-l~!:::;: <g 2.0 rt 6 S!.c:., '" 30' 5 CIt0 .~ ~.'. Ul~ ::rc: 1.5.. I "0 ....c: r!'. 4 3'Vl ~~ ~t·o Q'"0 CIt.,,: 3 ......c: 1.0,: al!.. ,,' ......I:' 2,:.:0.5..o0.0 '--__....,:::;;;;a..----- --' 0-2 -1 0 2 3LOG-TIMEReal 1lJ1lll SlIriaIoIte D... for XUllII·I. 60.1. and.61.1.Figure 1RESIDUAL FRACTIONAL SHRINKAGEALONG LINE OF PLASTICShrinkageAfter Multiple 0.04 Second Exposures(Measurements token 5 minutes after eacn exposure)3.0 r-----.--..,....---,--,....-,..--,..-..,..........,87 <2-c:5 3"5 Ul:r..... 3'"""a3~2~Numoer of ExposuresC C XB5081-1 76.9 mJ/cm 2/expo.v 'II' F60.1 65.2 mJ/cm 2/expo ... F6i.1 665 mJ/c",2/expo.\lultiple 0.040 Second Exposures Ulllle R.eaI T'lJIlll SbriDJ<age AppatIIIII.Figure 2251o fr<x)-----I....... XFigure 3L3.02.5-----XB5081-1---F61.1..::g 2.0w~;; 1.50:iii0:i:'iz 1.0::l0.50.010...2 , , .'0-' , ,. '00 , , .. Ill' • , .. 100 • , .. 10'SCAN RATE (om/_>- -- -- - -~-::.::....-- ----SHRINKAGE VS. TIME CURVE INDICATINGVARIABLES USED TO CALCULATERESIDUAL SHRINKAGEFigure 4Shrinkage vs. scan rate for a 10 cm line of plastic..(Actinic exposure level constant.)(Computer generated curves.)Figure 53.02.5 ---l-- _-I---f81.1.:g 2.0I 1.5ill; 1.00.50.0 L... ................. ..............__...................U--.l.:::::c=...i10-' Z J 4:1 100 1 J" 0\ 10' 2: J.. ,C)I 2".' 1CPUNE LENG11i (om)Shrinkage vs. length of line of plastic whendrawn at a fiXed scan rate of 10 cmsec;,'.(Computer generated curves.)Figure 6252

Material and Process Parameters that Affect Accuracy in Stereolithography

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Material and Process Parameters that Affect Accuracy in Stereolithography

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