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An Expanded Residence Stress Distribution Study in a Twin-Screw Extruder: The Effect of Stress Bead Strength

Graeme Fukuda, Roba Adnew, Harry Brown II, Jesse Kim, and David I. Bigio Mechanical Engineering,
University of Maryland, College Park, MD


The ability to measure Residence Stress Distribution (RSD) in real time provides a greater understanding of the extrusion process. A method has been developed to characterize stress history within a 28-mm co-rotating twin-screw extruder (CoTSE) through the use of stress beads that break at critical stresses. Three different strength stress beads were used to provide an expanded and robust methodology. A Design of Experiment (DOE) approach was used to present the bead breakup results.


Extrusion has been a widely researched technique used for mixing in many different fields. Studies have been conducted in the pharmaceutical, food, and rubber industries along with many others [1]. In addition, food packaging has been an increased area of interest due to improved properties for barriers protecting food from oxygen, carbon dioxide, and water vapor [2]. Furthermore, the advancement of processing polymer composites with carbon based microfibers and nanotubes has gained traction. Addition of these fillers can enhance mechanical, thermal, and electrical properties [3].

Mixing is a critical component to the characterization of extruded material. Screw configuration is one such element that alters mixing within an extruder. Many extrusion processes utilize a mixing section which contains blades, paddles, or pins [1]. The two mixing sections studied for this research were narrow and wide kneading blocks (KB). Narrow KB induce low magnitudes of shear stress but generate high strain this allows for better distributive mixing. On the other hand, wide KB focus on creating high magnitudes of shear stress, which is best suited for dispersive mixing. Distributive mixing helps create a uniform spread of particles within the extruded final product. While dispersive mixing allows for the capability of breaking agglomerates into smaller particles [4].

The degree of mixing achieved in a twin-screw extruder is one of the most important factors that affect the properties of the final product [5]. Erwin demonstrated that the use of a mixing section reorients the interfaces of the fluid for greater area growth and thus better mixing [6]. In order to successfully determine the degree of mixing that occurs within the extrusion process, accurate modeling of the induced stress for a given mixing section and operating condition is necessary.

Past studies have developed RSD measurement techniques but nothing in real time. Wetzel et al used a method of a single ultrasonic probe and a tracer to identify the time the material spends in the extruder, which can determine the RSD [7]. Curry et al used glass spheres to measure the stress history. However, the method was discontinuous because it required burning the polymer off and manually counting the number of broken glass spheres [8].

Recent studies using stress sensitive polymer beads have been used to measure the stress history in real time [9]. These studies were expanded upon to include multiple stress beads that varied in strength in order to observe the accuracy of the methodology. The study produced similar results to research done with one strength stress bead thus validating the method of experimentation [10].

To further expand the analysis of the stress bead approach this study was conducted using three different strength stress beads. The DOE approach depicted the percentage of stress bead breakup along a range of screw speed (N) and specific throughput (Q/N). The DOE technique also enabled a statistical analysis to determine significant processing parameters and generate predictive equations for percent breakup. The following paper presents the results of the three stress beads.


High-density polyethylene (HDPE) Alathon H6018 in pellet form from Equistar Chemicals was the base polymer for this experiment. HDPE has a density of 0.960 g/cc and a melt index of 18.0 g/10 min. The stress beads used were CAlibrated MicroEncapsulated Sensor (CAMES) beads provided by Mach 1 INC. in King of Prussia, PA. The CAMES beads measured the stress during extrusion by breaking at specific critical stress levels and releasing their encapsulated ink into the polymer melt. The critical stress level of the beads depends on the diameter and wall thickness of the bead. The three critical stresses of the beads used were 92 kPa, 119 kPa, and 158 kPa. The 92 kPa and 158 kPa beads were blue and the 119 kPa beads were red.

For the blue stress beads the same dye that is encapsulated in them, Automate Blue 8A, was used to stain the polymer melt as a reference shot. For the red beads, the dye used was Red B Disazo. The reference shots were prepared by dissolving super high impact polystyrene (HIPS) 935E pellets in a heated solvent. The reference dye shots represented the paths taken if 100% of the stress beads were broken. This 100% breakup can also be visualized as Residence Time Distribution (RTD) because it accounts for all the paths taken by all the different fluid elements.


The experiment was performed on a Coperion ZDSK-28-co-rotating, fully intermeshing twin-screw extruder. The screw diameter was 28-mm and the length to diameter ratio (L/D) was 32. Also, it should be noted that the extruder is a three-lobe machine. The extruder set up has a feed port and one vent port before the mixing section where the stress beads and the reference ink shots were dropped.

Two different screw geometries were investigated. Following a melting and conveying region that were the same, the first mixing section was comprised of four forward conveying right-handed narrow kneading blocks 6.0 cm of total length, followed by a reverse conveying element of 3.0 cm. This geometry ensured that the mixing section would be filled for all operating conditions. For the second screw geometry, three of the narrow kneading blocks were removed and replaced with one right-handed wide KB of 4.5 cm long. The reverse element was kept as the backup element for both configurations.

Figure 1. 28-mm Coperion Co-Rotating TSE and data acquisition setup

A reflective optical probe was placed above the end of the mixing section where the screws are filled. The probe consisted of a bifurcated optical fiber bundle enclosed in a stainless steel shell contained in a larger stainless steel shell with a sapphire window. The probe was inserted into a barrel through a standard Dynisco pressure transducer port. The probe uses a split fiber optic bundle, where white light is transferred from one bundle and enters the extrusion melt. The light is then scattered by the stained melt and enters back through the other fiber bundle. The light recorded is converted to a voltage signal using a photo diode and a signal amplifier.


For this experiment, operating conditions were chosen in accordance to machine specifications, in order to obtain a wide range of data. The five barrels of the extruder were set at 200°C and the die zone was set at 195°C for all experimental runs. Operating conditions were varied by specific throughput and screw speed.

Data was collected through the optical probe, and due to the transparent nature of HDPE melt, TiO2 was mixed into HDPE to provide a white background so the optical probe could take proper measurements. Since such small amounts of dye were mixed with the HDPE melt the concentration of the dye and polystyrene had a negligible effect on the viscosity of the HDPE melt. Impulses of stress beads and reference shots were injected in the melt once a baseline was established in the data acquisition program. Once the stained melt was completely extruded, and the baseline had returned to its original position the data acquisition program was reset for the next experimental run. In total, nine operating conditions were tested for each screw configuration, with an average of two reference shots and two stress bead shots per condition. Figure 2 below is an example of the RTD and RSD curves after analysis. The blue curve represents the reference shot and the magenta and green curves depict the stress bead shots.

Figure 2. Example RTD/RSD for the 1.8 lbs/hr 110 RPM experimental condition

Experimental Grid

The central composite design (CCD) grid was chosen for its statistical advantages and visual representation of the data. Additionally, the CCD grid clearly displays the relationship between percent breakup and operating conditions. The vertical axis represents the Q/N in units of mL/rev. The horizontal axis represents N which is in units of RPM. The values on the grid in Figure 3 represent the mass flow rates in lbs/hr for all nine experimental conditions. The axes were chosen because RTDs scale with N and Q/N.

Figure 3. CCD grid of experimental conditions

Experimental Results

Percent Breakup
The average percent breakup for all nine experimental conditions was calculated and the results inserted into the CCD grid as a way to compare and analyze the breakup trends for different bead strengths and screw geometries to operating conditions. To determine the percent breakup of the stress beads, the areas under the RTD and RSD curves were calculated and used in the following equation:


Where Ac is the area under the stress bead, or RSD, curve and Ar is the area under the dye, or RTD, curve. Three different strength stress beads were studied for this research, 92 kPa, 119 kPa, and 158 kPa. Figures 4 through 9 present the percent breakup results for each bead from lowest strength to highest using the CCD grid display.

Figure 4. Percent breakup of 92 kPa beads using narrow kneading block

Figure 5. Percent breakup of 92 kPa beads using wide kneading block

Figure 6. Percent breakup of 119 kPa beads using narrow kneading block

Figure 7. Percent breakup of 119 kPa beads using wide kneading block

Figure 8. Percent breakup of 158 kPa beads using narrow kneading block

Figure 9. Percent breakup of 158 kPa beads using wide kneading block

For all different strength stress beads certain patterns reappeared within the CCD grids. The wide KB geometry for every operating condition had a higher percent breakup than the narrow KB configuration. Additionally, the average breakup between grids decreased linearly with the strength of the stress bead, thus the lowest breakup results were seen with the strongest bead, the 158 kPa bead. Also the diagonals from the upper right to the lower left direction for all the grids, which approximately have the same mass flow, showed similar percent breakups. The diagonals from the lower left to the upper right direction showed an increase in breakup, displaying the significance of N and Q/N.

Each CCD grid was entered into JMP ® 9.0.0 statistical software for additional quantitative analysis. The results of the statistical report were organized in Table 1. The most notable result the statistical report indicated was which operating parameters proved significant on a 95% confidence interval. In all strength beads only two parameters were found to be significant, N and Q/N. The magnitude of the coefficients of N and Q/N are presented in Table 1. The last third of Table 1 provides statistical output for the concatenated wide and narrow geometry grids, which contributed a factor of change between the overall average and a specified screw configuration.

Equation 2 provides the general form of the predictive equation obtained. The predictive equation shows that percent breakup is only a function of screw speed and specific throughput. Coefficient A specifies the influence of screw speed on the breakup and coefficient B specifies the influence of specific throughput on the breakup. The constant C represents the average breakup for a specific grid or the intercept. The coefficients are also displayed in Table 1.

Table 1. Percent Breakup Predictive Equation Coefficients

The kneading block rows labeled “Combined” represents the average values of the narrow and wide KB equations. The “[Narrow]” column represents the percent shift required to bring the average breakup down to the breakup of the narrow KB grid. The negative sign indicates that the narrow KB breakups were all less than the average percent breakup.

Closer inspection of the comparison between grids brought about additional observations. When comparing the 92 and 119 kPa strength beads against each other there is a clear decrease in breakup from the 92 kPa to the 119 kPa beads. This result concludes that more of the fluid experiences the lower critical stress level of 92 kPa. For the narrow KB configuration the percent breakup increased by 10% when changing from the 119 kPa beads to the 92 kPa beads. Similarly, for the wide KB configuration the increase was 6%. An explanation for this, is that for the wide KB there was already a higher percent breakup, thus less of a chance for increase. Change in configuration between the 158 and the 92 kPa beads showed a similar difference. For the narrow KB there was a difference of 12% and for wide KB a change of 10%. Again the narrow KB showed more sensitivity to the change in bead strength. However, between the 158 and 119 kPa beads the difference for the wide KB was 5%, but the narrow KB only a 2% variation.

Examination of Table 1 yields a deeper understanding into the causes of breakup and the stress bead approach. The magnitude of the coefficients in Table 1 represent the sensitivity of the predictive equation to the changes in input parameters (N, Q/N). The coefficients of 92 kPa beads, compared to the other two beads, has the largest difference in magnitude between the N and Q/N coefficients for each screw geometry, with Q/N always playing a much greater role in percent breakup. The 119 kPa beads have the coefficients with the greatest magnitude, with values of approximately 9 and 10 for both N and Q/N for the wide and narrow KB configurations, which are about double those for the other two stress beads. This spike in magnitude for the 119 kPa beads shows that they are the most sensitive with respect to operating conditions. The last observation from Table 1 comes from the 158 kPa bead data. Although the 92 kPa beads have the largest difference between N and Q/N for each respective screw configuration, the coefficients for both N and Q/N for the 158 kPa beads nearly double when moving from the narrow KB results to the wide KB results. The other two bead strengths have approximately the same magnitude for both types of mixing sections. This indicates that the strongest bead, the 158 kPa, were most sensitive to the geometry change.

Figure 6. RSD curves 2.4/75 for all three strength beads under a single RTD

Figure 6 above displays the visual representation of the variation in bead strength with respect to stress distribution. The selected operating condition was 2.4 lbs/hr and 75 RPM because the curves in this range are mainly noise free. There are three RSD curves depicted, one for each stress bead studied. The RSD curve with the highest magnitude is the 92 kPa bead due to its low critical stress level. The 119 and 158 kPa beads follow in that order. This agrees with the quantitative results seen in the CCD grids. The delay times of all three RSD curves also exhibits an interesting trend. As the bead strength increases the delay time becomes longer. This phenomenon is attributed to more beads passing through unbroken. It has been shown that the material that comes through the fastest, travels through the center of the channel where the stresses are the lowest [11]. The lower critical breaking stress occurs closer to the center of the channel and will have a shorter delay time. The higher critical breaking stress will be experienced closer to the wall resulting in a longer delay time.


A real time measuring technique for RSD has been developed in an extruder, using a method involving stress beads and an optical probe to measure their breakup. Three separate strength stress beads were used to expand the findings of previous studies and to continue to validate the methodology. Through a DOE approach, data was analyzed by evaluating percent breakup as a function of operating conditions. Screw speed, N, and specific throughput, Q/N, were found to be significant in breaking of the stress beads for all conditions tested. Two different mixing sections of equal length were investigated in this study. One with only narrow KB and the other with only wide KB elements, both backed by a reverse element. All three beads showed to be more susceptible to breaking under the wide KB configuration. Furthermore, breakup results showed that the average breakup varied linearly with the strength of the bead, meaning as the bead strength went up the overall breakup went down for every operating condition. The compiled RSD curves also displayed other patterns with respect to bead strength. As the critical stress level of the bead increases the delay time also lengthens, and the magnitude of breakup decreases with increasing bead strength.

Results from the CCD grids and the table of coefficients provided additional information to characterize the stress history. The lowest strength bead, the 92 kPa, showed the greatest difference between magnitudes of coefficients for each respective geometry proving they were affected by specific throughput more than the other two beads relatively. The strongest critical stress bead, the 158 kPa, had an almost doubling of coefficient magnitude when moving from the narrow to wide KB geometry, making the 158 kPa bead the most vulnerable to a screw configuration change. However, the most interesting of all the results were with the 119 kPa coefficients. The coefficients for the 119 kPa beads was far greater than the both the other two beads. The high magnitudes indicate the 119 kPa beads are the most sensitive to operating conditions, and thus provide the greatest controllability for manufacturers. It is postulated that the average stress in the channel and the critical stress of the 119 kPa are closely matched. As one changes conditions one strongly changes the amount of fluid that experience the critical stress. The ability to categorize stress history in real time enables manufacturers to better understand how flow path truly affects their machine and ultimately their product. Future work will continue to broaden the range of beads studied along with a greater variation of screw geometry, material, and operating conditions.


I would like to acknowledge all the undergraduates that aided in running the experiments for this paper. Beyond the co-authors help from Betel Sime, Bunty Bhatia, Alexander Moses, and Hoyoung Khang was invaluable. Additionally, the help of Jason Nixon and Joe Martin on the MATLAB analysis code provided great assistance. Also, Mark Wetzel for his counsel and help in the direction of the experiment.


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