- Email: [email protected]
Study on the melting performance of single screw extruder with grooved melting zone and barr screw
Journal of Materials Processing Technology 214 (2014) 2834–2842
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Study on the melting performance of single screw extruder with grooved melting zone and barr screw X.-M. Jin a,1 , M.-Y. Jia a,b,∗ , P. Xue a,∗∗ , J.-Ch. Cai a,2 , L. Pan a,2 , D.-Q. Yu a,2 a b
Beijing University of Chemical Technology, Institute of Plastic Machinery and Engineering, Beijing 100029, China Xinjiang Institute of Engineering, Department of Mechanical Engineering, Xinjiang Uygur Autonomous Region, 830091, China
a r t i c l e
i n f o
Article history: Received 28 March 2014 Received in revised form 7 June 2014 Accepted 29 June 2014 Available online 6 July 2014 Keywords: Melting model Grooved melting zone Barr screw Melt starting point Melting length Energy consumption
a b s t r a c t A novel melting mechanism for single screw extruder with grooved melting zone and barr screw was established. The whole solid-plug, which came from the grooved feed zone, was ruptured and melted mainly by continuously changing the volume of the screw channels and the barrel grooves in the grooved melting zone. A new single screw extruder platform with hydraulic-clamshell type barrels was constructed to investigate the melting performance of different combinations of barrels and screws. The melting model was verified by experiments. Compared with conventional single screw extruder, the melting started earlier and the melting length was shorter in the single screw extruder with grooved melting zone. The melting efficiency was improved by the grooved melting zone and the melting stability was improved by the barr screw. The dimensionless analysis of energy indicates that the heat convection and viscous dissipation are the main melting heat sources for the single screw extruder with grooved melting zone. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Single screw extruders (SSEs) are widely used as one of the basic and convenient elements to melt and convey polymer materials. SSEs are composed of feed zone, melting zone and metering zone. Schneider (1968) machined axial grooves and later Machen (1981) machined helical grooves into the barrel to creat a hgih friction coefficient and thus improve the solid conveying efficiency. Pan et al. (2012) first proposed double-flight driving theory for SSE with grooved feed zone and studied the positive conveying in the feed zone. Compared with conventional SSEs, the SSEs with grooved feed zone can obtain high specific throughput. However, Potente et al. (2006) did lots of study on SSEs with helical grooves and pointed out that the increased solid throughput cannot be melt uniformly depending on the external heat source conducted from the barrel and the external friction heat generated by the friction of the polymer on the barrel and screw. Grünschloß (2002) presented the
∗ Corresponding author at: Beijing University of Chemical Technology, Institute of Plastic Machinery and Engineering, Beijing 100029, China. Tel.: +86 10 6443 6016. ∗∗ Corresponding author. Tel.: +86 10 6443 6016. E-mail addresses: [email protected] (X.-M. Jin), [email protected] (M.-Y. Jia), [email protected] (P. Xue), [email protected] (J.-C. Cai), [email protected] (L. Pan), yu12 [email protected] (D.-Q. Yu). 1 Tel.: +86 10 6442 6911. 2 Tel.: +86 10 6443 6016. http://dx.doi.org/10.1016/j.jmatprotec.2014.06.022 0924-0136/© 2014 Elsevier B.V. All rights reserved.
HELIBAR extruder which was composed of barrier screw and barrel with both grooved feed zone and melting zone. In consideration of the melting shortage of extruder with grooved feed zone, the HELIBAR extruder’s barrel grooves in the melting zone were simply used as channels of melt flow. The higher specific throughput and the poorer melting performance generated higher pressure in the extruder, which finally resulted in excessive wear and low energy efficiency. Currently, poor melting quality is the main issue of the development of SSEs with grooved feed zone. Researchers offered several approaches to improve the melting quality. For instance, adding mixing elements to SEE was considered to be a useful way. However, mixing elements adversely affect the capacity of extrusion because they have no positive pumping capacity and are pressure consumption elements, which produce higher pressure drop and induce stagnation. Increasing lengthto-diameter ratio (L/D) and decreasing screw speed to improve the melting quality finally lead to long thermomechanical history, high-energy consumption and bulky equipment. Therefore, the approaches above cannot fundamentally improve the melting quality of SSE with grooved feed zone. Pan et al. (2012) did research on SSE with normal screw and grooved feed zone only and found that the melt film is easily formed because of the internal friction between the solid-plugs which were ruptured from the whole solid-plug at high extrusion pressure in the feed zone. The grooved feed zone of the barrel was usually cooled and thermally separated from the following heated barrel
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Nomenclature HD HC HV Ff Lc Ls P1end QV V0 Zc Zs b0 bo c h lm ls lc k q Tm
vc ˛ ˇ ϕc ϕs i o s m c c
ratio of heat conduction to total energy consumption ratio of heat convection to total energy consumption ratio of viscous dissipation to total energy consumption internal friction force (N) melting length in the barrel groove (m) melting length in the screw channel (m) pressure at the end of the feed zone (Pa) average volumetric flow rate of the extruder (m3 s−1 ) circumferential velocity of barrel (m/s) unwound melting length in the barrel groove (m) unwound melting length in the screw channel (m) sensitivity of viscosity to temperature change (1/◦ C) sensitivity of viscosity to temperature change (0.03/◦ C) specific heat coefficient (2400 J/kg ◦ C) melt film thickness (m) the melt starting point (m) melt starting point in the screw channel (m) melt starting point in the barrel groove (m) thermal conductivity (W/m ◦ C) internal friction heat (W/m2 ) the melting point of the material (107 ◦ C) velocity of the solid-plug along the axis y (m/s) thermal diffusivity (1.1 × 10−7 m2 /s) melt thermal conductivity (0.25 W/m ◦ C) barrel groove helical angle (◦ ) screw channel helical angle (◦ ) melting latent heat (1.3 × 105 J/kg) internal friction coefficient of material (0.37) external friction coefficient of material (0.19) material solid density (485 kg/m3 ) material melt density (920 kg/m3 ) material shear strength (5.8 × 106 Pa) material shearing resistance (N) viscosity (Pa s)
zones to ensure the solid conveying. The wide use of cooling system indicated that the energy of friction heat in grooved feed zone was enormous. By extending the grooves in the feed zone of the barrel to the melting zone and applying this melting mechanism in the grooved melting zone, the solid is melted by significant internal friction heat rather than poor external friction heat. The internal friction was not suppressed but adequately is deliberately used to plastificate the material. By analyzing the forces on the whole solid-plug in the barrel groove and the screw channel, the boundary conditions that the whole solid-plug being cut off into smaller solid-plugs were determined and then a new melting theory was proposed. A new SSE platform with hydraulic-clamshell type barrels was constructed. The melt starting point and the melting length of different combinations of barrels and screws were also discussed to analyse the effect of screw speed. Besides, by the dimensionless analysis of energy, the main melting heat source for the SSE with grooved melting zone was found. 2. Physical model Fig. 1 illustrates the melting of SSE with grooved melting zone and barrier screw. Pan et al. (2012) proved that a whole solid-plug in the grooved feed zone did exist and indicated that the whole
2835
solid-plug did not experience any internal circumferential shear fracture and then entered the melting zone. All the following theoretical analysis in the study is based on the fact that the whole solid-plug does exist and then is reptured into smaller solid-plugs. In the melting zone, the barrel grooves and the barrier screw channels (the solid channel and the melt channel) are coupled which means the volume (cross-sectional area) of the barrel grooves and the screw channels vary accordingly. In the down channel direction, the volume of the barrel groove is reduced by reducing the barrel groove depth and/or narrowing the barrel groove width. The volume of the solid channel is reduced by reducing the melt channel depth while the volume of the melt channel is increased by deepening the solid channel depth. The solid-plug in the barrel groove is pushed downward by the volume-decreased barrel groove and that in the solid channel is pushed upward by the volume-decreased solid channel. The decreasing volume of the barrel groove and the increasing volume of the screw channel together divide the whole solid-plug into two smaller solid-plugs. Then the two smaller solidplugs are forced to move by the active sides of the barrel groove and the barrier flight. Due to the tremendous internal friction heat generated by the two smaller solid-plugs rubbing against each other, the solid at the interface melts firstly and melt film is developed. Please note that the melting efficiency here is improved because the friction here is the internal friction rather than the external friction in traditional extruders. The heat generated from the internal friction is much higher than that from the external friction due to the higher internal friction coefficient. Then, by pressing the solid-plug in the barrel groove against that in the solid channel, a radial velocity profile is induced in the melt film, which results in removing the newly melted polymer from the location of melting and forming a melt pool in the melt channel. The volume-increased melt channel provides just enough room for the increased melt pool. In order to keep a steady melting of the solid, the newly melted polymer must be moved into the melt channel in time and the change of volume of the barrel groove and the solid channel deforming the solid-plugs to keep the continuous close contact with each other. With more and more melting, the solid in the barrel grooves and the solid channel gradually melts and the melted polymer is then pumped through the metering zone and finally through a die to form the desired product shape. The barr screw was introduced in this model and was chosen for two reasons. First of all, the barr screw can physically separate the solid bed from the melt pool and prevent the solid-plug in the solid channel from breaking up as all barrier screws did. Secondly, the solid channel and the melt channel are constant and the solid channel is wider than other types of barrier screws. Rauwendaal (1986) evaluated the barr screw and pointed out that the width of the solid channel of the barr screw is corresponding to the melting rate because the width of the channel directly determined the width of the solid bed.
3. Mathematical model 3.1. Basic assumption (1) The process is steady. (2) The film thickness is much smaller than its width. (3) The temperature of the polymer melt remains at the sharp melting point, Tm , throughout the melting. (4) The temperature of the solid-plugs in the barrel grooves and the solid channels remains constant, Tc and Ts , respectively. (5) The pressure differences between the top and sides of the barrel grooves and the barr screw channels are negligible. (6) The flow is incompressible. (7) It is a two-dimensional problem.
2836
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Fig. 1. The melting of SSE with grooved melting zone and barrier screw.
(8) The friction coefficient, in terms of the Coulomb’s Law, is a constant. (9) The solid-plug occupying the full width of the solid channel and the barrel groove. (10) The solid-plugs in the barrel grooves and the screw channels are assumed to be ductile and unbreakable.
In order to simplify the analysis, the whole solid-plug was divided into three parts including solid-plug in the barrel groove, the gap and the screw channel. The forces on the three solid-plugs, as represented in Fig. 2, were analyzed to investigate the boundary conditions where the whole solid-plug is being ruptured and starting to melt. The interface shear forces on the outer surface of screw ( screw ) and the inner surface of barrel ( barrel ) is determined by the analysis of the torque balance around the screw axis and the force balance alone the down channel direction. The expressions of screw and barrel are given
barrel
screw > c
and/or
screw > Ff
3.2. Melt starting point
P1end s Wc2 (Hs2 + Ws2 ) [s cos(˛s − ϕs ) − sin(˛s − ϕs )] sin(ϕs + ϕc )
(1)
P1end c Ws2 (Hc2 + Wc2 ) = [c cos(˛c + ϕc ) + sin(˛c + ϕc )] sin(ϕs + ϕc )
(2)
screw =
polymer was assumed to be removed away from the interface as soon as it forms. Therefore, the interface was kept as the interface of solid to solid. The generated internal friction heat is enough to melt the solid. The rupture conditions are obtained.
where P1end is the extrusion pressure at the end of the feed zone given by Pan et al. (2012), c the external friction coefficient of the polymer on the barrel, s the external friction coefficient of the polymer on the screw, ˛c the transmission angle of solid-plug in the barrel groove, ˛s the transmission angle of solid-plug in the screw channel, ϕc the barrel groove helical angle and ϕs the screw channel helical angle. If the interface shear force is larger than the material shearing resistance ( c ), the whole solid-plug is ruptured into two smaller solid-plugs and then if the interface shear force is also larger than the internal friction force (Ff ) between the two closely contacted solid-plugs, the two solid-plugs start to move or have the tend to move relatively. As a result, the internal friction heat is generated between the two solid-plugs. The generated friction heat is the origin of heat flux at the interface. It should be noted that the melted
barrel > c
(3)
barrel > Ff
c = c Ws2 Wc2 sin(ϕs + ϕc ) and Ff = Plend Ws2 Wc2 where sin(ϕs + ϕc )i , i is the internal friction coefficients of polymer, c the material shear strength, Ws2 the screw channel width in the melting zone, and Wc2 the barrel groove width in the melting zone. The simplified rupture conditions are found. ˝1 =
˝2 =
˝3 =
Plend i − 1 > 0 c (Hs2 +Ws2 ) 2
Ws2 sin (ϕs +ϕc ) (Hc2 + Wc2 ) 2
Wc2 sin (ϕs +ϕc )
(4)
−[s cos(˛s − ϕs )−sin(˛s − ϕs )]
i > 0 (5) s
−[c cos(˛c +ϕc )+sin(˛c + ϕc )]
i > 0 (6) c
The screw speed affects the pressure at the end of the feed zone (P1end ). According to the expression of P1end and Eq. (4), the expression of screw speed and the internal friction coefficient is as follows: c −1 < A1 n2 [exp(−A2 (A3 − A4 n2 ) ) − 1] = Plend i
(7)
where A1 − A4 are functions of structure parameters of extruder only. There are various types of changes of the barrel groove depth of the melting zone (Hc2 ) and the screw channel depth of the melting zone (Hs2 ). A type that appears reasonable physically and
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
2837
Fig. 2. Forces on the solid-plug embedded in the barrel groove, the gap and the screw channel.
mathematically and that has been successfully applied to this study is a linear change.
H − H ⎧ c3 c1 ⎪ (lc − L2 ) ⎨ Hc2 = Hc1 + L2 ⎪ ⎩ Hs2 = Hs1 + Hs3 − Hs1 (ls − L2 )
(8)
L2
where Hc1 is the barrel groove depth of the feed zone, Hc3 the barrel groove depth of the metering zone, Hs1 the screw channel depth of the feed zone, Hs3 the screw channel depth of the metering zone, L2 the length of the melting zone, ls the melt starting point in the screw channel and lc the melt starting point in the barrel groove. Solving Eqs. (5), (6) and (8), lc and ls are given
ls =
lc =
of the solids because the solids cannot travel beyond the barrier section, unless they can cross the barrier clearance. In order to obtain maximum melting efficiency, the solid channel should be filled from flank to flank with solid polymer with only a thin melt film between the solid-plugs in the barrel groove and the solid channel. The assumption of the solid-plug occupying the full width of the solid channel and the barrel groove can be used to determine the maximum possible melting rate. Fig. 3 describes channel-groove coupling melting model for SSE with grooved melting zone and barr screw. The melting model is taken as two cuboid-shaped solid-blocks which are placed in contact with each other. The heating of internal friction is generated
2 [s cos(˛s − ϕs ) − sin(˛s − ϕs )] i Ws2 sin (ϕs + ϕc ) − s (Ws2 + Hs1 ) +1 s (Hs3 − Hs1 )
L2
2 [c cos(˛c + ϕc ) + sin(˛c + ϕc )] i Wc2 sin (ϕs + ϕc ) − c (Wc2 + Hc1 ) +1 c (Hc3 − Hc1 )
However, only a short time is needed to melt all the solids in the extremely narrow clearance between the two solid-blocks. The solid-plug in the barrel groove starts to melt as soon as the solidplug in the screw channel starts to melt and vice versa. Therefore, the melt starting point (lm ) can be written as follows: lm = min(ls , lc )
(11)
Eq. (11) indicates that the melting starting point is not only the function of the friction coefficients and structural parameters but also the function of the extrusion pressure. 3.3. Melting length Besides the melt starting point, the lengths to finish melting, named as the melting length, in the barrel groove and the screw channel are also of fundamental importance because they not only reflect the melting rate but also affect the melting quality. A good SSE is the one with shorter melting length and better melting quality. To a length-fixed extruder, the shorter the melting length, the longer the metering zone and the better the melting quality. In order to get the expression of the melting length of SSE with grooved melting zone and barr screw, channel-groove coupling melting theory was established in this study. As soon as the melt film is formed, the barrier section is introduced. At the beginning of the barrier section, a barrier flight is introduced into the screw channel. Thus, the barr screw has a solid channel and a melt channel which ensures complete melting
(9)
(10)
L2
because of the relative motion between the two solid-blocks, which leads to the melting of the solid and hence the formation of melt film. The coupled barrel groove and solid channel act to squeeze out the newly melted polymer and forced it flow into the increasing volume of the melt channel. Since the melting is driven by the internal friction heat, the fact that the melted polymer being squeezed out and into the melt channel keeps the two solid-blocks continuously closely contacting with each other. The temperatures of the two solid-blocks’ sides (1–10) are constant. Since heat is gained only through the bottoms of the blocks (11, 12) and the bottom is assumed to be at the constant melting point throughout the melting, the heat transfer occurs only in the direction perpendicular to the bottom and the internal friction heat is the main melting heat source. Coordinate system is converted to simplify the analysis for the relative speed between solid-blocks in the barrel groove and in the screw channel ( v) with an angle of ϕc + ˛c , as shown in Fig. 3. The transformation formula between the two coordinate systems is x =
z cos(ϕc + ˛c )
(12)
The energy balance at the solid–fluid interface is
−k
∂T ∂y
= s ( + c Tc ) vc + y=h
dh dt
(13)
2838
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Fig. 3. Channel-groove coupling melting model for SSE with grooved melting zone.
where k is the thermal conductivity, the melting latent heat, c the conduction coefficient, vc the velocity of the solid-plug along the axis y , Tc the temperature difference between the solid and the barrel and h the melt film thickness. The shear force in the z direction is much more important than that in the x direction. The energy equation is simplified as below. 2
∂ T
=− k ∂(y )2
∂Vz ∂ y
2
=− k
v 2
(14)
h
The boundary condition at the interface is
∂T ∂ y
= y =0
q k
The momentum equation is 2
∂Pz ∂ u = ∂(x ) ∂(y )2 The boundary conditions are u|y =0 = 0,
y =h
(16)
The solid-block in the barrel groove is firstly analyzed. The energy equation at the solid–fluid interface takes the form
2
( v) dh − q = s ( + c Tc ) vc + h dt
(17)
When the whole solid-plug is ruptured into small solid-plugs, there are generation of frictional heat. The generated frictional heat is the origin of heat flux at the interface. It should be noted that the melted polymer was assumed to be removed away from the interface as soon as it forms. Therefore, the interface is kept as the interface of solid to solid. In Eq. (17) q is the internal friction heat and defined as follows: q = Ff v
sin(˛g + ıc ) tan(˛g )cot(ıg ) 2 − 2 cos(˛s − ˛c ) tan(˛g ) + cot(ıg ) sin(˛c + ıc )sin(˛g ) (19)
where ˛g is the transmission angle of solid-plug in gap, ıg and ıc the transmission angle used in the velocity analysis. The flow is incompressible, so the continuity equation takes the form.
∂u ∂v ∂w + + =0 ∂(x ) ∂(y ) ∂(z )
(20)
where u, v and w are velocities along x , y , z direction, respectively.
∂Pz ∂(x )
y (y − h) +
1 udy = 12
0
v y h
(23)
∂Pz − ∂(x )
h3 +
1 vh 2
(24)
where Pz is pressure profile along the z direction. According to the law of conservation of mass, the following equation is obtained.
∂Qx − vc = 0 ∂(x )
(25)
The pressure boundary conditions according to the assumptions are obtained as follows:
Pz
x =0
= Pwall ,
Pz
x =Wc2
= Pwall
(26)
where Pwall is the pressure of barrel channel and screw channel. Substituting Eq. (26) into Eq. (25) leads to the pressure Pz . Pz =
(18)
where v is determined according to the velocity analysis developed by Potente and Reckert (2002). v = V0
h
Q =
( v) q + k h k
(22)
The polymer melt flows only along the x direction, so the volume flow rate along the x direction (Qx ) is x
2
=−
1 2
where is the shear viscosity. Combining Eqs. (14) and (15), we get
∂T ∂ y
u|y =h = v
Solving Eqs. (21) and (22) gives the velocity along the x direction. u=
(15)
(21)
6a vc (Wc2 − x )x + Pwall h3
(27)
Kacir and Tadmor (1972) assumed Pwall was half of the pressure Pz . Pwall = 0.5Pz
(28)
Solving Eq. (27) with Eq. (28), Pz is given by the following equation. Pz =
12vc (Wc2 − x )x h3
(29)
The following equation is gained by solving Eqs. (12), (17) and (29). ( v2 − qh) 1 dh Pz h3 cos2 (ϕc + ˛c ) − + =0 12(Wc2 cos(ϕc + ˛c ) − z)z dt s ( + c Tc ) h
(30)
The film thickness is assumed constant. The total film thickness is added up to the barrel groove depth of the feed zone (Hc1 ). The total unwound melting length of the barrel groove (Zc ) is added up
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
2839
Table 1 Combinations of barrels and screws and the set of barrel temperatures. Combination
Screw
Barrel
A B C
1 2 3
1 2 2
Temperature(◦ C) Feed zone
Melting zone
Metering zone
Die
<50
130 100 107
130
130
by the separated melting length in the barrel groove (z). Then Eq. (30) can be written as Eq. (31).
4. Experimental
1 z 2 + 2 z + 3 = 0
4.1. Apparatus and processing settings
(31)
Similarly, the unwound melting length in the screw channel (Zs ) is solved by analyzing the solid-block in the screw channel. Zc and Zs can be calculated as follows:
⎧ ± 2 2 − 4 1 3 ) (− H H ⎪ 2 c1 c1 ⎪ ⎨ Zc = h z = h 2 1 2 ⎪ ⎪ ⎩ Zs = Hs1 z = Hs1 (− 5 ± 5 − 4 4 6 ) h
h
(32)
2 4
where 1 = 122 ( v2 − qhc ) 2 = −122 Wc2 cos(ϕc + ˛c )( v2 − qhc ) 4 P ( + c T ) cos2 (ϕ + ˛ ) 3 = Hc1 c c c z s
4 = 122 ( v2 − qhs ) 5 = −122 Ws2 cos(ϕs + ˛s )( v2 − qhs ) 4 P ( + c T ) cos2 (ϕ + ˛ ) 6 = Hs1 s s s z s
The melting length in the barrel groove (Lc ) and the screw channel (Ls ) along the screw axis can be calculated by
Ls = Zs sin ϕs Lc = Zc sin ϕc
(33)
The visualization study of melting performance in conventional extrusion is carried out by “Cooling experiment” or equipping glass windows on the barrel. However, both methods are not suitable for SSE with grooved feed zone because adding grooves to the feed zone usually generates high extrusion pressure which could cause unclear observation and high intensity structure requirement. A new clamshell type barrel SSE platform with grooved feed zone and melting zone was constructed. The clamshell barrels were opened by a hydraulic device, with which the melting performance can be monitored in real time. Thus, the melt starting point and the melting length were determined with good accuracy. The barrels and screws are shown in Fig. 4. Each barrel was divided into three sections, which not only simplified the manufacture of barrel with spiral grooves but also made the change of the barrel sections much easier. Different combinations of barrels and screws and the set of barrel temperatures are shown in Table 1. Screw speed (n) varied from 0 to 45 r/min. The pressure at the screw tip (die pressure) has been set in all trials to 2.0 MPa. The date of melt starting points and melting lengths in this paper is the average values of five repeated experiments, macroscopically observed by opening the barrels. 4.2. Material Low-density polyethylene (LDPE, LD607 type, MFI 7.5 g/10 min) was purchased from Beijing Yanshan Plant. In this study, in order to
Fig. 4. Schematic diagrams of test barrels and screws.
2840
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Fig. 5. The critical melt starting point and the critical screw speed as a function of the friction coefficient ratio.
simplify the theoretical derivation, the internal friction coefficient (i ) and the external friction coefficient (o ) were assumed to be independent of temperature, determined by friction test. The value of s was assumed to be equal to the value of c . 5. Discussion 5.1. Critical conditions The effect of the friction coefficient ratio (i /o ) on the critical melt starting point and the critical screw speed is shown in Fig. 5. The conditions that the whole solid-plug being cut off by the active flights of the barrel groove and the screw channel were obtained by solving Eqs. (5)–(7). It can be seen from Fig. 5 that the whole solid-plug is ruptured only when screw speed is above 9.8 r/min and the melt starting point (lm ) is more than 8.6 D away from the hopper (i /o = 0.37/0.19 = 1.95). The apparatus of combinations B and C are designed according to this, that is to say the solid in combinations B and C are supposed to start melting 8.6 D away from the hopper. The melt starting points show a linear movement to the extruder die with i /o . According to Eqs. (5) and (8), the melt starting points in the screw channel (ls ) increase with i /o because the value of (Hs3 − Hs1 ) is positive. On the contrary, the melt starting points in the barrel groove (lc ) decrease with i /o due to the negative value of (Hc3 − Hc1 ) according to Eqs. (6) and (8). In general, the theoretical value of ls is smaller than that of lc . Therefore, the melt starting point is dominated by ls according to Eq. (11). Fig. 5 also reveals that the critical screw speed decreases with i /o , which can be explained according to Eq. (11) that the extrusion pressure needed to rupture the whole solid-plug increases with internal friction coefficient (i ) or i /o when o was kept constant. Fig. 5 also showed that the critical screw speed decreased with i /o . When substituting all the parameters into Eq. (7), the values of the coefficients for combinations B and C are gained (A1 = 2,948,545, A2 = 1818, A3 = 485, A4 = 356.9). The left side of Eq. (7) decreased with i , which indicated that the pressure needed to rupture the whole solid-plug is decreased and so did the screw speed. In order to rupture the whole solid-plug easier and earlier, the screw speed and the internal friction coefficient can be increased. In this study, the whole solid-plug cannot be ruptured unless the screw speed is more than 9.8 r/min, which is confirmed by the following experiment. 5.2. Melt starting point Fig. 6 is the trend of the melt starting points of different combinations. As exhibited in the figure, the melt starting points of
Fig. 6. The melt starting points as a function of screw speeds for different combinations.
combination A are different from that of combinations B and C. In combination A, the solid throughput increases more than the melting ability with screw speed, which results in the movement of the melt starting point to the extruder die. Moreover, the solid experienced shorter time in the extruder with higher screw speeds. As a result, the temperature of the solid is lower than usual and needs more time to melt. The melt starting points of combinations B and C are physically determined, which are well agreed with the theoretical melt starting points, indicating the correctness of the calculation of melt starting point. The positive flights of the barrel groove and screw channel together cut the whole solid-plug into small solid-plugs at the preset melt starting point. The figure also shows that the melt starting points of combination C move to the theoretical melt starting point and gradually stabilize with screw speed. At low screw speed, it is hard to supply sufficient pressure to cut the whole solid-plug when the solid reaches the preset melt starting point. The whole solid-plug is further compressed by the volume-decreased barrel groove and then the whole solid-plug is cut by the active flights when the pressure is enough. It also can be seen that the melt starting points of combination B are almost the same. The barr screw is used in combination B. The breaking section of barr screw is set before the barrier section to insure the rupture of the whole solid-plug. According to the analysis of combination C, the melt starting points of combination B are supposed to be closer to the extruder die than the theoretical ones. However, the introduction of the barrier section makes the whole solid-plug rupture at the beginning of the barrier section because the solid cannot get into the melt channel. It can be concluded that the melt starting points in combination B are more stable than that in combination C.
5.3. Melting length Fig. 7 presents the measured data of melting lengths in the screw channel of different combinations. The melting lengths of combination A increase with screw speed. It can be seen from the figure that the solid is not melted in the extruder at n = 45 r/min. It can also be seen from the figure that the melting lengths of combination B are a little smaller than the theoretical values while that of combination C are bigger than the theoretical values. With the barrier section in combination B, the melting lengths are physically determined. Without the barrier section in combination C, the melting length resulted in fluctuation.
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
2841
they did not take the effect of pressure into consideration, which simplified the energy study a lot. The Graetz number is a measure of the importance of heat convection along the centerline of the screw length related to heat conduction and is defined as Graetz number (Gz ) =
heat convection QV Hs3 = ˛Ws3 L3 heat conduction
(37)
where QV is the average volumetric flow rate and is calculated by dividing the total throughput at the die by the density of the melted material and L3 the length of the metering zone. Similarly, the Griffith number is a measure of the importance of viscous dissipation relative to heat conduction. The Griffith number is defined as Griffith number (Gr ) = Fig. 7. Melting lengths in the screw channel as a function of screw speeds for different combinations.
Compared with combination A, the melting lengths of combinations B and C are almost not affected by screw speed and this irrelevance can be explained according to Eq. (18). q ∝ v ∝ n
(34)
When considering the order of magnitudes of friction heat, q, (about 105 W/m2 when n = 45 r/min), the relations, 1 » 3 , 2 » 3 , are obtained. Eq. (33) is simplified as 2 Lc = Zc sin ϕc = − sin ϕc = Wc2 cos(ϕc + ˛c )sin ϕc 1
(35)
The unwound melting length in the barrel groove (Zc ) is only a function of solid conveying angle in the barrel groove (˛c ), which is calculated as follows:
˛c = arctan
c cos ϕc + sin ϕc c sin ϕc − cos ϕc
(36)
where is a function of structure parameters of extruder. It can be concluded form Eqs. (35) and (36) that the effect of screw speed on the melting length is negligible. 5.4. Energy dimensionless analysis The energy study involves a lot of uncertain factors. The energy study is difficult under various conditions of flow or pressure. The energy study is also necessary because it can reveal the melting mechanism of SSE. Kelly et al. (2006) used the dimensionless groups Graetz and Griffith numbers to evaluate the relative importance of heat conduction, heat convection and viscous dissipation in the metering zone of the extruder. The magnitude of these numbers at a range of process conditions indicates the source of heat generated within the polymer melt, i.e. from conduction from the barrel wall or from viscous shearing through power generated by the motor. One of the advantage of these dimensionless numbers was that
viscous dissipation (nD)2 b0 = heat conduction ˇ
(38)
where was measured at a range of wall shear rates using a twin bore capillary rheometer. When the heat conduction assumes a value of 1, the ratios of heat conduction to total energy consumption (HD ), heat convection to total energy consumption (HC ) and viscous dissipation to total energy consumption (HV ) can be calculated by
⎧ 1 ⎪ HD = ⎪ ⎪ 1 + G ⎪ z + Gr ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
HC =
Gz 1 + Gz + Gr
HV =
Gr 1 + Gz + Gr
(39)
All the dimensionless numbers were calculated and the results are included in Table 2. It can be seen from Table 2 that the main melting heat source heat of combination A is the heat conduction and viscous dissipation. The heat convection plays a minor role in solid melting, about 18% at 45 r/min. Sundstrom and Young (1972) found the heat convection plays an important role in solid melting, about 20% higher than the no convection model. The well agreement between the experiment and the prediction of Sundstrom and Young showed the correctness of the dimensionless groups. The viscous dissipation in combination A increases rapidly with screw speed which raises the risk of polymer degradation of overheating. On the contrary to combination A, the main heat source of melting heat of combinations B and C is the heat convection, contributing more than 65% of the total energy consumption. In combinations B and C, the viscous dissipation does not increase sharply as it did in combination A, which not only reduced the risk of polymer degradation but also lowered the temperature of the extrudate. The solid melting under shear conditions is an important operation in the processing of most thermoplastics. Researchers usually ignored heat convection on the melting of solid in theoretical calculation due to the speed of the melt flow was relatively slow. Yates (1968) evaluated the rather significant effect of the down-channel convection on temperature,
Table 2 The calculated dimensionless numbers of combinations A, B and C. Combination
n (r min−1 )
QV (10−6 m3 s−1 )
(Pa s)
HD (%)
HC (%)
HV (%)
A
12 30 45 12 30 45 12 30 45
0.356 0.803 1.14 2.45 6.32 9.26 2.55 6.52 9.96
1852 1054 822 5457 3108 2422 7772 4425 3449
75.8 51.3 38.9 13.9 5.7 3.7 21.8 9.4 6.1
10.6 16.4 17.9 75.6 79.2 79.0 66.8 73.2 73.7
13.6 32.3 43.2 10.4 15.1 17.3 11.4 17.4 20.2
B
C
2842
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
and later refined by Fenner (1975) and Elbirli and Lindt (1984). In combinations B and C, the melted polymer is pushed by the two forced-moving solid-plugs, which results in high pressure gradient between the melt and the solid-plugs. The polymer melt may be pumped into the small gaps in the solid-plug, providing the unique conditions for heat transfer from the hot polymer melt to the cold solid. On the one hand the heat transfer lowers the temperature of the hot melt which is in favor of cold extrusion. On the other hand the heat preheats the solid-plugs, improving the solid melting rate, which is corresponding to the shorter melting lengths in combinations B and C than that in combination A. Taking combination B when screw speed increases from 12 r/min to 30 r/min as an example, the increase of HC is about 4.76% as shown in Table 2, which is close to the decrease of melting length (5%) as shown in Fig. 7. 6. Conclusions A novel melting mechanism, named as channel-groove coupling melting theory for SSE with grooved melting zone was established. The new SSE platform with hydraulic-clamshell type barrels was constructed and the melting performance of different barrel and screw combinations were investigated. The melting model was verified by the experiment and the result was found to match with the experimental data. Compared with conventional SSEs, it was found that melting starts earlier and melting was finished in shorter region in the case of SSE with grooved melting zone and barr screw. The whole solid-plug started to melt at the tail of the eighth pitch from the hopper in both the barrel groove and the screw channels. The melting lengths in the barrel groove and in the screw channel were slightly affected by screw speed. The grooved melting zone improved the melting efficiency and the barr screw enhanced the
melting stabilization. By introducing the dimensionless groups (HD , HC and HV ), the heat convection and viscous dissipation were found to be the main melting heat source for the SSE with grooved melting zone and barr screw. Acknowledgement The authors would like to acknowledge the support of the National Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (No. 2014211A022). References Elbirli, B., Lindt, J., 1984. A note on the numerical treatment of the thermally developing flow in screw extruders. Polym. Eng. Sci. 24 (7), 482–487. Fenner, R., 1975. The design of large hot melt extruders. Polymer 16 (4), 298–304. Grünschloß, E., 2002. A new style single screw extruder with improved plastification and output power. Int. Polym. Proc. 17 (4), 291–300. Kacir, L., Tadmor, Z., 1972. Solids conveying in screw extruders part III: the delay zone. Polym. Eng. Sci. 12 (5), 387–395. Kelly, A.L., Brown, E.C., Coates, P.D., 2006. The effect of screw geometry on melt temperature profile in single screw extrusion. Polym. Eng. Sci. 46 (12), 1706–1714. Machen, J.F., 1981. High-speed Direct-Drive Extruder, United States. Pan, L., Jia, M.Y., Xue, P., Wang, K.J., Jin, Z.M., 2012. Studies on positive conveying in helically channeled single screw extruders. Express Polym. Lett. 6 (7), 543–560. Potente, H., Heim, H.P., Kleineheismann, S., 2006. Experimental investigations on the plasticating process short single screw extruder for biopolymers. ANTEC, 2. Potente, H., Reckert, F., 2002. Extruder concept for the direct plastification of cereal materials. Macromol. Mater. Eng. 287 (11), 791–799. Rauwendaal, C., 1986. Extruder screws with barrier sections. Polym. Eng. Sci. 26 (18), 1245–1253. Schneider, K., 1968. Der Fördervorgang in der Einzugszone eines Extruders, Aachen, Germany. Sundstrom, D.W., Young, C.C., 1972. Melting rates of crystalline polymers under shear conditions. Polym. Eng. Sci. 12 (1), 59–63. Yates, B., 1968. Temperature Development in Single Screw Extruders. University of Cambridge, Cambridge.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Study on the melting performance of single screw extruder with grooved melting zone and barr screw X.-M. Jin a,1 , M.-Y. Jia a,b,∗ , P. Xue a,∗∗ , J.-Ch. Cai a,2 , L. Pan a,2 , D.-Q. Yu a,2 a b
Beijing University of Chemical Technology, Institute of Plastic Machinery and Engineering, Beijing 100029, China Xinjiang Institute of Engineering, Department of Mechanical Engineering, Xinjiang Uygur Autonomous Region, 830091, China
a r t i c l e
i n f o
Article history: Received 28 March 2014 Received in revised form 7 June 2014 Accepted 29 June 2014 Available online 6 July 2014 Keywords: Melting model Grooved melting zone Barr screw Melt starting point Melting length Energy consumption
a b s t r a c t A novel melting mechanism for single screw extruder with grooved melting zone and barr screw was established. The whole solid-plug, which came from the grooved feed zone, was ruptured and melted mainly by continuously changing the volume of the screw channels and the barrel grooves in the grooved melting zone. A new single screw extruder platform with hydraulic-clamshell type barrels was constructed to investigate the melting performance of different combinations of barrels and screws. The melting model was verified by experiments. Compared with conventional single screw extruder, the melting started earlier and the melting length was shorter in the single screw extruder with grooved melting zone. The melting efficiency was improved by the grooved melting zone and the melting stability was improved by the barr screw. The dimensionless analysis of energy indicates that the heat convection and viscous dissipation are the main melting heat sources for the single screw extruder with grooved melting zone. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Single screw extruders (SSEs) are widely used as one of the basic and convenient elements to melt and convey polymer materials. SSEs are composed of feed zone, melting zone and metering zone. Schneider (1968) machined axial grooves and later Machen (1981) machined helical grooves into the barrel to creat a hgih friction coefficient and thus improve the solid conveying efficiency. Pan et al. (2012) first proposed double-flight driving theory for SSE with grooved feed zone and studied the positive conveying in the feed zone. Compared with conventional SSEs, the SSEs with grooved feed zone can obtain high specific throughput. However, Potente et al. (2006) did lots of study on SSEs with helical grooves and pointed out that the increased solid throughput cannot be melt uniformly depending on the external heat source conducted from the barrel and the external friction heat generated by the friction of the polymer on the barrel and screw. Grünschloß (2002) presented the
∗ Corresponding author at: Beijing University of Chemical Technology, Institute of Plastic Machinery and Engineering, Beijing 100029, China. Tel.: +86 10 6443 6016. ∗∗ Corresponding author. Tel.: +86 10 6443 6016. E-mail addresses: [email protected] (X.-M. Jin), [email protected] (M.-Y. Jia), [email protected] (P. Xue), [email protected] (J.-C. Cai), [email protected] (L. Pan), yu12 [email protected] (D.-Q. Yu). 1 Tel.: +86 10 6442 6911. 2 Tel.: +86 10 6443 6016. http://dx.doi.org/10.1016/j.jmatprotec.2014.06.022 0924-0136/© 2014 Elsevier B.V. All rights reserved.
HELIBAR extruder which was composed of barrier screw and barrel with both grooved feed zone and melting zone. In consideration of the melting shortage of extruder with grooved feed zone, the HELIBAR extruder’s barrel grooves in the melting zone were simply used as channels of melt flow. The higher specific throughput and the poorer melting performance generated higher pressure in the extruder, which finally resulted in excessive wear and low energy efficiency. Currently, poor melting quality is the main issue of the development of SSEs with grooved feed zone. Researchers offered several approaches to improve the melting quality. For instance, adding mixing elements to SEE was considered to be a useful way. However, mixing elements adversely affect the capacity of extrusion because they have no positive pumping capacity and are pressure consumption elements, which produce higher pressure drop and induce stagnation. Increasing lengthto-diameter ratio (L/D) and decreasing screw speed to improve the melting quality finally lead to long thermomechanical history, high-energy consumption and bulky equipment. Therefore, the approaches above cannot fundamentally improve the melting quality of SSE with grooved feed zone. Pan et al. (2012) did research on SSE with normal screw and grooved feed zone only and found that the melt film is easily formed because of the internal friction between the solid-plugs which were ruptured from the whole solid-plug at high extrusion pressure in the feed zone. The grooved feed zone of the barrel was usually cooled and thermally separated from the following heated barrel
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Nomenclature HD HC HV Ff Lc Ls P1end QV V0 Zc Zs b0 bo c h lm ls lc k q Tm
vc ˛ ˇ ϕc ϕs i o s m c c
ratio of heat conduction to total energy consumption ratio of heat convection to total energy consumption ratio of viscous dissipation to total energy consumption internal friction force (N) melting length in the barrel groove (m) melting length in the screw channel (m) pressure at the end of the feed zone (Pa) average volumetric flow rate of the extruder (m3 s−1 ) circumferential velocity of barrel (m/s) unwound melting length in the barrel groove (m) unwound melting length in the screw channel (m) sensitivity of viscosity to temperature change (1/◦ C) sensitivity of viscosity to temperature change (0.03/◦ C) specific heat coefficient (2400 J/kg ◦ C) melt film thickness (m) the melt starting point (m) melt starting point in the screw channel (m) melt starting point in the barrel groove (m) thermal conductivity (W/m ◦ C) internal friction heat (W/m2 ) the melting point of the material (107 ◦ C) velocity of the solid-plug along the axis y (m/s) thermal diffusivity (1.1 × 10−7 m2 /s) melt thermal conductivity (0.25 W/m ◦ C) barrel groove helical angle (◦ ) screw channel helical angle (◦ ) melting latent heat (1.3 × 105 J/kg) internal friction coefficient of material (0.37) external friction coefficient of material (0.19) material solid density (485 kg/m3 ) material melt density (920 kg/m3 ) material shear strength (5.8 × 106 Pa) material shearing resistance (N) viscosity (Pa s)
zones to ensure the solid conveying. The wide use of cooling system indicated that the energy of friction heat in grooved feed zone was enormous. By extending the grooves in the feed zone of the barrel to the melting zone and applying this melting mechanism in the grooved melting zone, the solid is melted by significant internal friction heat rather than poor external friction heat. The internal friction was not suppressed but adequately is deliberately used to plastificate the material. By analyzing the forces on the whole solid-plug in the barrel groove and the screw channel, the boundary conditions that the whole solid-plug being cut off into smaller solid-plugs were determined and then a new melting theory was proposed. A new SSE platform with hydraulic-clamshell type barrels was constructed. The melt starting point and the melting length of different combinations of barrels and screws were also discussed to analyse the effect of screw speed. Besides, by the dimensionless analysis of energy, the main melting heat source for the SSE with grooved melting zone was found. 2. Physical model Fig. 1 illustrates the melting of SSE with grooved melting zone and barrier screw. Pan et al. (2012) proved that a whole solid-plug in the grooved feed zone did exist and indicated that the whole
2835
solid-plug did not experience any internal circumferential shear fracture and then entered the melting zone. All the following theoretical analysis in the study is based on the fact that the whole solid-plug does exist and then is reptured into smaller solid-plugs. In the melting zone, the barrel grooves and the barrier screw channels (the solid channel and the melt channel) are coupled which means the volume (cross-sectional area) of the barrel grooves and the screw channels vary accordingly. In the down channel direction, the volume of the barrel groove is reduced by reducing the barrel groove depth and/or narrowing the barrel groove width. The volume of the solid channel is reduced by reducing the melt channel depth while the volume of the melt channel is increased by deepening the solid channel depth. The solid-plug in the barrel groove is pushed downward by the volume-decreased barrel groove and that in the solid channel is pushed upward by the volume-decreased solid channel. The decreasing volume of the barrel groove and the increasing volume of the screw channel together divide the whole solid-plug into two smaller solid-plugs. Then the two smaller solidplugs are forced to move by the active sides of the barrel groove and the barrier flight. Due to the tremendous internal friction heat generated by the two smaller solid-plugs rubbing against each other, the solid at the interface melts firstly and melt film is developed. Please note that the melting efficiency here is improved because the friction here is the internal friction rather than the external friction in traditional extruders. The heat generated from the internal friction is much higher than that from the external friction due to the higher internal friction coefficient. Then, by pressing the solid-plug in the barrel groove against that in the solid channel, a radial velocity profile is induced in the melt film, which results in removing the newly melted polymer from the location of melting and forming a melt pool in the melt channel. The volume-increased melt channel provides just enough room for the increased melt pool. In order to keep a steady melting of the solid, the newly melted polymer must be moved into the melt channel in time and the change of volume of the barrel groove and the solid channel deforming the solid-plugs to keep the continuous close contact with each other. With more and more melting, the solid in the barrel grooves and the solid channel gradually melts and the melted polymer is then pumped through the metering zone and finally through a die to form the desired product shape. The barr screw was introduced in this model and was chosen for two reasons. First of all, the barr screw can physically separate the solid bed from the melt pool and prevent the solid-plug in the solid channel from breaking up as all barrier screws did. Secondly, the solid channel and the melt channel are constant and the solid channel is wider than other types of barrier screws. Rauwendaal (1986) evaluated the barr screw and pointed out that the width of the solid channel of the barr screw is corresponding to the melting rate because the width of the channel directly determined the width of the solid bed.
3. Mathematical model 3.1. Basic assumption (1) The process is steady. (2) The film thickness is much smaller than its width. (3) The temperature of the polymer melt remains at the sharp melting point, Tm , throughout the melting. (4) The temperature of the solid-plugs in the barrel grooves and the solid channels remains constant, Tc and Ts , respectively. (5) The pressure differences between the top and sides of the barrel grooves and the barr screw channels are negligible. (6) The flow is incompressible. (7) It is a two-dimensional problem.
2836
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Fig. 1. The melting of SSE with grooved melting zone and barrier screw.
(8) The friction coefficient, in terms of the Coulomb’s Law, is a constant. (9) The solid-plug occupying the full width of the solid channel and the barrel groove. (10) The solid-plugs in the barrel grooves and the screw channels are assumed to be ductile and unbreakable.
In order to simplify the analysis, the whole solid-plug was divided into three parts including solid-plug in the barrel groove, the gap and the screw channel. The forces on the three solid-plugs, as represented in Fig. 2, were analyzed to investigate the boundary conditions where the whole solid-plug is being ruptured and starting to melt. The interface shear forces on the outer surface of screw ( screw ) and the inner surface of barrel ( barrel ) is determined by the analysis of the torque balance around the screw axis and the force balance alone the down channel direction. The expressions of screw and barrel are given
barrel
screw > c
and/or
screw > Ff
3.2. Melt starting point
P1end s Wc2 (Hs2 + Ws2 ) [s cos(˛s − ϕs ) − sin(˛s − ϕs )] sin(ϕs + ϕc )
(1)
P1end c Ws2 (Hc2 + Wc2 ) = [c cos(˛c + ϕc ) + sin(˛c + ϕc )] sin(ϕs + ϕc )
(2)
screw =
polymer was assumed to be removed away from the interface as soon as it forms. Therefore, the interface was kept as the interface of solid to solid. The generated internal friction heat is enough to melt the solid. The rupture conditions are obtained.
where P1end is the extrusion pressure at the end of the feed zone given by Pan et al. (2012), c the external friction coefficient of the polymer on the barrel, s the external friction coefficient of the polymer on the screw, ˛c the transmission angle of solid-plug in the barrel groove, ˛s the transmission angle of solid-plug in the screw channel, ϕc the barrel groove helical angle and ϕs the screw channel helical angle. If the interface shear force is larger than the material shearing resistance ( c ), the whole solid-plug is ruptured into two smaller solid-plugs and then if the interface shear force is also larger than the internal friction force (Ff ) between the two closely contacted solid-plugs, the two solid-plugs start to move or have the tend to move relatively. As a result, the internal friction heat is generated between the two solid-plugs. The generated friction heat is the origin of heat flux at the interface. It should be noted that the melted
barrel > c
(3)
barrel > Ff
c = c Ws2 Wc2 sin(ϕs + ϕc ) and Ff = Plend Ws2 Wc2 where sin(ϕs + ϕc )i , i is the internal friction coefficients of polymer, c the material shear strength, Ws2 the screw channel width in the melting zone, and Wc2 the barrel groove width in the melting zone. The simplified rupture conditions are found. ˝1 =
˝2 =
˝3 =
Plend i − 1 > 0 c (Hs2 +Ws2 ) 2
Ws2 sin (ϕs +ϕc ) (Hc2 + Wc2 ) 2
Wc2 sin (ϕs +ϕc )
(4)
−[s cos(˛s − ϕs )−sin(˛s − ϕs )]
i > 0 (5) s
−[c cos(˛c +ϕc )+sin(˛c + ϕc )]
i > 0 (6) c
The screw speed affects the pressure at the end of the feed zone (P1end ). According to the expression of P1end and Eq. (4), the expression of screw speed and the internal friction coefficient is as follows: c −1 < A1 n2 [exp(−A2 (A3 − A4 n2 ) ) − 1] = Plend i
(7)
where A1 − A4 are functions of structure parameters of extruder only. There are various types of changes of the barrel groove depth of the melting zone (Hc2 ) and the screw channel depth of the melting zone (Hs2 ). A type that appears reasonable physically and
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
2837
Fig. 2. Forces on the solid-plug embedded in the barrel groove, the gap and the screw channel.
mathematically and that has been successfully applied to this study is a linear change.
H − H ⎧ c3 c1 ⎪ (lc − L2 ) ⎨ Hc2 = Hc1 + L2 ⎪ ⎩ Hs2 = Hs1 + Hs3 − Hs1 (ls − L2 )
(8)
L2
where Hc1 is the barrel groove depth of the feed zone, Hc3 the barrel groove depth of the metering zone, Hs1 the screw channel depth of the feed zone, Hs3 the screw channel depth of the metering zone, L2 the length of the melting zone, ls the melt starting point in the screw channel and lc the melt starting point in the barrel groove. Solving Eqs. (5), (6) and (8), lc and ls are given
ls =
lc =
of the solids because the solids cannot travel beyond the barrier section, unless they can cross the barrier clearance. In order to obtain maximum melting efficiency, the solid channel should be filled from flank to flank with solid polymer with only a thin melt film between the solid-plugs in the barrel groove and the solid channel. The assumption of the solid-plug occupying the full width of the solid channel and the barrel groove can be used to determine the maximum possible melting rate. Fig. 3 describes channel-groove coupling melting model for SSE with grooved melting zone and barr screw. The melting model is taken as two cuboid-shaped solid-blocks which are placed in contact with each other. The heating of internal friction is generated
2 [s cos(˛s − ϕs ) − sin(˛s − ϕs )] i Ws2 sin (ϕs + ϕc ) − s (Ws2 + Hs1 ) +1 s (Hs3 − Hs1 )
L2
2 [c cos(˛c + ϕc ) + sin(˛c + ϕc )] i Wc2 sin (ϕs + ϕc ) − c (Wc2 + Hc1 ) +1 c (Hc3 − Hc1 )
However, only a short time is needed to melt all the solids in the extremely narrow clearance between the two solid-blocks. The solid-plug in the barrel groove starts to melt as soon as the solidplug in the screw channel starts to melt and vice versa. Therefore, the melt starting point (lm ) can be written as follows: lm = min(ls , lc )
(11)
Eq. (11) indicates that the melting starting point is not only the function of the friction coefficients and structural parameters but also the function of the extrusion pressure. 3.3. Melting length Besides the melt starting point, the lengths to finish melting, named as the melting length, in the barrel groove and the screw channel are also of fundamental importance because they not only reflect the melting rate but also affect the melting quality. A good SSE is the one with shorter melting length and better melting quality. To a length-fixed extruder, the shorter the melting length, the longer the metering zone and the better the melting quality. In order to get the expression of the melting length of SSE with grooved melting zone and barr screw, channel-groove coupling melting theory was established in this study. As soon as the melt film is formed, the barrier section is introduced. At the beginning of the barrier section, a barrier flight is introduced into the screw channel. Thus, the barr screw has a solid channel and a melt channel which ensures complete melting
(9)
(10)
L2
because of the relative motion between the two solid-blocks, which leads to the melting of the solid and hence the formation of melt film. The coupled barrel groove and solid channel act to squeeze out the newly melted polymer and forced it flow into the increasing volume of the melt channel. Since the melting is driven by the internal friction heat, the fact that the melted polymer being squeezed out and into the melt channel keeps the two solid-blocks continuously closely contacting with each other. The temperatures of the two solid-blocks’ sides (1–10) are constant. Since heat is gained only through the bottoms of the blocks (11, 12) and the bottom is assumed to be at the constant melting point throughout the melting, the heat transfer occurs only in the direction perpendicular to the bottom and the internal friction heat is the main melting heat source. Coordinate system is converted to simplify the analysis for the relative speed between solid-blocks in the barrel groove and in the screw channel ( v) with an angle of ϕc + ˛c , as shown in Fig. 3. The transformation formula between the two coordinate systems is x =
z cos(ϕc + ˛c )
(12)
The energy balance at the solid–fluid interface is
−k
∂T ∂y
= s ( + c Tc ) vc + y=h
dh dt
(13)
2838
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Fig. 3. Channel-groove coupling melting model for SSE with grooved melting zone.
where k is the thermal conductivity, the melting latent heat, c the conduction coefficient, vc the velocity of the solid-plug along the axis y , Tc the temperature difference between the solid and the barrel and h the melt film thickness. The shear force in the z direction is much more important than that in the x direction. The energy equation is simplified as below. 2
∂ T
=− k ∂(y )2
∂Vz ∂ y
2
=− k
v 2
(14)
h
The boundary condition at the interface is
∂T ∂ y
= y =0
q k
The momentum equation is 2
∂Pz ∂ u = ∂(x ) ∂(y )2 The boundary conditions are u|y =0 = 0,
y =h
(16)
The solid-block in the barrel groove is firstly analyzed. The energy equation at the solid–fluid interface takes the form
2
( v) dh − q = s ( + c Tc ) vc + h dt
(17)
When the whole solid-plug is ruptured into small solid-plugs, there are generation of frictional heat. The generated frictional heat is the origin of heat flux at the interface. It should be noted that the melted polymer was assumed to be removed away from the interface as soon as it forms. Therefore, the interface is kept as the interface of solid to solid. In Eq. (17) q is the internal friction heat and defined as follows: q = Ff v
sin(˛g + ıc ) tan(˛g )cot(ıg ) 2 − 2 cos(˛s − ˛c ) tan(˛g ) + cot(ıg ) sin(˛c + ıc )sin(˛g ) (19)
where ˛g is the transmission angle of solid-plug in gap, ıg and ıc the transmission angle used in the velocity analysis. The flow is incompressible, so the continuity equation takes the form.
∂u ∂v ∂w + + =0 ∂(x ) ∂(y ) ∂(z )
(20)
where u, v and w are velocities along x , y , z direction, respectively.
∂Pz ∂(x )
y (y − h) +
1 udy = 12
0
v y h
(23)
∂Pz − ∂(x )
h3 +
1 vh 2
(24)
where Pz is pressure profile along the z direction. According to the law of conservation of mass, the following equation is obtained.
∂Qx − vc = 0 ∂(x )
(25)
The pressure boundary conditions according to the assumptions are obtained as follows:
Pz
x =0
= Pwall ,
Pz
x =Wc2
= Pwall
(26)
where Pwall is the pressure of barrel channel and screw channel. Substituting Eq. (26) into Eq. (25) leads to the pressure Pz . Pz =
(18)
where v is determined according to the velocity analysis developed by Potente and Reckert (2002). v = V0
h
Q =
( v) q + k h k
(22)
The polymer melt flows only along the x direction, so the volume flow rate along the x direction (Qx ) is x
2
=−
1 2
where is the shear viscosity. Combining Eqs. (14) and (15), we get
∂T ∂ y
u|y =h = v
Solving Eqs. (21) and (22) gives the velocity along the x direction. u=
(15)
(21)
6a vc (Wc2 − x )x + Pwall h3
(27)
Kacir and Tadmor (1972) assumed Pwall was half of the pressure Pz . Pwall = 0.5Pz
(28)
Solving Eq. (27) with Eq. (28), Pz is given by the following equation. Pz =
12vc (Wc2 − x )x h3
(29)
The following equation is gained by solving Eqs. (12), (17) and (29). ( v2 − qh) 1 dh Pz h3 cos2 (ϕc + ˛c ) − + =0 12(Wc2 cos(ϕc + ˛c ) − z)z dt s ( + c Tc ) h
(30)
The film thickness is assumed constant. The total film thickness is added up to the barrel groove depth of the feed zone (Hc1 ). The total unwound melting length of the barrel groove (Zc ) is added up
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
2839
Table 1 Combinations of barrels and screws and the set of barrel temperatures. Combination
Screw
Barrel
A B C
1 2 3
1 2 2
Temperature(◦ C) Feed zone
Melting zone
Metering zone
Die
<50
130 100 107
130
130
by the separated melting length in the barrel groove (z). Then Eq. (30) can be written as Eq. (31).
4. Experimental
1 z 2 + 2 z + 3 = 0
4.1. Apparatus and processing settings
(31)
Similarly, the unwound melting length in the screw channel (Zs ) is solved by analyzing the solid-block in the screw channel. Zc and Zs can be calculated as follows:
⎧ ± 2 2 − 4 1 3 ) (− H H ⎪ 2 c1 c1 ⎪ ⎨ Zc = h z = h 2 1 2 ⎪ ⎪ ⎩ Zs = Hs1 z = Hs1 (− 5 ± 5 − 4 4 6 ) h
h
(32)
2 4
where 1 = 122 ( v2 − qhc ) 2 = −122 Wc2 cos(ϕc + ˛c )( v2 − qhc ) 4 P ( + c T ) cos2 (ϕ + ˛ ) 3 = Hc1 c c c z s
4 = 122 ( v2 − qhs ) 5 = −122 Ws2 cos(ϕs + ˛s )( v2 − qhs ) 4 P ( + c T ) cos2 (ϕ + ˛ ) 6 = Hs1 s s s z s
The melting length in the barrel groove (Lc ) and the screw channel (Ls ) along the screw axis can be calculated by
Ls = Zs sin ϕs Lc = Zc sin ϕc
(33)
The visualization study of melting performance in conventional extrusion is carried out by “Cooling experiment” or equipping glass windows on the barrel. However, both methods are not suitable for SSE with grooved feed zone because adding grooves to the feed zone usually generates high extrusion pressure which could cause unclear observation and high intensity structure requirement. A new clamshell type barrel SSE platform with grooved feed zone and melting zone was constructed. The clamshell barrels were opened by a hydraulic device, with which the melting performance can be monitored in real time. Thus, the melt starting point and the melting length were determined with good accuracy. The barrels and screws are shown in Fig. 4. Each barrel was divided into three sections, which not only simplified the manufacture of barrel with spiral grooves but also made the change of the barrel sections much easier. Different combinations of barrels and screws and the set of barrel temperatures are shown in Table 1. Screw speed (n) varied from 0 to 45 r/min. The pressure at the screw tip (die pressure) has been set in all trials to 2.0 MPa. The date of melt starting points and melting lengths in this paper is the average values of five repeated experiments, macroscopically observed by opening the barrels. 4.2. Material Low-density polyethylene (LDPE, LD607 type, MFI 7.5 g/10 min) was purchased from Beijing Yanshan Plant. In this study, in order to
Fig. 4. Schematic diagrams of test barrels and screws.
2840
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
Fig. 5. The critical melt starting point and the critical screw speed as a function of the friction coefficient ratio.
simplify the theoretical derivation, the internal friction coefficient (i ) and the external friction coefficient (o ) were assumed to be independent of temperature, determined by friction test. The value of s was assumed to be equal to the value of c . 5. Discussion 5.1. Critical conditions The effect of the friction coefficient ratio (i /o ) on the critical melt starting point and the critical screw speed is shown in Fig. 5. The conditions that the whole solid-plug being cut off by the active flights of the barrel groove and the screw channel were obtained by solving Eqs. (5)–(7). It can be seen from Fig. 5 that the whole solid-plug is ruptured only when screw speed is above 9.8 r/min and the melt starting point (lm ) is more than 8.6 D away from the hopper (i /o = 0.37/0.19 = 1.95). The apparatus of combinations B and C are designed according to this, that is to say the solid in combinations B and C are supposed to start melting 8.6 D away from the hopper. The melt starting points show a linear movement to the extruder die with i /o . According to Eqs. (5) and (8), the melt starting points in the screw channel (ls ) increase with i /o because the value of (Hs3 − Hs1 ) is positive. On the contrary, the melt starting points in the barrel groove (lc ) decrease with i /o due to the negative value of (Hc3 − Hc1 ) according to Eqs. (6) and (8). In general, the theoretical value of ls is smaller than that of lc . Therefore, the melt starting point is dominated by ls according to Eq. (11). Fig. 5 also reveals that the critical screw speed decreases with i /o , which can be explained according to Eq. (11) that the extrusion pressure needed to rupture the whole solid-plug increases with internal friction coefficient (i ) or i /o when o was kept constant. Fig. 5 also showed that the critical screw speed decreased with i /o . When substituting all the parameters into Eq. (7), the values of the coefficients for combinations B and C are gained (A1 = 2,948,545, A2 = 1818, A3 = 485, A4 = 356.9). The left side of Eq. (7) decreased with i , which indicated that the pressure needed to rupture the whole solid-plug is decreased and so did the screw speed. In order to rupture the whole solid-plug easier and earlier, the screw speed and the internal friction coefficient can be increased. In this study, the whole solid-plug cannot be ruptured unless the screw speed is more than 9.8 r/min, which is confirmed by the following experiment. 5.2. Melt starting point Fig. 6 is the trend of the melt starting points of different combinations. As exhibited in the figure, the melt starting points of
Fig. 6. The melt starting points as a function of screw speeds for different combinations.
combination A are different from that of combinations B and C. In combination A, the solid throughput increases more than the melting ability with screw speed, which results in the movement of the melt starting point to the extruder die. Moreover, the solid experienced shorter time in the extruder with higher screw speeds. As a result, the temperature of the solid is lower than usual and needs more time to melt. The melt starting points of combinations B and C are physically determined, which are well agreed with the theoretical melt starting points, indicating the correctness of the calculation of melt starting point. The positive flights of the barrel groove and screw channel together cut the whole solid-plug into small solid-plugs at the preset melt starting point. The figure also shows that the melt starting points of combination C move to the theoretical melt starting point and gradually stabilize with screw speed. At low screw speed, it is hard to supply sufficient pressure to cut the whole solid-plug when the solid reaches the preset melt starting point. The whole solid-plug is further compressed by the volume-decreased barrel groove and then the whole solid-plug is cut by the active flights when the pressure is enough. It also can be seen that the melt starting points of combination B are almost the same. The barr screw is used in combination B. The breaking section of barr screw is set before the barrier section to insure the rupture of the whole solid-plug. According to the analysis of combination C, the melt starting points of combination B are supposed to be closer to the extruder die than the theoretical ones. However, the introduction of the barrier section makes the whole solid-plug rupture at the beginning of the barrier section because the solid cannot get into the melt channel. It can be concluded that the melt starting points in combination B are more stable than that in combination C.
5.3. Melting length Fig. 7 presents the measured data of melting lengths in the screw channel of different combinations. The melting lengths of combination A increase with screw speed. It can be seen from the figure that the solid is not melted in the extruder at n = 45 r/min. It can also be seen from the figure that the melting lengths of combination B are a little smaller than the theoretical values while that of combination C are bigger than the theoretical values. With the barrier section in combination B, the melting lengths are physically determined. Without the barrier section in combination C, the melting length resulted in fluctuation.
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
2841
they did not take the effect of pressure into consideration, which simplified the energy study a lot. The Graetz number is a measure of the importance of heat convection along the centerline of the screw length related to heat conduction and is defined as Graetz number (Gz ) =
heat convection QV Hs3 = ˛Ws3 L3 heat conduction
(37)
where QV is the average volumetric flow rate and is calculated by dividing the total throughput at the die by the density of the melted material and L3 the length of the metering zone. Similarly, the Griffith number is a measure of the importance of viscous dissipation relative to heat conduction. The Griffith number is defined as Griffith number (Gr ) = Fig. 7. Melting lengths in the screw channel as a function of screw speeds for different combinations.
Compared with combination A, the melting lengths of combinations B and C are almost not affected by screw speed and this irrelevance can be explained according to Eq. (18). q ∝ v ∝ n
(34)
When considering the order of magnitudes of friction heat, q, (about 105 W/m2 when n = 45 r/min), the relations, 1 » 3 , 2 » 3 , are obtained. Eq. (33) is simplified as 2 Lc = Zc sin ϕc = − sin ϕc = Wc2 cos(ϕc + ˛c )sin ϕc 1
(35)
The unwound melting length in the barrel groove (Zc ) is only a function of solid conveying angle in the barrel groove (˛c ), which is calculated as follows:
˛c = arctan
c cos ϕc + sin ϕc c sin ϕc − cos ϕc
(36)
where is a function of structure parameters of extruder. It can be concluded form Eqs. (35) and (36) that the effect of screw speed on the melting length is negligible. 5.4. Energy dimensionless analysis The energy study involves a lot of uncertain factors. The energy study is difficult under various conditions of flow or pressure. The energy study is also necessary because it can reveal the melting mechanism of SSE. Kelly et al. (2006) used the dimensionless groups Graetz and Griffith numbers to evaluate the relative importance of heat conduction, heat convection and viscous dissipation in the metering zone of the extruder. The magnitude of these numbers at a range of process conditions indicates the source of heat generated within the polymer melt, i.e. from conduction from the barrel wall or from viscous shearing through power generated by the motor. One of the advantage of these dimensionless numbers was that
viscous dissipation (nD)2 b0 = heat conduction ˇ
(38)
where was measured at a range of wall shear rates using a twin bore capillary rheometer. When the heat conduction assumes a value of 1, the ratios of heat conduction to total energy consumption (HD ), heat convection to total energy consumption (HC ) and viscous dissipation to total energy consumption (HV ) can be calculated by
⎧ 1 ⎪ HD = ⎪ ⎪ 1 + G ⎪ z + Gr ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
HC =
Gz 1 + Gz + Gr
HV =
Gr 1 + Gz + Gr
(39)
All the dimensionless numbers were calculated and the results are included in Table 2. It can be seen from Table 2 that the main melting heat source heat of combination A is the heat conduction and viscous dissipation. The heat convection plays a minor role in solid melting, about 18% at 45 r/min. Sundstrom and Young (1972) found the heat convection plays an important role in solid melting, about 20% higher than the no convection model. The well agreement between the experiment and the prediction of Sundstrom and Young showed the correctness of the dimensionless groups. The viscous dissipation in combination A increases rapidly with screw speed which raises the risk of polymer degradation of overheating. On the contrary to combination A, the main heat source of melting heat of combinations B and C is the heat convection, contributing more than 65% of the total energy consumption. In combinations B and C, the viscous dissipation does not increase sharply as it did in combination A, which not only reduced the risk of polymer degradation but also lowered the temperature of the extrudate. The solid melting under shear conditions is an important operation in the processing of most thermoplastics. Researchers usually ignored heat convection on the melting of solid in theoretical calculation due to the speed of the melt flow was relatively slow. Yates (1968) evaluated the rather significant effect of the down-channel convection on temperature,
Table 2 The calculated dimensionless numbers of combinations A, B and C. Combination
n (r min−1 )
QV (10−6 m3 s−1 )
(Pa s)
HD (%)
HC (%)
HV (%)
A
12 30 45 12 30 45 12 30 45
0.356 0.803 1.14 2.45 6.32 9.26 2.55 6.52 9.96
1852 1054 822 5457 3108 2422 7772 4425 3449
75.8 51.3 38.9 13.9 5.7 3.7 21.8 9.4 6.1
10.6 16.4 17.9 75.6 79.2 79.0 66.8 73.2 73.7
13.6 32.3 43.2 10.4 15.1 17.3 11.4 17.4 20.2
B
C
2842
X.-M. Jin et al. / Journal of Materials Processing Technology 214 (2014) 2834–2842
and later refined by Fenner (1975) and Elbirli and Lindt (1984). In combinations B and C, the melted polymer is pushed by the two forced-moving solid-plugs, which results in high pressure gradient between the melt and the solid-plugs. The polymer melt may be pumped into the small gaps in the solid-plug, providing the unique conditions for heat transfer from the hot polymer melt to the cold solid. On the one hand the heat transfer lowers the temperature of the hot melt which is in favor of cold extrusion. On the other hand the heat preheats the solid-plugs, improving the solid melting rate, which is corresponding to the shorter melting lengths in combinations B and C than that in combination A. Taking combination B when screw speed increases from 12 r/min to 30 r/min as an example, the increase of HC is about 4.76% as shown in Table 2, which is close to the decrease of melting length (5%) as shown in Fig. 7. 6. Conclusions A novel melting mechanism, named as channel-groove coupling melting theory for SSE with grooved melting zone was established. The new SSE platform with hydraulic-clamshell type barrels was constructed and the melting performance of different barrel and screw combinations were investigated. The melting model was verified by the experiment and the result was found to match with the experimental data. Compared with conventional SSEs, it was found that melting starts earlier and melting was finished in shorter region in the case of SSE with grooved melting zone and barr screw. The whole solid-plug started to melt at the tail of the eighth pitch from the hopper in both the barrel groove and the screw channels. The melting lengths in the barrel groove and in the screw channel were slightly affected by screw speed. The grooved melting zone improved the melting efficiency and the barr screw enhanced the
melting stabilization. By introducing the dimensionless groups (HD , HC and HV ), the heat convection and viscous dissipation were found to be the main melting heat source for the SSE with grooved melting zone and barr screw. Acknowledgement The authors would like to acknowledge the support of the National Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (No. 2014211A022). References Elbirli, B., Lindt, J., 1984. A note on the numerical treatment of the thermally developing flow in screw extruders. Polym. Eng. Sci. 24 (7), 482–487. Fenner, R., 1975. The design of large hot melt extruders. Polymer 16 (4), 298–304. Grünschloß, E., 2002. A new style single screw extruder with improved plastification and output power. Int. Polym. Proc. 17 (4), 291–300. Kacir, L., Tadmor, Z., 1972. Solids conveying in screw extruders part III: the delay zone. Polym. Eng. Sci. 12 (5), 387–395. Kelly, A.L., Brown, E.C., Coates, P.D., 2006. The effect of screw geometry on melt temperature profile in single screw extrusion. Polym. Eng. Sci. 46 (12), 1706–1714. Machen, J.F., 1981. High-speed Direct-Drive Extruder, United States. Pan, L., Jia, M.Y., Xue, P., Wang, K.J., Jin, Z.M., 2012. Studies on positive conveying in helically channeled single screw extruders. Express Polym. Lett. 6 (7), 543–560. Potente, H., Heim, H.P., Kleineheismann, S., 2006. Experimental investigations on the plasticating process short single screw extruder for biopolymers. ANTEC, 2. Potente, H., Reckert, F., 2002. Extruder concept for the direct plastification of cereal materials. Macromol. Mater. Eng. 287 (11), 791–799. Rauwendaal, C., 1986. Extruder screws with barrier sections. Polym. Eng. Sci. 26 (18), 1245–1253. Schneider, K., 1968. Der Fördervorgang in der Einzugszone eines Extruders, Aachen, Germany. Sundstrom, D.W., Young, C.C., 1972. Melting rates of crystalline polymers under shear conditions. Polym. Eng. Sci. 12 (1), 59–63. Yates, B., 1968. Temperature Development in Single Screw Extruders. University of Cambridge, Cambridge.