An Efficient Scanning Pattern for Layered Manufacturing Processes

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Gordon Reeves
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1 Proceengs of the 2 IEEE Internatonal Conference on Robotcs & Automaton Seoul, Korea May 2-26, 2 An Effcent Scannng Pattern for Layere Manufacturng Processes Y.Yang, J.Y.H Fuh 2, H.T.Loh 2 Department of Mechancal Engneerng, Natonal Unversty of Sngapore, Sngapore 926 an Y.G.Wang 3 Knergy Pte.Lt., Sngapore Abstract Path generaton s an mportant factor that affects the qualty an effcency of most layere manufacturng processes such as SLS, SLA an FDM. Ths paper ntrouces an effcent path generaton algorthm. The prncple of the algorthm an the mplementaton are presente. A comparatve stuy s use to analyze the effectveness of ths metho. The results of comparson on both path length an processng tme between the tratonal metho an the propose metho are scusse. Keywor: Rap Prototypng, Depth Tree, Scannng Pattern, Equstant Path.. Introucton Satsfactory surface qualty an fast processng spee have always been the am of all the RP manufacturers an researchers. RP processes create a physcal object through the bulng of layers ether by epostng (e.g. FDM) or by curng (e.g. SLA). The metho of scannng s a key factor that wll affect the surface qualty an the processng tme of the part. In ths paper, we wll scuss a metho to mprove the surface qualty an accuracy through mprovng the scannng pattern. Some research has been one to mnmze the shrnkage an to mprove the mensonal accuracy. Onuh [] propose the Dvergent Star Weave (DSW) an Dagonal Dvergent Star Weave (DDSW) hatch strategy. In ths metho, the scannng s commence from the m. le of the part, n such a way that half of the part s frst scanne from the mle to the one en an the other half s then scanne. Ths process s repeate n ether x or y recton (n DSW way), or at 45 O to the ther axes (n DDSW way). Ths wll reuce the shrnkage forces for the whole layer an thereby mnmze the part shrnkage an curl effect. Ths metho s also calle parallel-lne metho n essence. The shortcomng of ths metho s that t causes a hghly ansotropc structure, whch can be etrmental to the physcal property of the fnal part. On the other han, scontnuous paths wll cause the elay of process an the frequent acceleraton an eceleraton wll result n a slower process; furthermore, the en of the path s on the surface of the part. Snce t s mpossble to control perfectly the nozzle poston an ts spensng ue to the lmtatons of the controller, surface structure roughness s thus affecte. Therefore n RP processes, a path wth ranom orentaton s esre. Km [2] an Bertol [3] apple the elaunay trangulaton to ecompose the cross secton of a part an fll the trangulaton wth space fllng curves (Hlbert Curves). But ths metho was lmte to hghly regular objects an not applcable to arbtrary bounares. Moreover, the trangulaton of the plane polygon can be of at least O(n 2 ) complexty. If the slce nformaton s represente by polygons, for normal accuracy requrement, n cannot be a small number; an the algorthm may not be acceptable for the practcal applcaton. Wasser [4] ntrouce a fractal-lke bul style usng smulate annealng algorthm, ths metho s able to generate fllng patterns that allow the contnuous eposton of a sngle path to fll arbtrary shape oman. In hs metho, the area to be eposte s frst ecompose nto noes, an the number of the noes epens on the accuracy requrement n LM process. Although the complexty of ths algorthm s only O(n), t coul be very tme consumng when the requrement to accuracy s hgh. Kulkarn propose a spral metho n [5], however t s ffcult to realze when there are pockets or slans nse the contour. 2. Equstant Path Generaton Metho We propose an equstant path generaton algorthm to mprove the scannng effcency an surface qualty. Some lterature has scusse about ths eposton metho, but they are lmte to smple geometry an no mplementaton was reporte so far. In ths paper the algorthm an ts etale mplementaton wll be presente.. Grauate Research Scholar; 2. Assocate Professor, corresponence: mpefuhyh@nus.eu.sg; 3. R&D Drector //$. 2 IEEE 34

2 a e j b 2. Defntons The followng efntons wll be neee to escrbe the algorthm: Defnton : Smple Polygon. For a polygon, nonajacent eges o not ntersect wth each other. Let e ( =,,..., n) be the eges of the cycle, we have e I e j = φ, for all j +, an then we call t a smple polygon [6]. In Fgure, these polygons are non-smple polygons. Nearly all the commercal RP systems avalable n the market bul the 3D objects from layers obtane through the slcng of 3D CAD moels (n STL format). When the slcng algorthm s performe on the STL moel wthout any fault, the result must be a seres of smple polygons that o not ntersect wth each other. Defnton 2: Depth of the cycle. It refers to the number of cycles n the same contour that enclose t. The maxmum epth n a contour s calle the epth of a contour; the epth of a contour s also an ncaton of the planar complexty of the contour. As llustrate n Fgure 2, the epth tree shows the relatonshp of the cycles to a contour. The epth of ths contour s 3. For a gven contour, we employ the epth tree to escrbe ts complexty. Defnton 3: External an Internal polygon. Base on the efnton of epth, we can also efne the attrbute of a cycle: f the epth of a cycle s c e a (a) Contour g j Fgure 2. Depth tree structure f h b (b) Fgure. (a) Smple polygon an (b) non-smple polygon Depth 2 3 c g h f Fgure 3. Partton of areas nse a layer even, t s an external cycle; otherwse t s an nternal cycle. In Fgure 3, cycles a, b, e, f, j are external cycles, an the rest are nternal cycles. Defnton 4: Drecton of the polygon an chans. Lke most of efntons n the relevant lterature, we efne the recton as postve f the sol area s always to the left when walkng along the bounary. Chans are the segments along the bounary of the polygon. Obvously, for external cycles, the postve recton s counter clockwse; for the nternal cycles, the postve recton s clockwse. Accorngly, we efne the areas beses the chans as left se an rght se when walkng along the polygon n the postve recton. We can nfer from the above efntons that the left se of a chan s a sol part, an the rght se of the chan s a vo part. 2.2 Doman Partton In a typcal RP process, n orer to realze the physcal moel, the cross secton area of each layer has to be entfe an flle wth a pattern of vectors. In Fgure 3 the shae area s to be hatche. The cross secton shoul be parttone nto fferent contnuous areas that wll be processe at the same tme. Contnuous area can be taken as the area boune by the external cycle an the outmost nternal cycles nteror to t. In a epth tree, we can easly entfy the contnuous area bounares; they are those cycles wth the even epth an the cycles just below t n the epth tree. In Fgure 3, a, c, an f, g, h are all the bounares of contnuous area, an they can be processe together. Ths s also the pre-processng proceure of ths algorthm. 2.3 Offset Generaton Snce the ameter of nozzle s constant urng the eposton process, we assume the moton velocty of the nozzle s also constant. To get the constant eposton thckness, the basc requrement to the path generate s that the stance between the ajacent paths must be constant. The man ea of ths algorthm s to offset the contour an get a seres of equstant path. The algorthm begns from the offset of an external cycle. Wthout loss of the generalty, set the orgn of the temporary coornate system at the arbtrary vertces of 34

3 V the cycle V. L an L+ are the vectors forme by V V an V V + (Fgure 4). l r an l r + are the unt vectors of L an L +,.e. r r r l = x + y j r r r () l+ = x+ + y+ j Let L an L + be the equstant lne of L an L +. If the offset s R, then the followng equatons are erve: Snce L V L an L+ x y + x + y V yx + x y = R y x + x + y = + R (2) are not parallel to each other,. Solve equaton (2) to get: ( x+ x ) R x = x y y y+ ( y+ y ) R y = x y y y+ L + Fgure 4. Offset generaton A 3 R L + V + (3) Thus we can get the coornate values of all the offset ponts. 2.4 Self-ntersecton After the bounary cycle s offset nwarly, selfntersecton may happen (See Fgure 5). To keep the resultng cycle always the smple cycle, the selfntersectons shoul be elmnate. To calculate the ntersecton ponts, the metho s to go aroun the offset polygon ege by ege an check whether there are two non-ajacent eges ntersectng wth each other, an keep a lst of ntersecton ponts along the path. After checkng all the ntersecton ponts, a lst of ntersecton ponts s forme (e.g., pont A an B n Fgure 5). Then construct some smple cycles wth the chans between the two ntersecton ponts (as seen the new cycles A, A 2 an A 3 n Fgure 5). It s necessary to store the ponts n the orer n whch they appear n ther parent cycle. Then etermne the recton of the newly forme cycles, an elmnate the cycles whose recton s negatve (e.g., A 3 n Fgure 5). 2.5 Sharp Angle Another problem that s often encountere s a sharp angle. Sharp angles must be processe before further calculaton. On one han, a sharp angle s too small for eposton; on the other han, t may become a source of nstablty of the next offsettng. If the lnes form a very sharp angle, the x an y values n Eq. (3) can be unreasonable large, whch wll cause the eformaton of offset polygon (as shown n Fgure 6). Crtera : Angle V VV +. Ths s to etermne whether a sharp angle has forme; Crtera 2: Area of V VV +. Sometmes the sharp angle can be the feature of the contour geometry, f rule out wthout fferentatng, accuracy wll be lost, or bg vo space wll be create when hatchng. To avo the mstake, the area of V VV + s also chosen as the crtera. V A A 2 A B V + V A A 2 Fgure 5. Self-ntersecton an polygon egraaton 342 V Fgure 6. Sharp angle

C p C q P Fgure 9. Moel use for testng Q We can see from Fgure 7 that between each par of ntersecton ponts, there are two chans ( C p an C q ) facng to each other; one s of P an the other s of Q.

4 C p C q P Fgure 9. Moel use for testng Q We can see from Fgure 7 that between each par of ntersecton ponts, there are two chans ( C p an C q ) facng to each other; one s of P an the other s of Q. Base on our efnton, we can get: Fgure 7. Polygon fference =n P Q : U (C pl I Cql ) 2.6 Intersecton wth Internal cycle: = When the external contour s offset nwarly, t s lkely that the path wll ntersect wth the cycles nteror to t. Calculatng the resultng area to be hatche becomes the problem of fnng the fference of two cycles. Wthout loss of generalty, we assume that cycle P (L vertces) s an external cycle an cycle Q (M vertces) an nternal cycle (Fgure 7). Then accorng to the computatonal geometry theory, the ntersecton of P an Q s a polygon havng at most L+M vertces [6]. Both P an Q wll be ve nto some chans by the ntersecton ponts, an the bounary of P Q s a seres of chans that are alternatvely obtane from the two polygons. For the chans, we efne the area to the left of t as C l an the area to the rght as Cr. By ths efnton an the efnton of recton, we know that C l s the sol area an C r s the vo area. =n Q P : U (C pr I Cqr ) = For every contnuous area, the algorthm begns from offsettng the external cycle an repeats the aboveescrbe process untl all the area s flle (as shown n Fgure 8.a). 3. Performance Evaluaton The followng performances are teste n comparson wth the parallel lne metho: they are total path length, processng tme an surface fnsh. Fgure 9 shows the cross secton from the test moel of a han-phone shell. 3. Total Path Length We assume that there s no overlap or crevce prouce between the paths generate. The overlap area covere by the two ajacent segments (See Fgure ) s: A = (l + l2 ) * Where δ 2 sn δ ( tan ) (4) l an l2 are the length of segment, δ s the angle between l an l2, an s the wth of the path. (a) l2 l o δ (b) Fgure 8. Comparson of two scannng path (a) equstant metho (b) parallel lne metho Fgure. Area of the paths covere 343

5 Total Path Length (m) For the path generate by the parallel-lne hatch metho, all the δ =, an the area of hatche area s A = n p = l = For the other hatch metho, A = * o * (5) = n = l 4 2 = n = snδ δ ( tan ) 2 2 If s a constant, for a gven area A, the factor that affects the path length s δ. For normal path, we get: Ao A p L = = n l =, an A where A s the area to be hatche, thus we get: (6) << l, thus Theorem: For all hatch methos, f there s no overlap or crevce prouce, the total path lengths are approxmately equal. Fgure llustrates the relatonshp on the total path length versus offset value from a smulaton result. It shows that f the path wth s the same, the total path Velocty Fgure. Relatonshp between path length an offset value Vector Velocty (VV) Vector Acceleraton (VA) Fgure 2. Velocty profle of SB24 moton controller Equstant metho Parallel lne metho Offset (mm) Tme (7) 344 Processng Tme (s) Fgure 3. Relatonshp between processng tme an vector velocty Vector Velocty (m/s) length resulte from equstant metho s slghtly longer than the parallel lne way. The fference between them comes from the fferent overlaps n these hatch methos, whch s quantfe as the secon part of Eq. 6. Snce the value of ths part s very small, the fference s neglgble. 3.2 Processng Tme The am for the optmze scannng path generaton s to fn a soluton that requres the shortest processng tme. For a gven contnuous path, the moton starts from zero velocty at the startng pont, accelerates to a specfe velocty, keeps that velocty to a pont along the path an then ecelerates towar the en pont of the path, where the velocty becomes zero. Usually for a gven path, the moton controller [7] can ajust the vector velocty along a trapezoal profle automatcally no matter t s lnear or nonlnear path (as llustrate n Fgure 2). The length of path generate also lmts the moton velocty. If the length s not long enough to allow the moton be accelerate to the specfe velocty, then the constant spee stage can not be acheve,.e. the velocty begn to be ecelerate before t s accelerate to the specfe value. On the other han, the shorter the paths, there wll be more starts an stops. So the longer the sngle path s, the hgher the moton velocty wll be, an thus less processng tme s neee therefore the equstant metho has the avantage n terms of the process spee. We use the SB24 [7] seres of mult-axs moton controller to control the moton of nozzle. A comparson on processng tme s shown n Fgure 3. We can see that processng tme of our propose metho s sgnfcantly reuce. Atonally, for both hatch strategy, the requre processng tme rops wth the ncrease of vector velocty, but as the velocty ncrease to a certan pont, ths rop wll stop. 3.3 Surface Qualty The ens of the scannng path on the surface are the man factors that affect the surface qualty. Wth the parallel lne hatch metho, all the path ens are on the surface of the fnal parts, so the surface qualty s not so satsfactory.

6 Wth ths hatch pattern we have ntrouce, only one en of the path s on the surface for a contnuous area, an therefore the surface qualty can be mprove sgnfcantly. 4. Concluson Dfferent hatch strateges for the layere manufacturng process are analyze n ths paper, an an equstant hatch algorthm s put forwar an mplemente n ths work. Some expermental an smulaton analyss were performe base on ths algorthm, whch shows that ths metho can brng sgnfcant mprovements to the present RP process both n processng effcency an parts qualty. Ths algorthm was teste on the FDM system. It can also be apple to some other RP process, such as SLA an SLS wth lttle mofcaton. References [] S. O. Onuh, K.K.B.Hon (998), Applcaton of the Taguch metho an new hatch styles for qualty mprovement n stereolthography, Proc. of the Inst. of Mechancal Engneers Part B, v22, [2] Deok-Soo Km (998), Polygon offsettng usng a vorono agram an two stacks, Computer-ae Desgn, v3, n4, [3] M. Bertol, M.A.Yarmc an C.M.Pstor (998). Doman Decomposton an Surface Fllng Curves In Tool-path Plannng an Generaton, Sol Freeform Fabrcaton Symposum Proceengs. Austn, Texas [4] T. Wasser, A. Dhar Jayal, an C. Pstor (999). Implementaton an Evaluaton of Novel Bulstyles n Fuse Deposton Moelng (FDM), Sol Freeform Fabrcaton Symposum Proceengs, Austn, Texas, [5] P. Kulkarn an D.Dutta (999), Deposton Strateges an Resultng Part stffnesses n Fuse Deposton Moelng, ASME. Journal of Manufacturng Scence an Engneerng, v [6] J. O Rourke (994). Computatonal Geometry In C, Cambrge, Cambrge Unversty Press, Cambrge. [7] ACS Moton Controllers Software Gue, A.C.S Electroncs Lt. 345

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