Die design for rubber extrusion.
Die design for rubber can be divided into two steps:
* Controlling flow inside the die to give the desired velocity profile at the die exit; and
* determining the dimensional profile at the die exit that gives the desired product by properly accounting for swell, drawdown and distortion downstream from the die face.
This article looks at two ways to control flow within the die, including:
* Die face relief as a means to achieve balanced flow especially in thin sections of the die; and
* the use of finite element simulation to provide insight and guidance in the design of the die interior. The simulation is also used to "back calculate" the die opening shape from the specified profile to account for distortion in what is known as an inverse calculation.
These topics are included in the die design section of a Rubber Extrusion Technology short course given annually (ref. 1).
Face relieved dies
The traditional practice of relieving the back face of the die is very effective in terms of establishing a uniform velocity at the die exit, but has the undesirable tendency to cause flow of rubber from thin sections of the die, where it is most needed, into adjacent thick sections. In the schematic drawing for the back-relieved die in figure 1 (top), rubber flows perpendicular to the dashed lines, representing constant pressure from high pressure to low pressure. Flow of a particle represented by the dot is away from the thin outside edge of the die and toward the thicker central section, as indicated by the solid arrow. With the face-relieved die in figure 1 (center), the flow of rubber from high to low pressure is biased toward the thin outside edge, as indicated by the dot and arrow. Extruded samples of a low elasticity rubber, shown on the right in figure 1, have torn edges for the rubber extruded through the back-relieved die and smooth edges for the face-relieved die.
[FIGURE 1 OMITTED]
The use of face-relieved dies was examined in a tire sidewall application with back-relieved and unrelieved (straightcut) dies as a comparison (refs. 2 and 3). Schematic drawings of dies for angled back relief (back of the die cut away at a fixed angle); linear face relief (local die land proportional to die opening gap) and quadratic face relief (local die land proportional to square of die opening gap) are shown in figure 2. The expression relating the local die land L to the local die opening thickness H is given by
(1) L/[L.sub.max] = [(H/[H.sub.max]).sup.p]
where p = 1 for linear and p = 2 for quadratic relief and max indicates the maximum value of the die thickness or die land.
[FIGURE 2 OMITTED]
A white sidewall compound was extruded using a 120 mm pin barrel extruder through special dies made according to these designs and also an unrelieved die (not shown). The dies contained small notches spaced at about 10 mm intervals along the top surface at the exit that allowed linking a location on the extruded profile surface to the location where that material exited the die. The local gapwise average velocity profile at the die exit was calculated at 1 mm intervals using conservation of mass from the measured profile of the extruded part and the profile of the die opening. The die opening profile, the extrudate profile and the calculated velocity profile for the back-relieved die are shown in figure 3. The back-relief strategy resulted in a somewhat flatter velocity profile than was obtained for an unrelieved die (not shown), but the adjacent thick and thin sections in the center of the die (arrow in figure) resulted in rubber flowing from the thinner to adjacent thicker section as indicated by the local minimum in the velocity profile. This local minimum was not present in the measured velocity profile for the unrelieved die.
[FIGURE 3 OMITTED]
The same analysis applied to the linear face-relieved die gave the results shown in figure 4. Note that the velocity profile is more uniform and extends closer to the edge of the die than was the case for the back-relieved die. The local minimum in the extrusion velocity at the center thick-thin junction has been eliminated. Extrusion through the quadratic face-relieved die, shown in figure 5, resulted in a pronounced minimum in the velocity profile at the thickest portion of the die, and improved fill on the left edge of the die. These results suggest that an exponent between one (linear) and two (quadratic) would give a result close to the desired flat velocity profile.
[FIGURES 4-5 OMITTED]
Finite element simulations performed by Lee (refs. 2 and 3) as part of this work showed trends similar to the experimental data, and in particular, predicted the local velocity minimum shown for the back-relieved die in figure 3 and the minimum at the thickest opening for the quadratic face-relieved die in figure 5. These simulations also suggested a decreased dependence on flow properties for the back and face-relieved dies compared to the unrelieved die. Velocity profile predictions for the power-law viscosity model (n = 0.3) and Newtonian viscosity were much more similar for the relieved dies than for the unrelieved die.
In summary, face-relieved dies help fill thin edges, eliminate tearing and avoid local velocity minimums in thin regions adjacent to thick regions. The analytical method for calculating die relief illustrated here indicates the possibility for automated die design and direct numerical programming of die cutting machinery. In addition, it may be possible to fine tune relief on the die face without removing the die from the extruder.
Finite element simulation
Simulation of injection mold filling is now commonly practiced in the plastics industry. The drivers for this effort in plastics are the relative complexity and high costs of tooling and the fairly simple task of simulating the filling of a region between fixed walls. Previously, simulation of extrusion dies has been limited because of the lower cost of dies and the complexity of unconstrained flow downstream from the die. Now, with faster computers and more sophisticated codes to handle free-surface flow downstream, including flow-induced distortion, computer simulation is providing direction and insight for challenging die designs. Examples include a vehicle seal made of thermoplastic elastomer (ref. 4), silicone rubber medical tubing with design optimized by simulations including swell and an inverse calculation (refs. 5 and 6), and an unbalanced die for a pipe seal made of SBR (ref. 7). As was the case for injection mold simulation two decades ago, extrusion tool simulation is now moving from an academic activity to industrial practice.
An illustration of computer die design involving several iterations, similar to die trials, is shown in figure 6 for a simulation using the Polyflow code. This simulation includes flow through the extruder head (140 mm diameter) and into a die with a short 15 mm land. The material simulated was EPDM that was fit to a power law viscosity model (power law index = 0.33). This computation was at a constant temperature and with a simple rheological model, which does not predict swell. The simulation code can handle both swell and heat transfer, but computation time would be increased beyond the 20 minutes typically needed for each iteration described here.
[FIGURE 6 OMITTED]
The specified shape for the extruded profile is given by the filled contour shown in figure 7. The velocity profile shown in the contour is for a straight cut (unrelieved) die. The predicted local velocity is high in the yellow and higher still in the red areas where the local die cross-section is relatively open. The velocity is low in the dark blue regions where the die opening is thin. The changes to the back of the die proposed by the designer for the next computer simulation are shown by the red line, which opens up regions of low velocity and restricts regions of high velocity. The die opening shape was held constant for the 5 mm distance directly behind the die face; back relief was applied to the remaining 10 mm of the land. After three more iterations, the back face of the die (shown on the left of figure 8) gave the velocity contours shown on the right side of this figure. With this back relief, the exit velocity at the die face is much more uniform. However, the calculated shape of the extrusion profile downstream showed a slight distortion from the specified shape. To correct for this distortion, an inverse algorithm (ref. 8) was used to alter the opening on the die face as shown in figure 9. The inverse algorithm takes the specified product shape and works backward to determine a die opening that will give the specified shape. The relieved die contours and the extruder head are shown in figure 10.
[FIGURES 7-10 OMITTED]
The insight gained from simulation of a representative die, when combined with experience and intuition, can be applied broadly to dies for products with similar shapes. Simulation is also a quick way to test the feasibility of new design concepts without interfering with production die work or tying up manufacturing extrusion lines. Computer simulation will not eliminate die trials, but the starting point for the first trial is expected to be much closer to the final design, particularly if the simulation correctly identifies designs that handle subtle problems like distortion downstream from the die.
(1.) J.F. Stevenson and J.S. Dick, Rubber Extrusion Technology, University of Wisconsin, Milwaukee, WI (2003).
(2.) C.-C. Lee and J.F. Stevenson, "The face-relief strategy for design of profile dies," Intern. Poly. Proc. 7, 186 (1992).
(3.) C.-C. Lee and J.F. Stevenson, "Evaluation of die design strategies by simulation and experiment," SAE paper 880027, SAE International Conference and Exposition, Detroit (1988).
(4.) Y. Rubin, L. Fondin, T. Marchal, T. Burton and A. Goossens, "Numerical balancing of extrusion dies: A validation study with a TPV automotive weatherseal profile," International Rubber Conference, Prague (2002).
(5.) C. Reese, "Use of die modeling to improve the manufacturing process for extruded silicone rubber," Society of Plastics Engineers 52nd Antec proceedings, p. 94 (1994).
(6.) D.A. Andrejewski, "Polyflow: A treatise on inverse die/ mandrel design for high consistency silicone elastomer," Society of Plastics Engineers 55th Antec proceedings, p. 308 (1997).
(7.) E. Cavka and T. Marchal, "Pipe seal-extrusion die design with Polyflow," 4th International Esaform Conference on Material Forming, Liege, Belgium (2001).
(8.) V. Legat and J.-M. Marchal, "Die design: An implicit formulation for the inverse problem," Intern. J. Numer. Method Fluids, 16, 29 (1993).
James E Stevenson, Honeywell International