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Effectiveness of a backward mixing screw element for glass fiber dispersion in a twin-screw extruder.


Twin-screw extruders (TSEs) are widely used in resin compounding processes due to their high operability and high kneading performance. In resin compounding processes, uniform kneading of various additives within the molten resin is important in molding process and product design from the viewpoint quality and manifestation of the functions of additives. Consequently, it is essential to understand the dispersibility of additives resulting from the screw element configuration within the extruder. On the other hand, because screw element configurations that have a strong dispersing ability cause resin degradation through viscous heating, the set range of extrusion conditions is extremely limited. In addition, there has been an increasing demand for resin compounds as substitute materials for metals in automobile and electronic components, making mass production by increasing production speed desirable. When using an extruder of the same size, it is necessary to increase the rotation speed of the screws to increase the production speed while maintaining dispersibility. This reduces the kneading time in the extruder and the thermal degradation of the resin. Consequently, the establishment of a quantitative assessment technique for extruder conditions and screw element configuration is important for controlling the trade-off relationship between additive dispersion and thermal degradation prevention.

In this report, we use glass-fiber-reinforced plastic (GFRP) as a representative resin compound. Dispersion techniques for GFRP can be broadly divided into two classes: glass fiber fracture prediction techniques in which fibers are broken to a target length and glass-fiber bundle dispersion techniques that dissociate the raw material glass-fiber bundles. Many studies have investigated glass-fiber fracture prediction techniques. Forgacs and Mason [1] theoretically found that the fracture stress for glass fibers has an exponential dependence on the aspect ratio (i.e., the ratio of the fiber diameter to the fiber length). Many groups, including Inceoglu et al. [2], Yilmazer and Cansever [3], and Shimizu et al. [4], have investigated the relationship between glass fiber fracture and the operation conditions of TSE. In addition, Ramani et al. [5] investigated the effect of screw elements on glass fiber fracture.

On the other hand, there have been very few studies of glass-fiber bundle dispersion techniques. If glass-fiber bundles are insufficiently dispersed, fiber bundles will remain within the product pellets. If glass nondispersed pellets are present, the nozzle of the molding machine may clog in the injection molding process, causing quality problems such as separation of glass-fiber bundles on the molded product surfaces. However, nondispersion does not occur much at low production speeds. This is because at low production speeds, a long kneading time is required in the extruder and there is a wide range of extruder operating conditions enabling countermeasures to be easily adopted. Briefly, it is essential to determine the mechanism for the occurrence of the nondispersion of glass fibers at productions speeds used in actual production levels. Melody et al. [6] performed basic experiments concerning the dispersion mechanism of fiber bundles and found that there were the two modes for rupture and erosion in the dissociation of glass-fiber bundles. They also found that complete dispersion occurs at or above a critical shear stress that depends on the flow structure. Our group has performed extrusion experiments over a broad range of operating conditions up to those used in actual production levels. We have performed the quantitative assessments shown in Fig. 1 for the probability of glass nondispersion based on extrusion conditions and type of screw element [7, 8]. These results experimentally demonstrate that of the screw elements investigated, a backward mixing screw (BMS) was effective at preventing nondispersion of glass-fiber bundles. However, this has not led to a quantitative assessment of the glass-fiber bundle dispersion mechanism or a proposed unified dispersion index.

Computational fluid dynamics (CFD) is actively used to investigate the flow processes in extruders. While there are many difficulties in analysis of the inside of an extruder (e.g., phase changes from solid to liquid, the presence of free surfaces, the analysis time), the analysis results are based on many assumptions. Although this kind of analysis has limits, CFD can be used to obtain much data regarding the flow behavior in an extruder. Tracer particle tracking, about which there have been an increasing number of reports since the 1990s, is an effective tool for assessing the additive dispersion processes. Lawal and Kalyon [9-11] have assessed the kneading properties of various screw element configurations. They proposed using Lyapunov exponents as distributive mixing indices. Zhang et al. [12-14] constructed a detection system that had two probes in the extruder and compared simulation results focusing on local residence times. They performed studies using the degree of elongation of an object surface, which is a distributive mixing index proposed by Ottino et al. [15], The Funatsu and Kajiwara group [16-22] used marker tracking and proposed various distributive and dispersive mixing characteristics regarding kneading elements such as the residence time distribution, the distance between tracer particles, and the absolute shear stress. Manas-Zloczower et al. [23-25] investigated dispersive and distributive mixing in the kneading region of TSEs using commercially available flow analysis software (FIDAP) and demonstrated that the shear stresses that develop during distributive mixing and elongational flow components are important. Bravo et al. [26-28] compared the pressure distribution obtained by a pressure indicator and speed visualization results using an acryl device with numerical simulation results. The above studies have demonstrated that the physical quantities along the flow path are extremely important for assessing kneading properties under different operating conditions.

The present study seeks to quantitatively elucidate the mechanism for the effectiveness of the BMS configuration for glass-fiber bundle dispersion using three-dimensional flow analysis. We used three-dimensional flow analysis and tracer particle tracking under the same conditions as previous extrusion experiments performed (see Table 1). We established a dispersion index for glass-fiber bundles. In addition, using this dispersion index, we obtained insight into screw element configurations that are compatible with the production speed and dispersion.


Screw Geometries

A three-dimensional simulation was performed to clarify the dynamics in a TSE, TEX44 (Japan Steel Works) using the commercial software Screwflow-Multi (R-flow). Figure 2 shows the analysis models used. The forward full flight screw (FF) and backward full flight screw (BF) were respectively located before and after the kneading disk elements to completely fill the mixing zone with polymer, as in the experimental screw configurations.

Governing Equations

We assumed that the material is fully filled in the analysis model and that the flow is incompressible. We also assumed that inertial effects were negligible due to the low Reynolds number. The governing equations are given below, where (1) is the continuity equation, (2) is the equation of motion, and (3) is the energy balance equation:

[nabla] x v = 0 (1)

0 = - [nabla]p + [nabla] x [tau] (2)

[rho][C.sub.p]v x [nabla]T = k[DELTA]T + [tau] : D (3)

where p is the pressure tensor, [tau] is the deviatoric stress tensor, [rho] is the mass density, [C.sub.p] is the specific heat capacity, T is the temperature, k is the thermal conductivity, and D is the strain-rate tensor. These equations were discritized by the finite volume method and solved by the SIMPLE method.

Constitutive Equations

The melt polymer was assumed to be a viscous shear-thinning fluid that follows the Arrhenius law.

[tau] = 2[eta]D (4)


[H.sub.0] (T,[T.sub.0]) = [C.sub.3] exp ([C.sub.4]/T) (6)

[??] = [square root of 2D : D] (7)

The parameters of the Arrhenius model given in Table 2 were determined by fitting the above functions to the experimental shear viscosity of the melt-PBT compound (glass fiber: 30 wt%), as shown in Fig. 3.

Boundary Conditions

Tables 3 and 4 list the boundary conditions for the flow and heat analysis, respectively.

Tracer Particle Analysis

Particle tracer analysis was performed to obtain local data from the flow patterns. In tracer particle analysis, about 7000 tracer particles were uniformly distributed in the screw section shown in Fig. 2. We assumed that these tracer particles are glass fiber bundles. The throughput rate, screw rotational speed, and cylinder temperature were set to their experimental values. The temperature in the in-flow plane was that measured before the simulations.


Numerical Evaluations of Melt-Mixing Processes by FKD and BMS

To compare the kneading process by FKD and BMS, tracer particle analysis was performed during a single rotation of the screw. The screw element configuration was taken to be L/D = 2.0 (as shown in Fig. 2b) and ~7000 particles were uniformly distributed in the central section of the first kneading element. The results of previous extrusion experiments indicate that glass-fiber bundle dispersion is affected by the extrusion throughput and the screw rotational speed. We thus focused on the particle movement and the shear stress distribution during screw rotation.

Particle Distribution. Figure 4 shows the particle distribution in the extrusion direction after one screw rotation at Q = 650 kg [h.sup.-1] and Ns = 650 rpm. The horizontal axis in Fig. 4 indicates the distance at which the initial set position of a tracer particle is taken as the starting point ([[DELTA].sub.z] = 0.0056 m). For both screw configurations, most tracer particles moved forward from their initial positions. However, the BMS gives a narrower particle size distribution than the FKD. The fraction of particles rapidly transported in the forward direction (indicated by the gray region in Fig. 4) is considered to indicate an important difference in the kneading properties because it represents a limited kneading time flow trajectory. Glass-fiber bundles in the flow path for a limited kneading time may pass through without undergoing sufficient kneading. In the particle distribution after one FKD rotation, particles rapidly transported in the forward direction are seen in a constant proportion. In contrast, such rapid forward transport is mainly not observed in the particle distribution after 1 BMS rotation.

Shear Stress History. Figure 5 shows the shear stress distribution in a cross-section of the kneading element at Q = 650 kg [h.sup.-1] and Ns = 650 rpm. Because both elements have the same outer and inner screw diameters, they give the same minimum and maximum shear stresses and average shear stress. The cross-section in Fig. 5 can be easily divided into three regions based on the shear stress. As shown in Fig. 5, the low shear stress region is the root part, the moderate shear stress region is the flank, and the high shear stress region is the tip part. All screw elements have a low shear stress region.

Figure 6 shows the maximum shear stress distribution during one rotation. The critical aspect of this figure is the fraction of particles in the low shear stress region. This fraction of particles represents particles that are transported within the extruder without once exiting the low shear stress region. In other words, for the BMS, all the tracer particles in the low shear stress region passed through the high shear stress region during one rotation. From this, mixing by the BMS is considered to occur between the low shear stress region and some other section. On the other hand, for the FKD, there is a constant fraction of particles present that have not left the low shear stress region even after one rotation. Table 5 shows the probability of a tracer particle passing through the three aforementioned shear stress regions. The above results obtained using tracer particles, which considers the flow trajectory, clarify the differences in the kneading process of BMS and FKD.

Operation Windows for Glass-Fiber Dispersions

To consider the effect of stress while passing through the melt mixing section, the time-integrated shear stress along the flow trajectory is considered given by


where [[GAMMA].sub.i] is the minimum value of time-integrated shear stress, [t.sub.i] is the residence time of the ith tracer and [tau] is the shear stress. The time-integrated shear stress was calculated numerically as follows. Tracer particles were uniformly distributed in the central part of the full flight element, as shown in Fig. 2; all particles were calculated from the analysis model until 90% or more flowed out, and (8) was evaluated for each tracer. Figure 7 shows the locations of the tracer particles after 0.5 s. As Fig. 4 shows, the BMS gives a narrower tracer distribution than FKD. In addition, with FKD many particles pass through the flank and root part of the screw element by transport flow. From this figure, we conjecture that many flow trajectories pass through the low shear stress region with FKD.

Figure 8 shows the distribution of the time-integrated shear stress in the overall screw element configuration when Q = 650 kg [h.sup.-1] and [N.sub.s] = 650 rpm. The distribution of the time-integrated shear stress in BMS was mainly unimodal. In contrast, a shoulder was observed at low values for FKD. In addition, the minimum time-integrated shear stress was higher for BMS than for FKD. Consequently, the uniformity of the operating stress experienced in the melt mixing section was higher with BMS than FKD and the fraction subjected to insufficient kneading action is thought to be lower.

Operation Windows for Glass-Fiber Dispersions

Undispersed Glass Fiber Bunches and Stress History. For glass-fiber bundles to dissolute in melt section, it is thought to be necessary to subject them to at a certain minimum operating stress. The number of nondispersed pellets is conjectured to depend on the minimum time-integrated shear stress. Figure 9 shows the correlation between the ratio of the minimum time-integrated shear stress obtained by numerical calculations for the same conditions as the extrusion experiments to [(Q/[N.sub.s]).sup.3] and the number of pellets containing undispersed glass-fiber bundles in 10 kg obtained by the extrusion experiments. This figure shows that there is a correlation dependent on Q/[N.sub.s] between the number of non-dispersed pellets and the minimum time-integrated shear stress. The correlation is given by


[alpha] = 11.50, [beta] = -2.20, [gamma] = 3.00

where [[GAMMA].sub.min] is the minimum value of time-integrated shear stress, [alpha] and [beta] are assumed to be constants that depend on the quantity of glass fiber to polymer and the kind of the binder, and [gamma] is assumed to be constant that depends on the saturation rate of the melt-zone in a TSE. The parameters [alpha], [beta], and [gamma] are thought to depend on factors such as the matrix polymer, the glass fiber ratio within the polymer, the type of binder. We can set the threshold of glass fiber dispersion arbitrarily. Thus, we have defined the threshold for undispersed condition as about 1.0 pellets/kg. This value is the threshold that there are no troubles in terms of quality and injection molding process. Thus, time-integrated shear stress is calculated about 75 kPa [s.sup.-1] from the approximate equation based on the results in Fig. 9. It was empirically found that with this treatment (PBT, glass fiber 30 wt%), defects do not occur in the polymer processing or quality aspects at operating conditions in which the minimum time-integrated shear stress is 75 kPa [s.sup.-1] or higher. Consequently, for these analysis conditions, 75 kPa [s.sup.-1] is assumed to be the lower limit for non-dispersed pellet control. Figure 10 shows the minimum time-integrated stress for each screw element configuration at Q/Ns = 0.8. The extrusion throughput that reaches this lower limit for non-dispersed pellet control is said to be the maximum production speed to realize glass-fiber bundle dispersion for each screw configuration.

Temperature Rise. If the time-integrated shear stress is increased by the extruder operating conditions or screw element configuration, the temperature increases greatly due to viscous heating of the resin. If the resin temperature rises, thermal degradation of the resin will be accelerated. Accordingly, to determine the operating conditions in the dispersion process for additives, it is necessary to consider inhibitory control of the rise in resin temperature. The resin temperatures under each operating condition were calculated using the temperature balance Eq. (3). Figure 11 shows the outflow temperature for each screw element configuration at Q/Ns = 0.8. Because PBT thermally decomposes at 300[degrees]C, the upper limit for the resin temperature was set to 290[degrees]C. According to this condition, it is possible to predict the extrusion conditions that do not exceed the upper temperature limit for each screw element configuration. It is generally not strictly required that the resin be at or below 290[degrees] C. That is, in cases where the focus is on the average mechanical strength of a molding product such as tensile strength or FS, there may be cases when kneading can be performed at conditions that exceed the thermal decomposition temperature. In such cases, the upper temperature limit should be set based on the property regarded to be most important.

Prediction of Production Speed Based on Control of Dispersion Failure and Heat Deterioration. Figure 12 shows glass-fiber bundle dispersion lines (solid line) and thermal degradation lines (broken line) for FKD and BMS at Q/[N.sub.s] = 0.8. The throughputs of GF line are the throughput values in the case for minimum time-integrated shear stress of 75 kPa [s.sup.-1], and the throughputs of polymer temperature line are the throughput values in the case for polymer temperature of 290[degrees]C at each screw configuration. The region below the glass-fiber bundle dispersion lines and the thermal degradation curves represents the suitable operation window. These results quantitatively demonstrate that the BMS configuration has a much broader operating range than FKD. In addition, if we assume that the glass-fiber bundle dispersion and thermal degradation curves are both approximately linear, qualitative comparisons of quantitative assessments of screw elements can be readily performed.


Three-dimensional flow analyses and tracer particle analyses were performed to assess the effect on the dispersion properties of glass-fiber bundles resulting from extruder operating conditions and screw element configuration in the melt-mixing region within a TSE. Based on previous experimental results, the aim was to establish dispersion indices for glass-fiber bundles focusing on BMS elements where a significant difference was confirmed. From flow analysis for one screw rotation, flow paths that promptly left the kneading region were confirmed in the FKD configuration and many flow paths were found to pass through only the low shear stress region. On the other hand, with the BMS configuration, tracer particles in the low shear stress region passed through the moderate or high shear stress regions during the course of one screw rotation and the total shear stress experienced before passing through the kneading region was found to be high. From these results, we focused on the time-integrated shear stress, and due to the low probability of glass-fiber bundle nondispersion phenomenon occurring, we paid particular attention to its minimum value. We confirmed that there is a clear correlation between the minimum time-integrated shear stress and the number of nondispersed bundles. Using the correlation equation, it was possible to determine suitable operating conditions for dispersion of glass-fiber bundles. A more realistic operation window was obtained by also considering thermal degradation of the resin. Screw element structures such as BMS that induce complex flow trajectories were shown to be effective for glass-fiber bundle dispersion.


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Kunihiro Hirata, (1) Hiroshi Ishida, (2) Motohito Hiragohri, (2) Yasuya Nakayama, (3) Toshihisa Kajiwara (3)

(1) Research & Development Division, Technical Solution Center, Polyplastics Co., Ltd., 973 Miyajima, Fuji, Shizuoka 416-8533, Japan

(2) Production Department, Polyplastics Co., Ltd., 973 Miyajima, Fuji, Shizuoka 416-8533, Japan

(3) Department of Chemical Engineering, Kyusyu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

Correspondence to: Kunihiro Hirata; e-mail:

DOI 10.1002/pen.23752

Published online in Wiley Online Library (

TABLE 1. Operating conditions for TSE and polymer temperature
after passing through the melting section.

Parameters           Units

Throughput (Q)       kg/h           100   100   100
Screw speed (Ns)     rpm            100   125   200
Q/Ns                 kg/(h x rpm)   1.0   0.8   0.5
Inflow temperature   [degrees]C     255   259   267

Parameters           Operating conditions

Throughput (Q)       300   300   300   650   650
Screw speed (Ns)     300   375   600   650   807
Q/Ns                 1.0   0.8   0.5   1.0   0.8
Inflow temperature   250   257   276   255   265

TABLE 2. Material data for PBT compound (GF 30 wt.%).

Parameters                       Units

Density ([rho])                  kg/[m.sup.3]   1290
Specific heat (C.sub.p)          J/(kg x K)     1700
Thermal conductivity (k)         W/(m x K)      0.26
Arrhenius model parameter (C1)                  3.688 x [10.sup.-4]
Arrhenius model parameter (C2)                  6.393 x [10.sup.-1]
Arrhenius model parameter (C3)                  2.066 x [10.sup.-9]
Arrhenius model parameter (C4)                  1.410 x [10.sup.4]

TABLE 3. Flow boundary conditions.

Inlet cross section      V = Q/(3600[rho]A)
Barrel inner surface     No-slip condition
Disc surface             V = [PI]DNs/60
Outlet cross section     d/dZ=0

TABLE 4. Temperature boundary conditions.

Inlet cross section    Constant temperature mesured experimentaly
Barrel inner surface   220[degrees]C
Disc surface           dT/dR = 0
Outlet cross section   dT/dZ = 0

TABLE 5. Particle probability in each shear stress section.

      Low shear   Intermediate    High shear
       stress     shear stress      stress
      0-100 kPa    100-200 kPa     200-300
       (Root)     (Flank, Bore)   kPa (Tip)

FKD     12.8          47.2            40
BMS      0.0          38.1           61.9
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Author:Hirata, Kunihiro; Ishida, Hiroshi; Hiragohri, Motohito; Nakayama, Yasuya; Kajiwara, Toshihisa
Publication:Polymer Engineering and Science
Article Type:Report
Date:Sep 1, 2014
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