CAD CAE CAM 與快速成形.pdf

forso time is wasted. This study initially uses dynamic finitedetermine the distortion of the outer profile of the part and thusrapid prototyping systems.Computers in Industry 56 (2005)In a rapid prototyping system, the optical lightsource used in the light source transmission structurecan be a point light source (such as a laser or LEDlight), a linear light source (such as an LED-array), or* Corresponding author. Tel.: +886 2 2737 6487;fax: +886 2 2737 6460.E-mail addresses: .tw (Y.-M. Huang), (H.-Y. Lan).0166-3615/$ see front matter # 2005 Elsevier B.V. All rights reserved.doi:10.1016/pind.2005.01.002compensation CAD model is produced and loaded into a RP machine for practical prototype processing, to increase the accuracyof the process. Finally, the H-4 diagnostic part is used as an example to verify the experimental results. The results of thesimulation and experiment on the final after compensation were accurate.# 2005 Elsevier B.V. All rights reserved.Keywords: Computer-aided engineering; Stereolithography; Rapid prototyping; Finite element method; Curl distortion1. IntroductionIndustrial competition has accelerated the devel-opment of rapid prototyping (RP) systems. The use ofrapid prototyping systems can accelerate R&D and themarket-placement of products. Consequently, redu-cing the processing time and ensuring the precision ofthe production have dominated the improvement ofreduce the deformation. Then, a reverse distortion correction is applied to the outer profile of the part. A new reversebuilt prototype, the geometric profile is easily damaged and deformed,element simulation code to simulate photo-polymerization, toDepartment of Mechanical Engineering, National Taiwan University of Science and Technology,43 Keelung Road, Section 4, Taipei 106, TaiwanReceived 5 July 2004; accepted 13 January 2005Available online 17 March 2005AbstractsStereolithography is a rapid prototyping (RP) process that uses photopolymers as the raw materials from which theprototypes are built. The photo-polymeric RP system uses lasers or other light sources to expose selectively the surface of theliquid resin. The absorption of energy causes photo-polymerization that changes the liquid resin into a solid, expanding the curedvolume expanding but shrinking simultaneously. The volume shrinkage and curl distortion of the resin during photo-polymerization are the main reasons for the poor accuracy of the built prototype, especially when the part is hollow, in whichcase the bending is greater because of the bending stress and cannot be compensated for. Normally, a designer builds a support inthis stage to limit the further bending and deformation of the prototype. However, after the support has been removed from theYou-Min Huang*, Hsiang-Yao LanCAD/CAE/CAM integrationof mask rapid prototypingincreasing the /locate/compind442456in Industry 56 (2005) 442456 443Fig. 1. The flowchart of the reverse compensation process.Fig. 2. Schematic of energy distribution of square mask typea source of light uniformly distributed over an area.Each of which is produced to meet the requirements ofthe designer. The light source used herein is an areasource of Digital Light Processor (DLP) light. Thesolidification of a region exposed to this rapidprototyping is based on the principles of the exposureand sheltering of a mask, so the optical light sourcepasses through the exposed portion onto the poly-merized resin that thus undergoes polymerization.Therefore, the heating is uniform, the dimensions ofthe product are stable, and the rate of production isfast, which factors all effectively reduce the proces-sing time of the products. It is therefore one of themost popular rapid prototyping systems.The poor accuracy of the constructed prototype iscaused mainly by the volume shrinkage of the resinduring photo-polymerization. The use of the lightsource produces free radicals that promote photo-polymerization, and the bonding of small molecules(monomers) into large molecules (polymers) thatcomprise several monomer units 1. Linking is exo-thermic and curing in a tiny volume instantly increasesthe temperature. The cured volume expands as theexothermic reaction proceeds, and shrinks after thetemperature is lowered after the liquid photopolymer,which is not cured, reaches thermal equilibrium.Shrinkage is the most serious cause of errors in thebuild-up process. Hence, much research has focusedon observing and simulating the problem of shrinkage.Narahara et al. 2 set up experimental apparatus toelucidate the basic dynamic solidification duringphoto-polymerization. Bugeda et al. 3 developed afinite element program to simulate the structuralbehavior of SL resins using a linear elastic model witha constant Youngs modulus and a constant Poissonratio. Tanaka et al. 4 developed a model of dynamicresin materials based on the properties of the resinafter photo-polymerization.The solid ground curing (SGC) system 1,commercialized by Cubital Company, is a typicalmask-type stereolithography RP system. Huang et al.5 developed an innovative RP system, using a liquidcrystal display (LCD), to generate a dynamic mask fordirect mask photo curing (DMPC). Murakami et al. 6used refrigerated stereolithography to form maskpatterns by drawing a special solgel transformablephotopolymer resin. Micro RP systems representY.-M. Huang, H.-Y. Lan / Computersanother area of become recent development. Themask-based stereolithographic technique and opticalcomponents have been used to yield the requiredresolution. For example, Hatashi et al. 7 used a thinfilm transistor LCD to create a mask pattern andwithout lamination, to fabricate optical lenses. Huangprototyping.and Jiang 8,9 used the dynamic finite elementmethod (DFEM) to simulate stereolithography, basedon the dynamic properties of photo-polymerization.Many of these studies have focused on analyzing theeffect of curing during build-up. However, only a fewstudies have sought to improve curl distortion,especially when the built part is hollow; this bendingis very obvious and cannot be compensated bybending stress.This study presents verification and validationmethods to improve the curl distortion using low-costequipment. First, The equation based on DFEM theory8,9, is used herein in numerical simulation with inputparameters that correspond to a practical processes.Then, the distortion of the built parts is predicted.Second, reverse distortion compensation is used toproduce a new CAD model that is based on thepredicted distortion. Thirdly, the new CAD model isconverted into a stereolithographic (STL) file. Finally,this new STL file is sent to a RP machine for furtherprocessing. Accordingly, the low-cost machinesgreatly improve the accuracy of the part. The finalresults of the simulation and experiment are com-pared. Fig. 1 shows a flowchart of this process.2. Numerical analysisA modified mathematical model is proposed, basedon the aforementioned reference and experimentalY.-M. Huang, H.-Y. Lan / Computers in Industry 56 (2005) 442456444Fig. 3. The flowchart of the simulation process.ment in the effective nodal force; B represents thestrain ratevelocity matrix; BTis the transpose of thematrix B; b Dec is the stressstrain matrix; V is thevolume of the reaction area; s represents the nodalviscous stress that is the function of time (t); k is thevolume modulus; a is the linear expansion coefficient;T is the increment in temperature, and Db(I)isdefinedin Industry 56 (2005) 442456 445Fig. 4. FEM liquid mesh of H-4 diagnostic part (units: mm).Fig. 5. The deformation of H-4 part in simulation (units: mm).(a) Three-dimension deformation. (b) Two-dimension deformation(for convenience of observation, the distortion of every node isobservations of the curing process for mask-typestereolithographic systems. This process is a phasetransition from the liquid state to the solid state,proving that all factors are functions of the duration ofthe exposure to light, and the intensity of that light.2.1. Dynamic finite element methodHuang and Jiang proposed a dynamic solidificationmodel of photo-polymerization 8,9. The behavior ofthe cure resin is a function of the intensity of that lightI and the elapsed time t. The uncured liquid becomesmore viscous as it absorbs the heat produced by thecured resin. For the convenience to express, in thispaper substitutes the strain rate feg for the incrementof strain De. Therefore, the deformation of resinconsists of the following elements. 10fegfeegfeTgfevgfeggfepg (1)where feeg represents the elastic strain rate; fevg is theviscous strain rate that is the function of time, so it canbe expressed as s(t) 11; s(t) is the viscous stressthat is the function of time (t); feTg is the thermalstrain rate that can be rewritten as aTC8C9; fegg is thestrain rate caused by cure shrinkage and is given byDb(I, t); and fepg is the plastic strain rate. Duringphoto-polymerization, the plastic strain is low and canbe neglected. In the case in which fsg equals DeC138fegand feg equals BC138fug, substituting the above relation-ship andRvBC138TdV into Eq. (1), yields the followingequation:ZvBC138TDeC138BC138fugC0BC138TfsgC0BC138T3kfaT DbIgC138 dV 0 (2)Consequently, the constitutive equation in thedynamic finite element analysis of the stereolitho-graphic process can be expressed asKC138fugC0ffg0 (3)whereKC138ZvBC138TDeC138BC138C138dV (4)ffgZvBC138TfsgBC138T3kfaT DbIgC138 dV (5)In the above equation, K is the stiffness matrix; fugY.-M. Huang, H.-Y. Lan / Computersis the increment in nodal displacement; ffg is incre- magnified five times).as the strain associated with cure shrinkage, which is afunction of the intensity of that light (I) and elapsedtime (t).2.2. Energy distribution in mask type prototypingAs light passes through the mask onto the surface ofthe resin, the distribution and uniformity of thediffusion of the energy on the surface affects thethickness of solidified layers. Therefore, the energy ofthe light that passes through the mask and is projectedonto the surface of the resin must be calculated using amathematical model to determine the energy of themask. A square of side a is considered as an example.The energy intensity of the light source is I0. Thecentral point of the square mask is defined as x = 0 andy = 0, with an energy as depicted schematically inFig. 2. After the light had passed through the mask, theintensity at any point in the square profile is given by12Id14I0C2xC2y C2xS2y S2xC2y S2xS2y (6)where the relative coefficients, C and S, are defined asfollows:CxZp2p1cos 0:5pu2du (7)SxZp2p1sin 0:5pu2 du (8)CyZq2q1cos 0:5pu2du (9)SyZq2q1sin0:5pu2du (10)wherep12mpxaC0 0:5C16C17(11)p22mpxa 0:5C16C17(12)q12mpyaC0 0:5C16C17(13)Y.-M. Huang, H.-Y. Lan / Computers in Industry 56 (2005) 442456446Fig. 6. The reverse compensation CAD mesh of H-4 part insimulation (units: mm). (a) Three-dimension deformation. (b) Two-dimension deformation (for convenience of observation, the distor-tion of every node is magnified five times).Fig. 7. The after compensation CAD mesh of H-4 part insimulation (units: mm). (a) Three-dimension deformation. (b)Two-dimension deformation (for convenience of observation, thedistortion of every node is magnified five times).in Industry 56 (2005) 442456 447mechanicq22mpya 0:5 (14)presents the parameters used in the simulation. TheC16C17Y.-M. Huang, H.-Y. Lan / ComputersFig. 8. Mask-type RP system by using DLP technique. (a) Integralprocessing.andm 2lb C0 za2(15)where l is the wavelength of light, and b represents thedistance between the resin surface and the light mask.Hence, based on the BeerLambert Law, the equationthat specifies the light energy absorbed by the resin is,Ix; y; zIdx; y; zeC0z(16)where w is the rate of absorption of wavelength l bythe resin. Thus, the energy to which every point isexposed is given by E(x, y, z)=I(x, y, z)t, where t isthe period of exposure.2.3. DFEM simulationA cubic element with eight nodes is used to reflectrealistically the characteristics of the RP layer. Thedeveloped simulation code is based on the dynamicfinite element method. Fig. 3 shows a flowchart of thesimulation process. The liquid mesh is pre-created andread into a matrix core, as shown in Fig. 4, which is anH-4 diagnostic part 4,13,14. This case studyinvolves 1680 elements and 2366 nodes. Table 1structure. (b) Schematic of analytic model of DLP systemsimulation of the DFEM yields the displacement ofevery node of the part. This information can be used toimprove the profile of the part after deformation, andyield the new matrix of every node after compensa-tion. Fig. 5(a) shows the simulated three-dimensionaldeformation of the H-4 part. In this figure, thedeformation of every node is very small. TheFig. 9. Prototype of H-4 solid (STL file).deformation of every node is increased by a factor of 5and shown as a two-dimensional profile, as shown inFig. 5(b), to clarify the deformation of the outerprofile. Fig. 6 presents the simulated reverse compen-sated CAD meshes of the H-4 part in thesimulation. Fig. 7 presents the results after thecompensation of the CAD mesh of the H-4 partin the simulation.Y.-M. Huang, H.-Y. Lan / Computers in Industry 56 (2005) 442456448Table 1The parameters of experiment and simulationPart Element number Node number Thickness (mm) Layer Exposure time (s) Simulation time (min)H-4 part 1680 2366 0.1 150 10 150Note: Simulated in PC with p42.5G CPU, 512M RAM.Fig. 10. The process of reverse compensation H-4 model. (a) Curve diagramof region 1 by curves. (c) Curve surfaces of region 1 merged to a solid modelfrom all regions. (e) CAD file changed to a STL file.of region 1 profile by Pro/E .ibl file. (b) Create surface diagram(cross section denotes solid model). (d) CAD model is assembled3. Experimental apparatusThe photopolymer of the resin used in this study isNAF202, made by Nippon Kayaku Company. Aspecial photo-initiator is added to NAF202 to initiatephoto-polymerization in the range of visible light. Theexperimental apparatus is set up based on the principleof a mask-type stereolithographic rapid prototypingsystem, as shown in Fig. 8, at an expense of almostUS$ 10,000. The system is one kind of bottom-exposure SL system and can be easily maintained anduses an inexpensive resin.This experimental apparatus exposes the liquid resinat the bottom of the resin container to the platform, andan elevator driver controls the position of the platform.The distance between the platform and the bottom of theresin container is the thickness of the first layer that wasfabricated. The platform rises when the current layer iscompletely solidified, and the liquid resin then fills thevacant region. The mask data of the next layer aresimultaneously prepared. This procedure is repeateduntil the object is completely fabricated.Most users use the term H-4 4,13,14 presentedin Fig. 9 when evaluating the accuracy of three-dimensional SL products. Because the H-4 part notonly indicates bulk shrinkage but also indicate the bulkdistortion. The H-4 diagnostic part used in thisstudy has the following process parameters: theY.-M. Huang, H.-Y. Lan / Computers in Industry 56 (2005) 442456 449enceFig. 11. H-4 parts built by DLP mask-type RP system (for convenimechanic structure). (a) Deformation before compensation. (b) Deformatioof measurement, this figure is shown upside-down from the actualn after compensation.ers Industry 56 (2005) 44245613. Comparison of two-dimensional deformation of H-4before and after compensation. (a) Deformation profile of12. Characteristic dimension and distortion trend of H-4number of layers is 150; each slicing layer has athickness of 0.1 mm, and the exposure time is 10 s perlayer. These parameters are the same as those used inthe simulation and presented in Table 1.3.1. Design and production of reverse-compensationthree dimension modelThe original CAD and STL files of the requiredH-4 part of the experiment were produced using thePRO/E software, as shown in Fig. 9. Two methods areused in designing the more complex reverse compen-sation three-dimensional CAD model. One is the useof reverse engineering software, and the other involvesa series of procedures, firstly dividing the morecomplicated patterns into several simpler regions, andthen completing each simpler region using PRO/Esoftware. This software joins the points into curves;turns the curves into curved surfaces, and merges thecurved surfaces into a solid model. Finally, the newreverse compensation CAD model is assembled fromeach finished simple region. This work applies thesecond method to reduce the use of package software.In the design of the more complicated reversecompensation three-dimensional CAD model in thiswork, the H-4 part is initially disconnected intothree regions and then the new reverse compensationCAD model is assembled from each finished simpleregion. The procedure is as follows. First, the originalcoordinates and the distortion data of every nodedetermined in the DFEM simulation are converted toan IBL file that can be accepted by PRO/E software,using the VB6.0 or C+ Builder program. Later, theIBL-formatted file is loaded into PRO/E software forprocessing. Consequently, the curved figure of theouter profile is produced, as required by the reversecompensation CAD model. Fig. 10(a) plots therelevant results. Secondly, the convergence curvesof the profile are paved into a curved surface, as shownin Fig. 10(b). Thirdly, a solid model is producedthrough the formation and merging of the curvedsurfaces. The reverse compensation three-dimensionalCAD model of a region is based on this model, asshown in Fig. 10(c). Fourthly, all of the