E驅≈3S ournal of the European Ceramic Society 21(2001)883-892 w.elsevier. com/locate/jeurc Design and characterisation of a co-extruder to produce trilayer ceramic tubes semi-continuously Z. Liang S blackburn* IRC in Materials for High Performance Applications and School of Chemical Engineering, The University of Birmingham, Edgbaston Birmingham B15 2TT, UK Received 20 June 2000: accepted 2 October 2000 Abstract A co-extruder with three separate barrels operated by a single ram has been designed to produce trilayer tubes semi-continuously A vital step in the design was to predict the pressure required to generate a sufficiently high extrudate velocity while being able to retain the extrudate integrity. a physically based model was used to predict the pressure drops in the co-extrusion process at three different extrusion velocities for five pastes with different rheological characteristics. In general, predicted and measured values were in good agreement. Other important aspects in the co-extruder design, such as velocity and pressure matching of different flow streams are also highlighted. Trilayer ceramic tubes were successfully produced from the designed co-extruder. C 2001 Elsevier Science ltd. All rights reserved Keywords: Al2O3; Clays; Composites; Plasticity; Shaping: Extrusion 1. Introduction in that each die can produce only one shape, but this generally acceptable in the production environment Co-extrusion has been used to produce fine-scale In this work, a design procedure for developing a co- complex ceramic objects. These complex shapes were extruder with three separate barrels to produce trilayer formed by first producing lay-up feed rod assemblies. ceramic tubes semi-continuously without the need for When extruded the extrudates were re-assembled into a hand assembly is described further feed rod and extruded again. This process was Tube forming requires the pastes to flow through dies repeated to reduce the size and multiply the number of with a central mandrel. Conventionally a spider sup- shaped patterns. USing similar procedures, multilayer ports this mandrel and the paste must rejoin after pas ceramic tubes were produced by Liang and Blackburn. 2 sing the spider arms. This can lead to defects known as While this process can produce very complex fine struc- "lamination"which weaken the tube structure. Stronger tures, it is time-consuming and lacks continuity because tubes are formed, where no spider is used, but this nor of the need to produce lay-ups before each extrusion. mally requires a moving mandrel In the design for tri- Therefore, this route has not yet been fully accepted by layer tube extrusion, the problem of which design to use the ceramics industry is compounded by the need to bring the three materials Shannon and Blackburn'successfully designed a co- together to form three distinct and complete concentric extruder which ble to produce laminates from two layers. A compromise intermediate design was used separate feeds, but with only a flat plate configuration. whereby for each individual layer the paste was fed via a This highlights the difficulty with continuous processes manifold around the pin. 4 This requires the pin to have a reasonably large diameter to prevent distortion from try of the paste. The joining of paste behind the pin could form a"lamination"in each layer, but by geometrically arranging the flows these 4 Corresponding aut laminations could be offset in the three layers minimiz E-mail address: s blackburn ( a bham ac uk(S Blackburn). ing the effect. 0955-2219/01/S. see front matter C 2001 Elsevier Science Ltd. All rights reserved. PII:S0955-2219(00)00292-2
!" # $ !" # !"""$ ! % !""" & ' & ' ( ) ' & ' * + ' * , ' % * - ' . ' !""/ 0 & $ % & &!%1$ 2$ 2 $ 3 $ $ 0 2 + 4 / . ' + 5 ' . ' 6 7 ' ! 5 + . 1 ' ' ' ' - + . ) ' , ' ' ' . ( - ' ' 2 4 . ' 88 99 ' ' ' ( , ' & ' ' ' : . ( . 4 88 99 - ' * 6 * "; !""/ 0 & 3,,? ";<<!!/;@""A""!;!! # 0 2 !/ @!""/A BB1CB;! ''' = =4 2 ' & D @ A
Z. Liang, S. Blackburn/Journal of the European Ceramic Society 21(2001)883-892 2. Co-extruder, structural design Based on this principle, a die assembly to transfer the three different materials from their The designs aim was to produce trilayer tubes, the respective barrels to form concentric layers around a material for each layer being supplied from three sepa- central mandrel (Pin 1). This was achieved by using an ate barrels. To achieve this each material was to be assembly of four dies. The flow paths for the three dif- applied consecutively around the central mandrel ferent materials through the first three dies are illu- through a series of manifolds. By assuring constant strated in Fig. 2. The central mandrel(Pin 1)was volumetric displacement, the design made use of a single screwed into the bottom of the barrel block containing constant speed drive from a load frame, pushing the the three barrels. Around this pin a die was placed three plungers through a force transmission plate. Three denoted Die I and shown in Fig. 3. Die I had two removable steel balls were placed between the plungers transition holes, a middle hole forming the die land, a and the top drive plate to tolerate any misalignment transition slot and a thin die wall extension. The middle between the different plungers. The key aspects of the and outer layer materials were transferred to Die 2 design are shown in Fig. 1 through the transition holes. The inner layer material filled the transition slot and flowed down the central hole around the inner mandrel(Pin 1). The metal tube extension at the bottom of die l forms the mandrel for Die 2 and is denoted Pin 2. This extension preserved the Force transmission plate shape of the inner layer extrudate during later layer am for inner layer Ram for middle layer formation. Dies 2 and 3 had similar structures to Die 1 but with reducing numbers of transition holes. Thus, there are three mandrels(Pins 1-3)associated with three dies dies 1-3)when the die set is assembled. The design ould therefo Central pirt materials with gaps between each layer as shown in Fig 4. A final conical die, Die 4(Fig. 4), compressed the layers to give the final trilayer tube structure around Pin 1. The assembly was held in place by location pins and clamp ring as shown in Fig. I Die 4 2. Co-extruder dimensions Fig. 1. The external view of the co-extruder. Having developed a flow scheme and physical struc- ure for the co-extruder, the dimensions of the compo nents were fixed by considering the following criteria Middle laye Transition hole I Transition slot Transi Fig. 2. Illustration of flow streams within the die assembly Fig 3. A schematic drawing of Die I
. 9 ' . ' . ' ' ' * . ' E / ' * @3 /A . ' . - ' + E ! . @3 /A ' ' & ' / ' E 1 / ' ' . ' ! . + - ' ' @3 /A . / ! 3 ! . ! 1 / ' . @3 /C1A ' @ /C1A ' . ' ' ' ' E : & + : @E :A + 3 / . ' ' E / #(!( ' ) * F - ' ' + ' E / . ' E ! , - ' ' E 1 & ' / BB: +( , ( - * . /* * #! 0#11!2 334536#
Z. Liang, S. Blackburn/Journal of the European Ceramic Society 21(2001)883 I. Without Die 4 in place, the three layers should Hence. the diameters of the barrels were obtained travel at the same velocity so that using eq ( 3) ouL.x 2. Pressure matching without Die 4 in place for dif- where Vix is the extrudate velocity for layer i at the ferent layers (Pin= Pmid= Pout) is a natural con- exit of the die assembly without Die 4 in place. If sequence of the design. The three plungers are one paste travels faster than others, delamination forced to move down at the same speed by the load or air bubbles may appear between adjacent layers frame. If the resistance on one plunger is higher than of the extrudate. Vi x can be calculated by the fol- that on the others, then that will govern the pressure lowing equation. development. However, any significant imbalance induced by the design or paste mismatching would lead to twisting in the system and potentially mechanical failure. Therefore the design aimed to where Aio is the area of the barrel for layer i, Aix is give the same pressure drop through each channel the toroidal area for layer i exiting Dies 1-3 with for a paste of the same rheology out Die 4 present. Vo is the ram speed. As the ram The pressure drop in the transition slot (PB) peed and the velocity at the exit of the die assem hould be much less than in the tube land (pc) bly are the same for all three layers, the barrel This pressure difference ensures the slot is fully fil diameters must be different, and Eqs.(1)and(2) to the tube die land can then be ged to give that uniform filling of the layers can be achieved 4. The load required for co-extrusion should not Ain.x Amid x Aouto Aix mechanical design of the barrel and die bly. Aix is normally defined by the final application of The limit here has been set at 100 kn by the load the products. In the experimental extruder the lay- frame used to drive the system. In addition, the ers at the exit of the assembly of dies 1-3 were set to load should be as low as possible to keep the be I mm thick, separated by walls I mm thick. extruder construction costs to a minimum With the exception of the first criterion, it is pressure The bottom of Die 3 drop which is the critical parameter. Pressure drops were predicted before constructing the co-extruder. The X and the top of Die 4 cross-sectional areas and lengths of transition slots and transition holes were varied until all the listed criteria 2 and 4 were satisfied. Details of the pressure prediction Pin 1 methods are given in a later section Die 1/Pin 2 2.2. Producing trilaver tubes by the designed co-extruder Die 2/ Pin3 Trilayer tubes were successfully produced by the designed co-extruder. Figs. 5 and 6 show samples of two types of trilayer tubes extruded from the design. The outer diameter of the tubes was 6 mm and the inner diameter was DIE 4 2 mm. The illustrated tubes had well defined roundness Pin I uniform wall thickness and smooth inner and outer sur faces. However, experience showed that successful co- extrusion with this co-extruder was strongly dependent on the paste properties. The paste properties could be adjus ted through formulation to allow successful processing 1. Of prime importance is that the pastes have well matched rheological properties. The dimensions of the co-extruder were determined based on this assumption. Any rheological resulted in force differences on the three plungers and velocit differences in Die 4. Force imbalance brought about Fig 4. A schematic drawing of Die 4. by different rheological behaviour in the three pastes
/ 5 : 7) 7) 7) ' 7) ' : , ' 4 7) ' ( 7) " ) 7" ' " ) /C1 ' : 7" & * 0( @/A @!A " ) " ) " " " ) ) + + , /C1 ' / ' / F ' 0( @1A ! 3 ' : @ A ( . ' , ' F ' + ' ' . 1 . @ A @ A . * + - ' + : . ( . /"" G , ' 5 + ' 3 ' . ' ! 1 : ' + #(#( * * ' ) * . ' E < H ' ' . ' H ' ! . ' + ' F ' ' ' ' . 4 ' / % ' . ' & * * * : E E : & ' : * +( , ( - * . /* * #! 0#11!2 334536# BB<
Z. Liang, S. Blackburn/Journal of the European Ceramic Society 21(2001)883-892 caused different flow characteristics, leading to as Pin, Pmid, and Pout, for the inner, middle and outer incomplete layer formation in the final extrudate layer of the tube, respectively, generalised as Pi. Each 2. The formulation and preparation of the pastes is flow path can be further divided into three sections. The critical, phase migration must be controlled. pressure drops into the transition hole, through and Uncontrolled phase migration leads to changing along the transition slot and along the tube land are rheological properties and can ultimately lead to therefore denoted as PA i, PB i and Pc i respectively iquid depletion and unacceptably high extrusion The pressure drop in transition hole, PA i, for any of pressures. If the pastes have different stability, then the three flow channels comprises two separate pressure blockage of one channel relative to others may drops, one being due to the area change from the barrel occur leading to potential equipment damage to the transition hole. the other due to now down the The pastes should be designed such that shape is transition die land. These two pressure drops are given by retained post extrusion. However, should not be too stiff as high forces may D0,4L1.i (o+B1)(6) the equipment The formulation of pastes with the above behavioural haracteristic is discussed by Benbow and Bridgwater. 5 The extruder had no spider, reducing the potential for defects to be introduced into the flow stream. most cracks, such as those shown in Fig. 5, occurred during where Di i is the diameter of the transition die and Lii is the drying and sintering process. The fixed mandrels its length, Do i is the diameter of the barrel, Vo. i is the Pins 1-3) would allow cutting in continuous operation. ram speed and Vi i is the velocity of paste travelling in the transition die in layer i. Eq.(6)is directly compar- able to Eq. (5)as the geometry is essentially the same 3. Characterisation of the co-extruder The pressure drop in transition slot PB. i can again be simplified to two sections, one being the pressure required Pastes can be characterised using an equation model to overcome the shear stress at the wall of the slot land developed by Benbow et al.: 5 and the other is the pressure required for the paste to deform and flow past the pin associated with layer i to P=2o0+c1)n+4(0+B (4) completely fill the slot. This combined pressure drop is where P is the total pressure, required for extrusion =2x2+x2(m+B1) through a square entry die of circular cross-section. The paste parameters are oo, the bulk yield stress, a, the bulk velocity factor, to, the die wall shear stress and B, the di +1b2-D2)(m+ak2) wall velocity factor. Do and D are the diameter of the barrel and die respectively, L is the die length and v the 丌D extrudate velocity. This original equation has been tDo.i voi and v2,i4(b:-D2 i)hi extended to deal with non-linear velocity dependence. such that where L,i, bi and hi are the length width and height of P=2(∞+a1jp7+4-(v0+B") (5) the transition slot respectively, D2. i is the diameter of the pin i. velocities of the paste travelling in the slot and where m and n are bulk and wall velocity exponents, respectively for layer, slot and the pin are v2, i and V in the gap between the respectively, adding two further paste parameters. Note The calculation of PB. i using Eq .( 8)assumes that that ai and Bi have different units to a and B in Eq. (4). there is paste flow along the second half of the transition It has been suggested in the literature that the paste slot and that there is no additional wall friction from the parameters and principles derived from Eq.(4) can be pin, only a contribution due to the cross-sectional area used to calculate the flow in more complex geometries. change. This is termed flow pattern I. However, later This principle was applied to predict the pressure drop experimental observation showed the flow pattern to be in flow through the adopted design different to the assumed flow pattern. The true flow path In the co-extruder without Die 4 in place, there are was better represented by that shown in Fig. 7(Flo three independent flow paths as shown in Fig. 2. The pattern II). Therefore, PB. i was recalculated based on pressure drops for each of these flow paths are denoted this observation and the result is given as PB. (il)
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
Z. Liang, S. Blackburn Journal of the European Ceramic Society 21(2001)883-892 887 Fig. 5. Al2O/ porous Al2O3 Al2O, trilayer tube fabricated in the co-extruder(outer diameter 6 mm) 彐 Fig. 6. A picture of a trilayer colourful fun clay tube produced in the co-extruder(outer diameter 6 mm)
E H & @ H A E < &!%1= &!%1=&!%1 @ H A +( , ( - * . /* * #! 0#11!2 334536# BBK
Z. Liang, S. Blackburn /Journal of the European Ceramic Society 21(2001)883-892 PB.ill h;×L2r+b; -(To.i+B1.iv2i) where the diameter of the die is D3. i and its length is L3.i b;×h and the extrudate velocity within the die is v3 The pressure drop required for co-extrusion without +n( bi-d2. i (∞+a1.m) Die 4 in place can therefore be calculated by (T D2. i+ rbi)hi+1/2(b-Da oi+B1.;2) Pi D=PA i+ PB. I(f)+PcIn) (14) (bi-D,ih (10) Pi(D= PA i+ PB. I(D)+PcI(m) (15) The calculation of Pci is similar to that of PAi except for the need to consider the influence of the associated or pin and the die wall. Initially the flow was considered to be from the total area of the feed slot to the die land Pi (m =PA i+ PB.1(lll)+PcI(lID) (16) configuration and denoted flow pattern I. However, the flow pattern observed later indicated that the flow The pressure drop in Die 4, Pw is the sum of three would be better represented by either the total of the components (Pw= PI+ P2+P3). PI is the pressure feed slot less the static region(shown in Fig. 7)reducing drop due only to the change in cross-sectional area. P2 into the die land orifice( Flow pattern ID) or finally to and P3 are the pressure drops that are required to assume that the paste enters the die land orifice as if fed overcome the wall resistance to flow along the perimeter from a barrel of a diameter equivalent to the slot width of the cylindrical die land and the conical die land b2. i, such flow being denoted Flow pattern Ill. Fig8 respectively. This gives summarizes these three flow patterns. Therefore, the pressure loss in the tube die land was calculated in three PI=(oo+a1V4)In R4 -R6 R (17) PC(1)=(∞0;+a P2=(+BKL4+2RL5) (18) R5-R 4L3.了 D (to;+B3) x(R3-R3) P3 丌(2tan6-R ztan8-R6 (19) Pci (D=(oo, i+alivad bL2/2+mb/8-xD2/4 (To+B13 ), where R4 is the entry radius of Die 4, Rs is the exit radius of Die 4, R is the radius of Pin 1, V4 is the (12) extrudate velocity, L4 is the length of the cylindrical land of Die 4, Ls is the length of Pin I beyond Die 3 Pc.(I1)=(o+a,;3; (Ls >L4), 0 is the cone half-angle, and z is the paste flowing direction Finally, the total load required for co-extrusion can Pin 2 Transition slot Active area □ Dead area Fig. 7. Illustration of nomenclature used in the PBan calculation for middle flow stream
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
Z. Liang, S. Blackburn /Journal of the European Ceramic Society 21(2001)883-892 Flow pattern I Middle hole and Pin 3 Diameter= D3 Diameter = D, b The bottom of Flow pattern II Middle hole and Pin 3 Diameter= D3 Diameter= D2 b2 The bottom of Flow pattern Ill Middle hole and Pin 3 Diameter= D Length=L3 Pin 2 Diameter=D, Fig 8. Illustration of the middle fow stream(shaded areas) used in the calculation of Pc F=Pin×Ain.0+Pmid×Amid0+Pout×Aou.0 paste through the co-extruder at a ram speed of 2 mm/s +Pw x(Ain,0+Amid, 0+Aout, o) (20) The paste was characterised using a ram extruder attached to a 100 kN load frame(Model 1195 Instron UK). The barrel was 25. 4 mm in diameter, to which was attached one of three dies the dies were all 3 mm in the whole computing procedures are given by Lan oo where Ai o is the generalised area of barrel i. Details of diameter with L/D ratios of 2, 4 and 8. Extrusion pres sures were measured at six extrudate velocities for each die. The data was used to solve Eq. (5). Table I lists the 3. 1. Model verification paste formulation and paste rheological parameters Table 2 shows the calculated results for co-extrusion for To demonstrate the applicability of the model, pres- each die section, accounting for the three flow patterns sure drop was determined when passing an alumina defined by Eqs. (14(16). The predictions from the
: " " " % " " " ' " ' H 4(!( ; . ' ' ! = . ' /"" G @I //;< , 7LA . ' !<: ' ' . ' 1 ' ,8 ! : B 0 ' . ' 0( @<A . / . ! ' - ' + 0( @/:AC@/HA . E B , - ' @ A +( , ( - * . /* * #! 0#11!2 334536# BB;
Z. Liang, S. Blackburn/Journal of the European Ceramic Society 21( 2001)883-892 three flow patterns gave similar results, the difference extruders give positive displacement. Thor being within 5%. This result shows that the difference problems with producing matched flow rates are envi- caused by uncertainty within the transition slot is of little aged in twin screw systems without close control and consequence to the overall pressure drop. Therefore, extensive development only one flow pattern, flow pattern I, was applied for predictions for different paste formulations and of 3. 2. Comparison of predicted and measured pressure course the original extruder design. In general, three flow drops of five pastes through the co-extruder paths without Die 4 in place are predicted to generate similar pressure drops(Pin A Pmid N Pout). The pressure To further verify the applicability of the calculation distribution in each flow path is also shown in Table 2. five pastes were prepared for flow characterisation For all three paths, the pressure drops in the slot ar through the co-extruder. Three pastes were of one for much lower than those in the tube die land (PB< Pc). mulation group, denoted Type A, their behaviour mod- The estimated load required for co-extruding this paste ified by different liquid contents. The fourth paste, Type inder the selected operating conditions was around 25 B, had a similar formulation to Paste A(2)with addition kN, which is much lower than the limit of the load frame. of 0.07 wt. glycerol. The last paste, Type C, was In summary, the design adopted for the co-extruder colourful fun clay, a modelling dough. The formula- satisfied to the required level all criteria outlined earlier. tions of these pastes, where available, are listed The adopted design gave good continuity with the Table 3 three independent barrels, it ensured that trilayer cera- he rheological properties of the five pastes were mic tubes could be produced semi-continuously, mean- measured by capillary rheometer as before and analysed ing that production ceased only when the barrels were using Eqs.(4)and(5).5 Fig 9 shows the pressure drop empty. In the future these independent barrels used in and extrudate velocity relationship for paste A(2). All the experimental extruder could be refilled auto- pastes exhibited pseudo-plastic behaviour and hence the matically or the barrels could be replaced by twin screw best fit was always obtained using 5). The mea- sured rheological parameters of the pastes are listed in ple l Tables 4 and 5 for the two equations. The following Paste formulation and paste rheological parameters for the Al2 0, reasons are suggested for the generation of the negative paste used in the development of the co-extruder a values reported for thecolourful fun clay.In the long die frictional heating effects may have softened the Paste contents material during the extrusion. Alternatively, the higher Al2O3100.0 do0.30 MPa pressure generated during long die extrusion may hav Binder 8.0 g aI 11.09 MPa s Bi 11.35 MPa Solvent 14.4 resulted in material break down or re-arrangement, so g n0.46 that the material became more fluid Table 2 Predicted loads and pressure drops for the Al2O3 paste(Table 1)in the co-extruder Load (kN) Flow pattern I Flow pattern Il Flow pattern Ill 3.2 3.16 fiddle Outer Total 26.2 Pressure(MPa) Pin iqIn 3.67 24.0 Middle Outer 24.8 5.18 9.26 10.810.3 Table 3 Paste formulations Table 4 Paste parameters from four-parameter characterisation T A(1)A(2)A(3)BC 82481780.981.6 (1)A(2) A(3)B 84 0.8470.670.35 Solvent(wt % 11.3 11.8 12.3 11.8 colour fun clay a(MPa s m-)2766 142.738.1 Glycerol(wt % 0.1 0.6 0.406 0.240.34 0.094 Liquid content(wt %) 17.6 18.3 19.1 18.4 (MPa s
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
Z. Liang, S. Blackburn /Journal of the European Ceramic Society 21(2001)883-892 All the pastes were passed through the co-extruder at Eq. (5)to the capillary data and these errors compro- three different extrusion velocities. The forces required mise the predictions in the co-extruder. Some gross were measured and are reported in Tables 6 and 7 simplifications are made in the prediction of flow in the The predicted values in Table 6 were calculated from co-extruder and this further contributes to the deviation the paste parameters derived from Eq (5)and reported between the measured and predicted values. Given these in Table 5 using Eqs.(6H(20). The error values reported constraints, the usefulness of the approach in design is indicate the degree of fit between the predictions and the demonstrated experimental data. For pastes of type A, the predicted forces were overestimated the difference being within 15%. For pastes of types B and C, the predicted values were lower than the experimental data, the error ranging from -20 to -30%. In general, the predicted data fol low the same trend as the measured values though the closeness of the fit is dependent on composition and lasticity of the pastes. errors are generated in fittin Table 5 fit Paste parameters from six-parameter characterisation 6-parameter fit A(1)A(2) C Jo(MPa) 0.85 0 a1(MPas-m)50.4511.0921.583.201.20 0.005 0.015 0.550.410.51 Velocity(m/s) BI(MPa s-n) 11.35 6.01 2.28 0.46 0.43 0.44 Fig. 9. Pressure velocity curve and model fits for paste A(2)at Table 6 Table 7 Prediction from six-parameter characterisation and experimental Prediction from four-parameter characterisation and experimen Error(%)=(Prediction-Experiment)/Experimentx 100 Error (%)=(Prediction-Experiment)/Experiment x100 Extrudate velocity (m/s) 1.04E-3 519E-4 260E-4 Paste type Extrudate velocity(m/s) 1.04E-3 519E-4 260E-4 1) Experiment(kN 32.8 rediction(kN) Prediction(kN 6.5 Error(%) Paste type Extrudate velocity (m/s) 1.04E-3 519E-4 260E-4 Paste type Extrudate velocity(m/s) 1.04E-3 519E.4 2.60E-4 ment(kN) 8.75 l4.5 A(2) 18.75 14.5 Prediction(kN) 19.2 14.7 Prediction(kN) 32.8 Error(%) A() pe Extrudate velocity(m/s) 1.04E.3 519E.4 2.60E-4 Paste type Extrudate velocity(m/s) 1.04E-3519E-4260E-4 Experiment (kN) Experiment(kN 10.75 Prediction(kN) Prediction(kN Error (%o) Paste type Extrudate velocity(m/s) 1.04E-3 5. 19E-4 260E-4 Paste type Extrudate velocity(m/s) 1.04E-3 519E.4 2.60E-4 Experiment(kN) 18.1 Experiment (kN) 23.25 Prediction (kN) Prediction (kN Paste type Extrudate velocity(m, 104E-35.19E-42.60E-4 Paste type Extrudate velocity(m/s) 1.04E-3 519E.4 2.60E-4 Experiment(kN) Experiment (kN) Prediction (kN) 6.36 Prediction (kN) 791 7.72 7.65 Error (% 24 Error(%)
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
Z. Liang, S. Blackburn/Journal of the European Ceramic Society 21(2001)883-892 pastes. The success of the design relies on velocity, rheology and pressure matching in the different layers Flow in the designed co-extruder was characterised by a hysically based model. The model, when used in its 15 more complex form gave reasonable agreement with measured values provided the paste was not highly plastic in nature. The alternative reduced parameter characterisation method could not be used to analyse the flow behaviour of pseudo-plastic pastes, especially Experimental data at low extrudate velocities 0E+002E044E046E048E041E03 Extrudate velocity(m/s) Acknowledgements Fig. 10. Fig 9 expanded at low velocities. The authors would like to thank the ors scheme and the school of Chemical Engineering for the funding to carry out this work. The EPSrc is acknowledged for its The predicted values in Table 7 were calculated using funding of the IRC in Materials for High Performance the paste parameters derived from Eq(4). The calcula- Applications, where this work was carried out ion follows the same procedures described above, except m and n were set to I for the whole calculation and oo, a, to and B adjusted accordingly. In this case, fit between prediction and experiment was poor, some References errors being greater than 100%. For these reasons the four-parameter characterisation can not be used to I. Van Hoy, C, Barda, A, Griffith, M. and Halloran, J. W, analyse the flow behaviour of such pseudo-plastic Microfabrication of ceramics by co-extrusion. Journal of the pastes, especially at low extrudate velocities in such American Ceramic Society, 1998. 81(1), 152-158 complex geometries. Fig 10 shows the pressure drop in 2. Liang, Z and Blackburn, S, Co-extrusion of multilayer tubes. dings,1998,58,113-124 a capillary at low velocities for paste A(2). It can be seen 3. Shannon, T. and Blackburn, S, The production of alumina/zir- that a large error is introduced by the application of eq conia laminated composites by co-extrusion. Ceramic Engineering (4), which results in poor load predictions for the co- and Science Proceedings, 1995. 16. 1115-1120 extrusion process. 4. Doshi, S.R., Charrier, J. M. and Dealy, J. M, A co-extrusion process for the manufacture of short-fibre-reinforced thermo- plastic pipe. Polymer Engineering and Science, 1988, 128(15), 964- 4. Conclusions 5. Benbow, J.J. and Bridgwater, J. Die design and construction. In Paste flow and extrusion ed.j.r crookall. m c. shaw and The design procedures for a co-extruder are reported N. P. Suh. Clarendon Press, Oxford, 1993, pp 83-97. Liang. Z. Design and characterisation of a co-extruder. In Co. A co-extruder has been constructed using these princi- extrusion of Multilayer Tubes, PhD thesis. The University of Bir- ples and used to produce trilayer tubes from ceramic
. . K ' 0( @:A . ' ' / ' " " 4 , + ' ' /""M E - ' ' E /" ' ' &@!A , 0( @:A ' . & . * E ' ' . ' ' ' . - ' ' . ' % 2 0 ' . 03 2 ' , 2 I F 3 & ' ' ' / J F 2 & N ) I F # 5 I /* /;;B @/A /<!C/<B ! 2 /;;B ! //1C/!: 1 . . =6 /;;< " ///<C//!" : 2 # I # I & + /;BB @/<A ;H:C ;K1 < ' # # ' # , : % ) * # 2 I 2 ' G 3 2 3 % /;;1 B1C;K H , ' ) * * * 3 . 7 /;;; E /" E ; ' B;! +( , ( - * . /* * #! 0#11!2 334536#