Mould wall friction effects on micro injection moulding based on simulation of MIS

Transcription

1 IOP Conference Seres: Materals Scence and Engneerng Mould wall frcton effects on mcro necton mouldng based on smulaton of MIS To cte ths artcle: Fan Sh et al 2010 IOP Conf. Ser.: Mater. Sc. Eng Vew the artcle onlne for updates and enhancements. Related content - 3D fllng smulaton of mcro- and nanostructures n comparson to so- and varothermal necton mouldng trals C Rytka, J Lungershausen, P M Krstansen et al. - Developments of three-dmensonal CAE smulaton Sang-Woo Km and Lh-Sheng Turng - Iso- and varothermal necton compresson mouldng of polymer mcroand nanostructures for optcal and medcal applcatons C Rytka, P M Krstansen and A Neyer Ths content was downloaded from IP address on 29/06/2018 at 13:08

2 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ Mould wall frcton effects on mcro necton mouldng based on smulaton of MIS Fan Sh 1, Xang Zhang 1,2, Qan L 1 and Changyu Shen 1 1 Natonal Engneerng Research Centre for Advanced Polymer Processng Technology, Zhengzhou Unversty, Zhengzhou , People s Republc of Chna 2 College of Mechancal Engneerng, Zhengzhou Unversty, Zhengzhou , People s Republc of Chna E-mal: zhangxang@zzu.edu.cn Abstract. Based on smulaton Code MIS, ths paper s manly on the mould wall frcton effects to understand more deeply about the flowng behavour n mcro necton mouldng. In ths study, how the mould wall frcton affects the melt flow s demonstrated by comparng the smulaton results, between the stuaton where mould wall frcton s consdered and the stuaton where the tradtonal non-slp assumpton near mould wall s consdered. Experment verfcaton s also presented. The fndngs of ths study have provded some fundamental supports n understandng the complex nfluence factors n mcro necton mouldng, and contrbutng on the more accurate smulaton for manufacturng. 1. Introducton Polymer mcro necton mouldng s an deal soluton for massve fabrcaton of mcro products wth low cost and hgh effcency, whch has aroused the keen nterests n scentfc and engneerng felds. There are many dfferences between mcro necton mouldng and wth the tradtonal necton mouldng, such as melt temperature, mould temperature, necton speed. Some scholars, such as Yao and Km [1], Zhao et al.[2], Yosh et al.[3], have done a lot of research, and have dscovered the mould temperature and necton speed are the most nfluental factors. As a matter of fact, all those most mportant factors are rooted n the hgh bulk-surface-rato. Therefore, t s of great necessty to nvestgate how the melt behaves under such extreme condtons, wth the sutable smulaton tool. However, the present smulaton methods are lmted n the followng aspects: Current studes are manly around the 2-dmensonal smulaton. Though 2D smulaton can acheve satsfactory results, both n tme consumng and accuracy for tradtonal necton mouldng, ts performance s not qute acceptable n mcro necton one; Therefore, a sutable 3D smulaton method needs to be developed. The present numercal smulaton solutons use the fnte element methods, whch appear to be less capable n front of the hgh shear-rate flud, fountan flow, hgh bulk-surface-rato n mcro-necton mouldng. Therefore, t s valuable to take account of 3D smulaton wth mesh free methods. For example, Kansa s method [4] has already been appled nto the smulaton of necton mouldng. SPH (smooth c 2010 Publshed under lcence by IOP Publshng Ltd 1

3 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ partcle hydrodynamc), s one of the mesh free methods, well establshed for smulatng flud flows. It uses partcles to represent the flud, and s more advantageous than the meshng methods: Beng not able to track the tme hstory [5], the meshng method tracks mass, momentum, and energy flux across grd nodes, so that t cannot obtan the nformaton of materal pont as SPH, n order to observe the fountan flow movement, whch has the crtcal meanng n the study of mcro-necton mouldng. For rregular geometry, the smulaton qualty of meshng methods depends on the mesh qualty n a great extent. Therefore, t has dffculty to predct necton mouldng of complex structure products, whle SPH s robust. Smlarly, meshng method has to re-mesh when handlng large deformaton flow, whle SPH does not, and can acheve hgh accuracy and effcency. SPH, frst was used n astronomy [6], and later ntroduced to the hydrodynamcs feld. The SPH method s used extensvely n related felds, such as mpressble flow by Monaghan [7], vscous flow [8], underwater exploraton [9], and hgh pressure de castng [10]. In the metal de castng smulaton (whch s related to polymer necton mouldng), the SPH method was ntally performed on very smple geometres of runner, gate and de, wth the water analogue experments. Based on success n hgh accuracy and good predcton detals, the SPH method was then compared wth the MAGMA software and the water experment on more complcated products n a 3 dmensonal way [11]. Agan, the SPH method met the satsfactory accuracy result, and also the rch detals of free surface. In ths study, the SPH method s modfed to ft the requrement of polymer mcro necton mouldngs, whch s more complcated than the low molecular weght flud, lke metal. In ths paper, our mesh free mcro necton mouldng smulaton code (MIS1.0) has been updated to MIS2.5, whch mproves ts dsposal method of mould wall frcton, replaces nternal energy (used n MIS1.0) wth enthalpy, uses pston n the barrel to drve polymer melt nto the cavty, and optmzes the calculaton effcency and RAM usage amount. 2. Introducton 2.1. SPH nterpolaton equaton As dscussed n the last secton, the SPH method dscretses the flud nto partcles to predct the flow behavors. The physcal values, such as pressure, densty, and temperature of a partcle are determned by the correspondng values of ts surroundng partcles. All n a nutshell, the SPH method uses the kernel functon as compact support to calculate how much a surroundng partcle effects a specfc value of the center partcle, as shown n equaton(1): m A ( r) = (, AW r r h) (1) ρ Where, A ( r) s a specfc physcal value of partcle, at a certan poston, expressed by the coordnate vector, whle A s the related physcal value of a partcle surroundng partcle. Partcle has mass m, densty ρ. W( r r, h) s the kernel functon, r r s the dstance between partcle and, and h the smoothng dstance. Smoothng length s a constant taken to determne whch partcle can be regarded as the surroundng partcle of partcle. The kernel functon determnes the compact support by comparng the dstance and the smoothng length. Accordngly, the nterpolaton equaton of gradents for partcle s gven by: m A ( r) = A W( r r, h ) (2) ρ 2

4 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ Contnuty conversaton equaton The contnuty equaton s: Dρ v = ρ (3) Dt x Where ρ s densty, t s tme. v and x are velocty and coordnate respectvely. s the ndcator for drecton. Dscretsed by equaton (1), here comes the SPH form of contnuty equaton as: N Dρ m W = ρ v (4) Dt ρ x = Momentum conversaton equaton The momentum equaton s: α α Dv 1 σ = (5) Dt ρ x Where, σ s the force, ncludng pressure force, vscosty force and mould wall frcton force. Dscretsed wth equaton (1), the dervatve of partcle can be expressed as: α N α Dv 1 σ W = m (6) Dt ρ = 1 ρ x In order to avod boundary nconsstency, here we ntroduce equaton (7): N N α α m N W ' ' σ W σ m W = 1 W( x x, h) dx = 1= 0 m = 0 = = 1 ρ x = 1 ρ ρ x ρ (7) 1 = ρ x Add equaton (7) to equaton (6), we have followng symmetrsed equaton: α N α α Dv σ + σ W = m (8) Dt ρρ x = 1 Thus, acceleraton s determned by melt partcles n support doman when the central partcle s far off boundary. Whle the value of the central partcle wll also supplement the defcency of melt partcles to reduce errors caused by boundary nconsstency, when the central partcle s near boundary. Besdes, the mold wall partcles are also assgned wth physcal values. In ths way, mould wall partcles wll also be ncluded n approxmaton for central partcle to further mprove calculaton accuracy. However, mould wall partcles wll not get evolved. 2.4 Energy conversaton equaton The energy equaton s: α De σ v = e= Ek + H, σ Dt ρ x = pδ + τ + f α α α α ( ) Where, p s the pressure, f s the frcton force and e s energy, whch ncludes knetc energy and enthalpy (nternal energy) H. Dscretsed wth equaton (1), the dervatve of partcle can be expressed n equaton (10). Where, the dervatve of enthalpy s composed by three parts: heat conducton part, vscous heatng part, and the frcton heatng part. k s the heat conducton coeffcent, μ s the vscosty of an partcle, η s the mould wall frcton coeffcent and s s the proecton area of partcle on the mould wall. v and r are the velocty and poston dfference vector between partcle and partcle. Last, pp s the unt vector perpendcular to the mould wall around the vrtual partcle. Smlar to momentum conservaton equaton, ths symmetrsed equaton wll help to reduce errors caused by boundary nconsstency, also enhanced by mould wall partcles. 3 (9) E k

5 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ Based on the basc mechancs of the SPH method, several tems and calculaton optmzatons are added nto the SPH method n our study, to maxmze mcro necton mouldng. The man modfcatons are shown below: N De 1 p p W = m v + dh Dt 2 1 ρ ρ = x N 4 N DH m kk 1 W 2m μμ ( ) ( ) 2 1 W = T v r (10) Dt = 1 ρ + ρ k + k r x = 1 ρ ρ μ + μ r x N m W η p s ( ) v pp = 1 ρρ x 2.5 Partcle pressure used n MIS The polymer melt consdered n ths study s ncompressble. However, due to trats of the mesh less method, t s necessary to ntroduce the artfcal ncompressblty to establsh the pressure of lqud. Based on compressble hydrodynamcs, for certan mass of lqud, ts bulk vares proportonally wth the change of pressure, as expressed n equaton (11), V s bulk of certan mass of lqud, and s the change of bulk. Δ p s the change of pressure, accordngly, s a constant, related to materal and condton: ΔV V 2 = p= c ρ (11) Δp Where, p and ρ are pressure and densty of certan mass of lqud respectvely. c s the sound speed n such lqud. In equaton (11), t s clear that, for certan masses of lqud, ts pressure s drectly proportonal wth ts densty. The dfference of densty, or to say, the varance of pressure among dfferent parts of the melt wll provde the propulson force for the melt to flow and the resstant force to prevent unphyscal penetraton of melt. The value of c needs great care to choose. On the one hand, t needs to be large enough to ensure the ncompressble flud behavor. On the other hand, t has to be small enough to reduce the requred senstve tme steps. Accordng to Morrs et al. (1997) [5], one soluton to ths problem s to select the maxmum value among pressure, vscous force and body force. Whle n ths study, where the vscosty of the polymer melt s much hgher than low molecular weght flud, the man attenton s pad to how vscosty affects the value of c. After careful consderaton and calculaton expermentaton on the computer, now the hll mathematcal module s chosen to descrbe the functon between c and vscosty: n η c = ηmax (12) n n k + η Where, η s the vscosty of the melt, and η max s the maxmum vscosty used n ths study. k s a constant used n ths model. The dagram between c and vscosty s shown n Fgure Cross-WLF vscosty module used n MIS The vscosty of polymer s extremely complex. In MIS, WLF equaton s added to descrbe melt vscosty, dependng on temperature, shear rate, and pressure: 4

6 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ * A1 ( T T ) * ~ η 0 A2 ( T T + ) * η = η ( 1 n) 0 D1e T D2 D3 P A2 A2 D3 P =, = +, = + ηγ 0 1+ * τ (13) Where, the meanngs of the symbols are demonstrated n Table 1: 2.7 Mould wall As ndcated above, there are two knds of partcles, one s the melt partcle, and the other s mould partcle. In ths verson of MIS (MIS2.5), when a melt partcle approaches the mould wall, the mould partcles whch are closest to the melt partcle wll be located. Then MIS wll calculate the dstance between the melt partcle and the mould partcle, to determne the penalty force as shown below: r 0 r0 Dln ( > 1) r r FP = (14) r0 0 ( 1) r r 0 s the nfluence dstance of the wall partcle, and r s the dstance between the melt partcle and mould partcle. When the dstance r s larger than r 0, then the melt partcle wll not receve the penalty force; when the dstance r s smaller than r 0, the melt partcle wll receve the penalty force. The magntude of penalty force ncreases when the melt partcle gets closer to the wall partcle, whlst the ncreasng speed slows down. Ths penalty calculaton equaton s proved to be sutable for polymer melt n MIS. 2.8 Partcle searchng used n MIS As dscussed n prevous contents, the SPH smulaton code s manly about the nfluence of neghbourng partcles on the centre partcle. Therefore, t s the maor work n SPH to fnd out the neghbourng partcles. There are 2 popular partcle searchng methods n SPH, one s drect searchng, and the other one s lnk_lst searchng. Drect searchng s sutable for small number of partcle, wth constant or varable smoothng length (an mportant parameter to decde the neghbourng range of a 2 centre partcle). However, ts searchng effcency s ON ( ), where N s the number of partcles taken nto one study, so t s not acceptable to handle wth large number of partcles. As to enhance the partcle searchng effcency, the lnk_lst searchng method s adopted nto MIS. The lnk_lst method creates a spatal grd wth a constant smoothng length and places a small number of partcles nto each cell produced by the grd. Therefore, the neghbourng partcles wll be searched only n the neghbourng cells, so that a great amount of computng tme wll be saved. The lnk_lst method searchng effcency s ON ( ), and very sutable for MIS, n whch a large amount of partcles wll be consdered wth constant smoothng length, as the polymer melt s an ncompressble melt and the partcle dstance s relatvely even. 2.9 Partcle ntaton To begn the whole smulaton work, all partcles should be ntated. CAD software s mplemented to create the 3D geometry of products, whch s used to produce 3D mesh and surface mesh, va commercal mesh software. The 3D mesh s converted nto the ntal set-up for melt partcles wth a pre-processor n MIS, whle the surface mesh s converted nto the ntal set-up for mould and pston partcles. One mprovement n MIS2.5 s that t uses pstons to drve the melt, n order to realze the 5

7 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ smulaton procedure closer to the real fabrcaton. In the followng, some physcal nformaton, such as mass, densty, temperature, pressure, vscosty wll be ntated for all partcles Solutons to tensle nstablty and tme step For actual melt, changng of physcal values s smooth n space. Therefore, t s logcal to keep the value changng of a central partcle to be n consstency wth ts surroundng partcles, ncludng tensle stablty. In MIS, for a central partcle, f ts varable quantty calculated wth conservaton equatons s wthn the value range of ts surroundng partcles, then the value of the central partcle wll be evolved based on ths quantty. If the varable quantty s beyond the range, the central partcle and ts surroundng partcles wll be taken as a whole wth a certan sum of momentum, energy and the same velocty. Then, the evolved value of the central partcle wll be calculated wth the perfect nelastc model ths way. Ths soluton wll avod tensle nstablty whch results n smulaton falure. To choose the approprate tme step, t s necessary to calculate the maxmum flow velocty along the man flowng drecton, based on the flow quantty and product geometry. Then the tme step s determned by rato of partcle nterval to maxmum flow velocty. Ths makes sure that the melt partcle moves wthn one partcle nterval wthn a tme step, and avods unphyscal penetraton. 3 Study Obect and Process 3.1 Study obect In ths study, an aerospace part, mcro cylnder s researched. The necton procedure s smulated by MIS2.5. A comparson of numercal smulaton results are placed between the stuaton where the mould wall frcton effect s consdered and the stuaton where the tradtonal non-slp assumpton are taken on. The 3D presentaton of ths mcro cylnder s shown n Fgure 2. Where the key dmensons are demonstrated n Table 2: Table 1. Key parameters n equaton (13) Symbol Physcal meanng Unt η vscosty Pa. sec γ& shear rate 1/sec T temperature deg.k T* D2 + D3 P deg.k P pressure pa ~ A 2 A2+ D3 P deg.k Others data-ftted coeffcents Table 2. The key dmensons of mcro cylnder Parameter Measurement R R2 7 L 75.4 Accordng to the characterstcs of ths mcro part, two fan-shaped flm gates are appled, to maxmze the fllng processng, as shown n Fgure Study parameters Mcro necton mouldng, as dscussed n secton 2, has more complcated flow behavours than tradtonal necton mouldng. Therefore, n order to obtan the more accurate smulaton results, 3D smulaton are employed. After the success of predcton accuracy n prevous work, n MIS 2.5 melts flowng n runner s added and smulated, n the purpose of obtanng more accurate smulaton results. The key parameters of the necton procedure, used throughout ths study, are demonstrated n Table 3. Based on necton condtons demonstrated above, now 2 research cases are arranged, wth dfferent necton parameters, as represented n Table 4. 6

8 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ Fgure 1. The functon dagram of c and vscosty Fgure 2. 3D graphcal presentaton of mcro cylnder Fgure 3. Fan-shaped flm gates used n ths study The arrows show the flowng drecton of the melt through the gates nto the cavty. The left part s the cavty, the rght part s the runner, and the mddle part s the gate. Table 3. The key parameters of the smulatons No. Parameter Value 1 Materal POLYPROPYLENES, JY 2 Melt Cavty 90 4 Maxmum 14mpa 5 Inecton m Table 4. For smulaton cases n ths study Consderaton of Mould Case Inecton Parameter Wall Frcton Effects 1 Constant necton speed 2 Constant necton speed In case 1 and 2, the polymer melt s nected nto the cavty wth a constant necton speed, whch means the pston wll be drvng the melt n a constant speed. Whle the mould wall frcton effects are consdered n case 1, t s not n case Study procedure Based on these parameters, the fllng courses are smulated wth MIS2.5 n dfferent necton cases. For MIS2.5, frst of all, Hypermesh s used, to generate the facal trangle meshes, n order to obtan the nodes postons n the 3D space. Then the nodes poston data s mported nto the mould wall processng part of MIS2.5, to create the contnuous mould wall, formed by mould partcles. The mould partcles wth the spacal ntervals 1mm, are shown n Fgure 4. Fgure 4. The vrtual partcles used n ths study The left part s the mould partcles formng the mould wall of the cavty, whle the rght part s the mould partcles formng runners. The mddle part s the mould partcles formng gates. 4 Smulaton results comparson 3D smulaton results n 4 cases are compared n the followng: 4.1 Comparson between the smulaton results n case 1 and case 2 The smulaton results comparson between case 1 and case 2 s show n Fgure 8: The left column shows the necton tme of each row. The rght two columns are smulaton results of case 1 and case 2 respectvely. In these two cases, the necton speed s constant, so wthn the 7

9 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ same tme, the cavty s fully flled both n case 1 and case 2. However, the melt shows dfferent behavours durng the whole course. In the begnnng of necton procedure, from tme 0s to tme 0.02s, there seems to be not many dfferences between the two cases, though the flow shape s not exactly the same. Shown n the comparson, the obvous varance starts from 0.025s, where the melt flow front s closer to the end of the cavty n case 1 than what s n case 2. Ths trend follows up untl tme 0.04s. The poston of flow front ndcates the velocty of melt n the drecton through the axs of the mcro cylnder, whch s also the man flowng drecton of the melt. Hence, the drecton through the axs of the mcro cylnder, the melt has hgher velocty n case 1 than n case 2. To observe more carefully, one phenomenon, that the melt n case 2, although does not flow as fast as what s n case 1, t does fll the cavty better, wth less gap n melt. Durng the tme from 0.04s to 0.045s, the melt n the two cases reaches the end of the cavty. After ths step, the melt front s forced back and merges together wth the melt behnd. Wth tme passng by, the melt flls up the gaps gradually, and completes the whole fllng procedure around 0.06s. In the tradtonal theory of non-slp condton near mould wall, where the melt close to the mould wall s statonary, no movement of melt s expected relatve to the mould wall, as shown n Fgure 5: The schematc dagram above shows us that the melt velocty s 0 near the mould wall, and the melt velocty ncreases when t gets closer to the centre lne of the flow front. In contrast, the melt velocty dstrbuton looks dfferent n the condton n whch the mould wall frcton s consdered, as shown n Fgure 6. In such condton, the melt velocty near the mould wall s not 0, but a small value nstead. There s a relatve movement produced between the melt and the mould wall. The flow quantty s n drect rato relatonshp as followng: Q v( x) dx (15) ds Where, Q s the flow quantty, ds s the dstance between the mould wall, v s the velocty parallel to the mould wall, and dx s the dfferental of ds, as shown n Fgure 7. Fgure 5. schematc dagram of non-slp condton Fgure 6. schematc dagram of the condton where mould wall frcton s consdered Fgure 7. schematc dagram of flow quantty In fact, the flow quantty s n drect rato to the shadow area n Fgure 7. In case 1 and case 2, the necton speed s constant. Therefore, n order to keep the flow quantty to be constant, the melt velocty close to the axs of the mcro cylnder n case 2 needs to be larger than what t s n case 1, whch results n the more knetc energy loss from the central melt to the mould wall, va the vscosty resstance among the dfferent areas of the melt wth varous velocty. In ths way, hgher necton pressure s requred to compensate hgher knetc energy loss n case 2, whch means larger flowng resstance. As analyzed above, the melt velocty dfferences between the areas near the mould wall and the areas close to the center provdes the maor source of flowng resstance. Besdes, the melt tends to flow to the place where the flowng resstance s lower. As a result, the melt wll keep ts contact 8

10 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ surface wth the mould wall as small as possble to reduce the flowng resstance. In the same necton amount, melt flowng straght forward wll make bgger contact surface wth the mould wall; whle melt spreadng wll make smaller contact surface relatvely. Thus, part of the melt flows along the crcle of the mcro cylnder. However, the spreadng trend depends on how dffcult t s for the melt to flow straght forward. In case 2, the larger flowng resstance leads the flow to spread more obvously than that n case 1, whch explans why the melt n case 2 seems to be flowng slower, but wth fewer gaps wthn the melt. 4.2 Verfcaton of MIS smulaton accuracy To verfy the smulaton accuracy of MIS, now a comparson s placed between a capllary rheometer experment [12] and a correspondng smulaton. The secton dameter of capllary s 500μm wth the rato of length to dameter L:D=16:1. In ths experment, PS s tested under temperature 230 and varous flow quanttes. The pressure dfference between nlet and outlet s related to the flow quantty. To follow the routnes, flow quanttes are changed nto shear rates near mould wall, as shown below: 3n+ 1 4Q & γ = (16) 3 4n π R γ& s shear rate near mould wall, Q s flow quantty, R s the secton dameter of capllary, and n s non-newtonan flud ndex. Comparson s shown n Fgure 9. From the experment curve, t s clear that pressure dfference gets larger when shear rate ncreases. The smulaton curve consderng mold wall frcton matches the experment curve better than the smulaton curve wthout consderng mold wall frcton. For smulaton consderng wall frcton, the predcton value of pressure dfference s slghtly lower than experment one when shear rate s small, and rses up to be a lttle hgher when shear rate becomes larger. Ths s due to the polymer chan beng dsentangled n actual melt, whch contrbutes to a wall slp phenomenon. However, the smulaton value lowers below experment one when shear rates ncreases further, because frcton and shear heat leads melt vscosty to be decreasng. As a whole, the smulaton result s wthn 10% error compared to the experment outcome. On the contrast, for smulaton wthout consderng mould wall frcton, the predcton value of pressure dfference s hgher than experment one, caused by mssng contrbuton from wall slp, and frcton heatng. The devaton becomes greater when shear rate ncreases and leads to error more than 20% over the experment outcome n general. 5 Conclusons On the foundaton of prevous work, wth mould wall frcton proposal method adusted, calculaton effcency greatly mproved and other components developed, MIS2.5 has been focused on presentng how the mould wall frcton affects the fllng procedure n mcro necton mouldng. The conclusons obtaned from the smulaton results can be summarzed nto the followng aspects: When the mould wall frcton effects are consdered, there s a relatve movement between the melt and the mould wall, whch reduces the flowng resstance and the necton pressure n the whole fabrcaton procedure, compared to the stuaton where the tradtonal non-slp condton s employed. Wth less resstance, the melt s nclned to flow straght forward when mould wall frcton effects are consdered, rather than spread to reduce ts flowng resstance by dmnshng ts contact area wth the mould wall. More accurate smulaton result s obtaned when the mould wall frcton effects are consdered, whch helps manufacturng engneers to choose more reasonable maxmum necton pressure, to avod overflow and short shot. Cut down the requrement of computer hardware. In the same smulaton accuracy wthn ths study, MIS1.0 asks for around 200 MB memory, whle MIS2.5 only requres about 30 MB memory. 9

11 IOP Conf. Seres: Materals Scence and Engneerng 10 (2010) IOP Publshng do: / x/10/1/ Acknowledgement We apprecate the suggestons and nspraton wth all of our sncerty, from my mum, Pro. Lxa Wang, and all the other professors and people n the mcro necton research group n Natonal Engneerng Research Centre for Advanced Polymer Processng Technology of Zhengzhou Unversty. Fgure 8. The smulaton results comparson between case 1 and case 2 Fgure 9. The comparson between the experment and smulaton results References [1] Yao D and Km B 2004 J. Manuf. Sc. Eng., 126, [2] Zhao J, Mayes RH, Chen G, Xe H and Chan PS 2003 J. Polymer EngSc, [3] Yosh M, Kuramoto H and Kato K 1994 J. Polymer Eng Sc, [4] Francsco Manuel Bernal Mart ınez 2008 D. Meshless methods for ellptc and free-boundary problems (Madrd:Unversty Carlos III of Madrd) [5] GR Lu and M B Lu 2003 Smoothed Partcle Hydrodynamcs (Sngapore: World Scentfc Publshng) [6] J J Monaghan 1977 J. Mon. Not. R. Astron. Soc [7] J J Monaghan 1994 J. Comp.Phys [8] H Takeda, S M Myama and M Sekya 1994 J. Prog. Theor. Phys [9] J W Swegle and S W Attaway 1995 J. Comput. Mech [10] P W Cleary and J Ha, V. Ahua 2000 Int. J. Cast Met. Res [11] J Ha, P W Cleary 2000 Int. J. Cast Met. Res [12] Jun Tang 2008 Research on Melt Vscosty and Wall-slp n Mcro-necton Moldng Fllng Flow (Dalan: Dalan Unversty of Technology) 10