Design and performance analysis of a self-regulating melt pressure valve.

INTRODUCTION

Feed systems are used in injection molding and other polymer processing operations to deliver the polymer melt from the plastication unit to one or more locations where the melt is formed. In many injection molds, for example, multiple branches and gates are used in a feed system to deliver the melt to a plurality of locations so as to simultaneously form multiple articles in a single cycle, or alternatively to manufacture larger articles that could not be produced via the distribution of the polymer melt through a single gate. In such conventional feed systems, including both cold and hot runners, the volumetric flow rate and pressure of the polymer melt is determined by the geometry of the feed system. Once specific lengths and diameters are machined, molding machines operating with static feed systems are not able to significantly change the dynamics of the polymer melt at one location without similarly affecting the polymer melt at other locations. As such, the behavior of the polymer melt at different locations in a mold are coupled, which inherently limits the capability of molding processes. In many cases, a compromise must be made between multiple quality attributes for which significant processing and tooling investments are required for mold optimization. Such issues, occurring late in the product development process, can incur significant cost and time penalties to the manufacturer.

Earlier research led to a valve design, represented by the cross section shown in Fig. 1a, for controlling the pressure at multiple points in an injection mold in real time [1]. This valve design controls the pressure drop and flow rate of the polymer melt with a tapered valve pin, wherein the valve pin position is moved axially to adjust the flow conductance and provide a corrective action in response to feedback from pressure transducers inside the mold cavity. This real time control allowed the flow rate at multiple locations to be adjusted to, for example, move the weld line in the part, adjust the packing pressure in different areas of a mold, and perform other process feats. A limitation of this design, however, is that the forward movement of the valve pin to shut off the flow forces the positive displacement of polymer melt into the mold cavity, which results in a pressure surge and less precise control of the melt flow than desired. Later research led to an improved valve design shown in Fig. 1b that provides the valve sealing surface away from the gate, i.e., the moving valve pin retracts from the gate area to close [2]. This retraction of the valve pin results in a negative volumetric displacement of the melt from the gate, and an immediate reduction in the melt pressure in the mold cavity when closing. This behavior is desirable, since the closing of the valve is normally intended and required to correct an over-pressure situation. While the resulting design provides improved process flexibility and consistency [3, 4], the performance of the system is limited by complexity, cost, size, shear degradation, energy consumption, and maintenance issues associated with the valve's design.

[FIGURE 1 OMITTED]

Both of these prior valve designs are subjected to the melt pressure, [P.sub.melt], acting on the entire projected area of the valve pin inside the feed system, and atmospheric pressure, [P.sub.atm], acting on the projected area of the valve pin outside the feed system. As a result, very high actuation forces, F, are required to control the location of the valve pin and flow through the valve:

F = [pi][R.sup.2]([P.sub.melt] - [P.sub.atm]) (1)

where R is the outermost radius of the valve pin. For example, an injection molding process with a melt pressure of 100 MPa and a valve pin diameter of 8 mm would require an actuation force of 5000 N. If a 5-mm stroke is required with a 10 m sec response time, then an actuator with at least 2500 W of power would be required. This power requirement precludes the use of electric motors and most pneumatic actuators, and in fact provides a practical limit to the number of hydraulic actuators that can be utilized in most molding applications. Furthermore, both of these valve designs require a closed loop control system that continuously corrects the valve pin position to ensure that the observed melt pressure is close to the desired melt pressure. Such a closed loop system requires instrumentation, cabling, electronics, and a user interface that increase the cost and reduce the robustness of the polymer processing system.

VALVE DESIGN

If dynamic control of the polymer melt is to become common, it is necessary to design more compact valves that have improved dynamic response with lower actuation forces. Other important objectives include ease of use, ease of maintenance, and positive shut-off of the molten plastic at the gate as in a conventional valve-gated hot runner system. Recognizing these objectives, a self-regulating valve design is presented in Fig. 2. In application, polymer melt is delivered to the valve such that the pressure at the valve inlet is greater than the desired pressure at the valve outlet. The valve houses a valve pin that has an aperture for communicating the polymer melt from the inlet of the valve to the outlet of the valve. The valve pin is designed in such a way that the melt pressure at the outlet of the valve acts on the exposed surface of the valve pin, and generates a force, [F.sub.pressure], that is proportional to the melt pressure at the valve outlet. The pressure force will act to close the valve and thereby reduce the pressure at the valve outlet.

[FIGURE 2 OMITTED]

The valve also requires the use of a compressive control force, [F.sub.control], that is applied to the valve pin, which will act to open the valve and increase the pressure at the valve outlet. If the melt pressure force and the control force are not equal, then the valve pin will tend to move in a direction that corrects the imbalance. For example, if the control force exceeds the pressure force, then the valve pin will move to open the aperture and thereby transmit additional melt pressure to the valve outlet. The valve pin position will be continually and automatically moved until the melt pressure naturally adjusts such that the control force and the pressure force balance. In this way, the valve is self-regulating such that the pressure force equals the control force; no sensors or external corrective control signal is required to deliver the desired melt pressure.

The control force may be applied to the valve pin in a number of ways, including springs, pneumatic actuators, hydraulic actuators, electric actuators, and others. Given that the actuator is matched with a valve, an intensification ratio may be utilized to relate the control signal to the outlet melt pressure. For example, a valve with a 5 mm valve pin diameter may be utilized with a 50 mm pneumatic cylinder diameter. In this design, the pneumatic cylinder has a surface area one hundred times greater than that of the valve pin. This difference in the "push areas" leads to an intensification ratio similar to the melt pressure exerted by the injection cylinder on a hydraulic molding machine:

I = [A.sub.cylinder]/[A.sub.annulus] = [R.sub.cylinder.sup.2]/[R.sub.annulus.sup.2] [approximately equal to] 100. (2)

If a pneumatic supply valve provides 0-1 MPa pneumatic pressure corresponding to a 0-10 V control signal, then a 10 V control signal would correspond to a 100 MPa pressure at the valve outlet; other intermediate voltages between 0 and 10 V would proportionally provide between 0 and 100 MPa pressure at the valve outlet. Higher melt pressures, if desired, can be achieved by utilizing a higher pressure hydraulic supply (hydraulic pressure is readily available to 20 MPa) or by utilizing a larger pneumatic cylinder with the same valve pin.

While not a requirement of the design, it is possible to use process instrumentation such as melt pressure or temperature transducers to provide feedback regarding the state of the polymer melt to a process or quality controller. Such feedback may be useful for a quality controller to identify fluctuations in the pressure and/or temperature of the polymer melt being provided to the inlet of the self-regulating valve. Alternatively, such feedback may be useful for a process controller to identify improper processing conditions (such as inadequate supply pressure to the inlet), and subsequently, suggest corrective action to the process operators. As yet another example, such process feedback may be used by a process controller to directly control the output melt pressure by providing closed loop control signals to adjust the control force to the valve pin.

VALVE ANALYSIS

Polymer melts are viscous in nature, and so there will be shear stresses that tend to pull the valve pin in the direction of flow, as well as a related pressure differential that tends to push the valve opposite to the direction of flow. Since these forces counteract and can be small compared to the control force, it is desirable to design the valve pin such that the forces resulting from polymer flow through the valve do not induce significant error in the outlet pressure. In general, the performance of the valve will improve with increases in the size of the valve body and valve pin, since a larger aperture results in lower shear rates and pressure drops acting on the surfaces of the valve pin at constant flow rates. However, increases in size are generally undesirable since the resulting valve requires more space and larger actuation forces. The aperture may be increased by reducing the inner annulus of the valve pin, but this can result in excessive stress in the valve pin and premature failure during usage.

The goal of the analysis is to develop and predict the performance of a self-regulating valve with minimal pressure drop, minimal shearing of the melt, minimal size, and fast response times. The flow of plastic is known to be influenced by both shear and elongational viscosities [5]. Given the geometry of the valve design, it is expected that both shear and elongational effects will be significant. For axisymmetric flow, the shear and elongational viscosities are respectively defined as:

[FIGURE 3 OMITTED]

[[tau].sub.rz] = [[eta].sub.s][dot.[gamma]] (3)

[[tau].sub.zz] - [[tau].sub.rr] = [[eta].sub.e][dot.[epsilon]] (4)

where [[tau].sub.i] denotes the various components of the stress tensor, [[eta].sub.s] and [[eta].sub.e] are the shear and elongational viscosities, and [dot.[gamma]] and [dot.[epsilon]] are the shear and elongational strain rates.

To capture the behavior of elongational viscosity of polymers that exhibit an increase in the elongational viscosity beyond the Newtonian range, followed by a power-law-type descent as the strain rate is further increased, the flow analysis utilizes the following model for elongational viscosity of the polymer [6]:

[[eta].sub.e] = [[eta].sub.0][3 + [delta]{1 - [1/[square root of (1 + ([[lambda].sub.I][e.sub.II])[.sup.2])]]}][1 + ([[lambda].sub.2][e.sub.II])[.sup.2]][.sup.(m-1)/2]. (5)

This model is consistent with previous experimental observations that have shown that the elongational viscosity approaches 3[[eta].sub.0] at low strain rates, where [[eta].sub.0] is the Newtonian limit of the shear viscosity, and [delta] characterizes the total increase in viscosity due to elongational thickening. Figure 3 plots the viscosity as a function of strain rate for varying magnitudes of [[lambda].sub.2], which determines the elongational thickening of the rheology model. It is noted that for [delta] = 0, [[lambda].sub.2] = [lambda], and m equal to n, this elongational viscosity model reduces to that of a generalized Newtonian formulation with a Carreau model for shear viscosity.

The 3D flow analysis was conducted using simulations from Moldflow (version 5.0) and PlasticFlow. The Mold-flow simulation utilizes a "unified" viscosity model for mixed shear and extension deformations, in which the apparent viscosity is modeled as a function of the extension rate and the shear viscosity using the extension viscosity model coefficients. These coefficients are determined using experimental pressure measurements in convergent flow. The apparent viscosity, [[eta].sub.a], is modeled as:

[[eta].sub.a](T, P, [dot.[gamma]], [dot.[epsilon]]) = f([dot.[epsilon])[[eta].sub.s](T, P, [dot.[gamma]]) (6)

where [[eta].sub.s] is the shear viscosity (Pa sec) calculated by the Cross-WLF model [7], and f is a transition function defined as:

f([dot.[epsilon]] = 1 + [[A[dot.[epsilon]]]/[B + [dot.[epsilon]]]]. (7)

In this model, A and B are data-fitted coefficients related to the magnitude of the elongational effect and the rate of transition to the elongational viscosity.

A series of simulations was conducted according to a design of experiments (DOE), shown in Table 1, to investigate the flow behavior for different nominal valve sizes, valve pin positions, flow rates, chamfers, and fillets. Runs 1 to 15 were conducted for a grade of PP for which elongation coefficients were available. Run 5 is considered as the standard case since this design was built and successfully validated as later discussed. This standard design was developed using a constraint-based design approach to ensure that the valve could be retrofit to the existing hot runner system, which resulted in an outer diameter of 5 mm, an inner diameter of 2.5 mm, a fillet of 0.5 mm, and a chamfer of 0.5 mm. The standard design of run 5 was replicated in runs 16, 17, and 18 to investigate the behavior of certain PC, SAN, and PA resins for which elongation coefficients were available. Run 5 was also repeated with and without the elongation viscosity. Table 2 provides the materials and related rheological model coefficients that were analyzed.

[FIGURE 4 OMITTED]

Figure 4 provides a view of one half of the tetrahedral mesh of the flow domain for the standard design of run 5. Nonuniform mesh densities were utilized to ensure a minimum of six elements across the juncture between the valve pin and the valve body. The flow velocity distribution through the standard valve design (ref. Run 5 of Table 1) is shown in Fig. 5. The polymer melt enters at the on the right side of the diagram, then flows around the core of the pin and down through the valve aperture. Close examination of the vectors indicates that the melt velocity on the side of the valve pin near the inlet is ~70 cm/sec, slightly higher than the melt velocity of 50 cm/sec, on the opposite side. The varying velocities are due to the added flow length and the reduced flow conductance required for the melt to circumnavigate the valve pin.

[FIGURE 5 OMITTED]

The pressure distribution through the valve for the standard case is shown in Fig. 6. For a flow rate of 5 cc/sec, the total pressure drop through the valve from the inlet to the outlet is ~5 MPa. As expected, the pressure drop is most significant through the aperture, which in this case has a gap of only 0.5 mm. Even so, the relatively large diameter provides a relatively high flow conductance such that the pressure drop is not large compared to typical pressures encountered in injection molding. Close examination of the pressure distribution reveals a 1-MPa pressure differential from the side of the pin closest to the inlet to the opposite side. This pressure differential is not only responsible for the different melt velocities shown in Fig. 5, but also suggests possible pin deflection that could limit the performance or prevent operation of the valve. Furthermore, the lateral loading on the polymer lubricated hydrodynamic journal bearing between the valve pin and the valve body may slow the movement of the valve pin or wear the surfaces of valve. For these reasons, coupled field flow-structural simulations were conducted with Moldflow 5.0 for the extreme cases of the valve operation corresponding to DOE runs 3 and 7. The maximum lateral pin deflection was found to be 0.0095 mm, which is negligible compared to the dimension of the pin diameter and gaps. Even so, these results suggest that the valve pin must be carefully designed with respect to both flow conductance and structural integrity.

[FIGURE 6 OMITTED]

Figure 7 provides the pressure drop through the valve as a function of the inlet flow rate and the pin position corresponding to runs 1-15 of the DOE listed in Table 1 for the PP listed in Table 2. The pressure drops vary from almost zero for a low flow rate and 2.5 mm pin position to ~17 MPa for a high flow rate and 0.1 mm pin position. The concave curvature of the pressure drop is related to the shear thinning behavior of the polymer melt. As the flow rate increases, the viscosity departs from the Newtonian regime and decreases in the power law regime. The spacing of the curves for different valve pin positions is related to the juncture loss through the aperture.

[FIGURE 7 OMITTED]

The pressure drop curves plotted in Fig. 7 are vital to understanding the self-regulating behavior of the valve. The valve pin is free to move such that the force(s) exerted from the melt balance with the control force. Consider, for example, a molding application in which the inlet pressure is 20 MPa and the desired melt pressure is 12.5 MPa. A 12.5 MPa melt pressure at the outlet will generate a melt pressure force, [F.sub.pressure] = [pi][R.sup.2][P.sub.outlet] = 245 N. If the valve is initially fully shut, with zero pressure at the outlet, an applied control force of ~245 N would result in a significant acceleration (on the order of 20 gravities, depending on the characteristics of the actuator) for the opening of the valve pin. As the valve pin opens, the melt pressure below the pin will increase and reduce the resultant force on the pin. For a 5 cc/sec flow rate, a pressure drop of 7.5 MPa (20 MPa at the inlet minus 12.5 MPa at the outlet) will be incurred with the valve pin equilibrating near a position of 0.5 mm.

The dynamic behavior of the self-regulating valve is related to the size of the pin, its initial position, and the imposed pressure/control loads. Both dynamic analysis and validation studies have shown that the valve is indeed self-regulating and inherently stable. Even so, it is highly desirable that the output melt pressure is proportional to the applied control force, e.g., the melt pressure is equal to the supplied pneumatic or hydraulic pressure in the actuator times the intensification factor. It is understood, however, that the forces acting on the valve pin due to the viscous flow of the polymer melt will tend to generate a steady state error in the outlet pressure that is a function of the flow rate and melt viscosity.

To calculate the steady state error due to the forces acting on the pin, the pressure, viscosity, and shear rates were sampled at multiple points along the path of the valve pin as shown in Fig. 8. The force due to the varying melt pressure, [F.sub.P], and the force due to the shear stress, [F.sub.[tau]], can be estimated as:

[F.sub.P] = [[line integral around closed path].sub.A] P sin[phi]dA (8)

[F.sub.[tau]] = [[line integral around closed path].sub.A] ([tau] = [eta][dot.[gamma]]) cos[phi]dA (9)

where P and t are the pressures and shear stresses acting on the surfaces of the valve pin, and [phi] is the angle between the surface tangent and the axis of the valve pin. Figure 9 shows the plots of the force due to the melt pressure, the force due to the shear stress, and the resultant force on the pin as a function of the flow rate. It is observed that the force due to the shear stress dominates, and that the resultant force on the pin due to the melt flow increases in magnitude with increasing flow rates. For the standard valve design with a target flow rate of 5 cc/sec, the resulting error force is on the order of 10 N. Comparing 10 N to the previous example with a 245 N control force, it is concluded that a steady state error of 4% results in this case; the steady state error will be less for higher melt outlet pressures or lower flow rates. From a processing perspective, the steady state error will be repeatable in a given molding application and may be corrected at the molding machine by specifying a slightly lower setting for the control force. From a control system perspective, a closed loop control system design may be utilized with feedback from a downstream melt pressure transducer to automatically correct the required control force. From a valve design perspective, the steady state error may be minimized by increasing the flow conductance of the valve, which may be accomplished by increasing the size of the valve and/or the cross-sectional area of the annulus.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

To investigate the effect of valve sizing, parametric valve designs of 2.5, 5, and 10 mm diameter were analyzed for the PP material listed in Table 2. For each parametric design, the valve pin annulus and position were set to 50% and 10% of the valve diameter. Figure 10 provides the pressure drop through valves of varying diameter for a constant flow rate of 5 cc/sec. It is observed that the pressure drop, [DELTA]P, appears to be inversely proportional to the valve diameter. In fact, a higher order function was fit to the data, resulting in the relation:

[DELTA]P = 690/[[phi].sup.4.5] (10)

where [phi] is the valve pin diameter in mm, the pressure drop is measured in MPa, and the value in the numerator is related to the apparent viscosity of the material and the geometry of the valve. This result occurs for two reasons. First, the flow velocity through the valve decreases as the valve diameter increases at constant volumetric flow rate. Second, the valve pin opening increases with valve diameter, which greatly increases the flow conductance. Both effects are additive, and so the pressure drop is greatly reduced with increasing valve diameter. This finding is extremely useful, since it indicates that slight increases in valve size can provide for very large increases in flow rate at equivalent pressure drops. For instance, a flow rate of 100 cc/sec (20 times the 5 cc/sec analyzed in the standard design) with a comparable pressure drop can be achieved by a valve diameter of 9.77 mm (only 1.94 times the 5 mm diameter of the standard design).

The effect of varying the annuli diameters on the pressure drop through the valve was also investigated, and indicated that reducing the inner radii provides lower pressure drops. A lower pressure drop in the annulus of the valve pin is beneficial to reduce the steady state error related to the pressure drop and the shear stresses acting on the surfaces of the valve pin. Accordingly, it is clearly desirable to select the minimum inner radius possible. However, the inner radius of the valve pin is constrained by the stress and deflection characteristics. There are two stress constraints that need to be considered: (1) tensile stresses in the pin shaft and (2) shear stresses through the head thickness. The shaft tensile stress is related to the outer radius of the valve pin, [R.sub.outer], the inner radius of the valve pin, [R.sub.inner], and the maximum melt pressure drop across the head of the valve pin, [DELTA]P, which will typically occur when the valve is fully shut. The governing equation is:

[[sigma].sub.shaft] = [DELTA]P[[[pi][R.sub.outer.sup.2]]/[[pi][R.sub.inner.sup.2]]]. (11)

For the standard design with the inner radius equal to half the outer radius, the tensile stress in the shaft would be ~400 MPa for typical melt pressures of 100 MPa in injection molding. This stress level may be significant, given concerns related to fatigue and over pressure situations; so the valve pin should be made of materials with high allowable tensile strength.

Finite element structural analysis (FEA) was conducted to check for stress concentrations, and indicated that the maximum principle stress occurs where the shaft connects to the head. At this location, the tensile stresses in the shaft are additive with shear stresses acting through the thickness of the head of the valve pin. The head shear stress is related to the projected area of the pin, the area of the shaft, the maximum melt pressure drop across the head of the valve pin, and the thickness of the head of the valve pin, [H.sub.head], according to the relation:

[[tau].sub.head] = [DELTA]P[([pi][R.sub.outer.sup.2] - [pi][R.sub.inner.sup.2])/[[pi][R.sub.inner][H.sub.head]]]. (12)

For the standard design with the inner radius equal to half the outer radius, the shear stresses on the head of the valve pin would be ~300 MPa for typical melt pressures of 100 MPa in injection molding. Since the tensile and shear stresses act in the same direction at the juncture between the shaft and the head of the valve pin, the maximum principle stress will be approximately seven times the maximum melt pressure drop imposed across the valve. While the described design is functional for most polymer processing applications, it may be desirable to enlarge the size of the valve and the inner radius of the valve pin annulus for applications with very high melt pressures.

To summarize the design, the nominal size of the valve should be determined considering the maximum flow rate and pressure drop requirements according to flow analyses (e.g., Eq. 10). Ideally, the diameters of the inlet and outlet portions of the feed system will be appropriately sized to match the dimensions of the valve section with appropriate chamfers and fillets to avoid no flow regions. For most applications, a reasonable trade-off between flow and structural requirements may be achieved by selecting the inner radius of the valve pin to one half the outer

radius of the valve pin. It is suggested that the valve travel equal the outer radius of the valve pin since longer travel distances will tend to promote dead spots in the flow and induce steady state error while not significantly reducing the pressure drop through the aperture.

VALVE VALIDATION

For the described standard design, a valve pin was machined from steel with an outer diameter of 5 mm and an inner diameter of 2.5 mm. With 3 mm maximum travel, the valve was found to provide excellent performance and longevity in a two-drop hot runner injection molding process for melt flow rates of 20 cc/sec and melt pressures of 100 MPa. To evaluate the performance of the self-regulating valve, a DOE was developed and implemented as shown in Table 3 on an 80-ton tiebarless HPM hydraulic injection molding machine. The material used in the experiments is polypropylene (PP Borealis HF135M). In this DOE, the single most important factor is the valve voltage; the supplied melt pressure and air pressure were added to the DOE to characterize the behavior of insufficient supply pressures. For this reason, four values of the valve control signal from 2.5 to 10 V were provided to a proportional air control valve while varying the supply pressure to the proportional air control valve as well as the melt pressure to the self-regulating melt pressure valve. For each run in the DOE, a data acquisition system recorded the air pressure at the cylinder (using sensors in the Festo MPPE 0310 EN proportional air valve) and the melt pressure in the cavity (Kistler 9213 piezoelectric sensors with Priamus 5050 charge amplifiers).

Figure 11 plots the observed melt pressure in the mold cavity as a function of the observed air pressure in a pneumatic actuator that provided the control force to a self-regulating valve. As indicated by the data points lying near the line of proportionality, the valve provided melt pressure control without melt pressure transducers in proportion to the control force. The small variations from the line of proportionality are due to pressure drops occurring between the outlet of the valve and the location of the pressure transducer in the mold cavity.

These results clearly validate the ability of the valve to provide melt pressure control without melt pressure feedback by simply supplying a proportional control force (in this case via a pneumatic pressure acting on a cylinder). It is important to understand the cause of the plateau in the observed melt pressure at ~19 MPa. Specifically, the three triangles correspond to runs 4, 6, and 8 in which high control forces and low melt pressures are supplied. In these cases, the valve opens fully due to relatively high control forces. Since the melt pressure at the outlet of the valve is not sufficient to cause the valve pin to retract, the low melt pressure is transmitted to the mold cavity through a fully open valve. (A 6 MPa pressure drop is observed between the inlet melt pressure and the observed cavity pressure not due to the pressure drop through the valve, but rather due to the pressure drop through the torpedo of the hot runner drop, which has melt passageways of only 1.5 mm in diameter.) Self-regulation of the melt pressure at these high control forces would be delivered when higher melt pressures are supplied at the valve inlet, as is observed for runs 12, 14, and 16 that are represented with the cross symbols.

[FIGURE 11 OMITTED]

CONCLUSIONS

Flow analysis and experimental validation have shown that a valve design can self-regulate the melt pressure in proportion to the control force. The developed valve design can provide continuous control of the melt pressure without melt pressure transducers, cabling, signal conditioning, or feedback controller that are required with closed loop control systems. Compared to earlier systems [3, 4] and machine-based cavity pressure controllers [8], the valve provides the capability to control the melt at multiple locations and with faster response. The increase in polymer processing consistency and productivity has been validated [9, 10]. Given the simplicity of the valve design, it is expected that the self-regulating valves will be used in many molding, extrusion, blow molding, and other applications where increased process flexibility and consistency are required. This expectation arises from the simple observation that the described self-regulating valve design, which provides independent control of the polymer melt, is no more expensive than a melt pressure transducer, which only provides observation of the polymer melt.

The melt flow in the self-regulating melt pressure valve has been analyzed with respect to steady state behavior, dynamic behavior, and steady state error. The analysis has shown that the current design provides good dynamic response, relatively low steady state error, and low pressure drops at flow rates less than 25 cc/sec. While not discussed here due to length limitations, the standard valve design was acceptable for a wide range of materials, though different valve sizes may be designed for different flow rate regimes; polymeric materials with fibers or particulates that are large compared to the clearances in the valve may require a different valve shut-off configuration. Analysis results have also led to recommendations on maximum valve displacement, annulus diameter, chamfer, and fillet design. Optimal valve performance requires careful design that maximizes flow through the valve while avoiding dead spots and excessive tensile and shear stresses in the valve pin. The flow and pressure behavior of the polymer melt through the valve is highly complex (thermoviscoelastic). Currently, research is underway to (1) further validate the steady state error and dynamic response of the self-regulating valve for varying geometries and polymeric systems and (2) develop a robust methodology for design of polymer processing systems to ensure low risk, low cost, lights out manufacturing.

ACKNOWLEDGMENTS

This work does not represent the opinions of Mold-Masters, the National Science Foundation, or the United States government.

REFERENCES

1. D.O. Kazmer, U.S. Patent 5,556,582 (1995).

2. D.O. Kazmer and M. Moss, U.S. Patent 6,436,320 (2002).

3. D.O. Kazmer and P. Barkan, Polym. Eng. Sci., 37, 1865 (1997).

4. D.O. Kazmer and P. Barkan, Polym. Eng. Sci., 37, 1880 (1997).

5. M. Gupta, Polym. Eng. Sci., 40, 23 (2000).

6. D. Sarkar and M. Gupta. J. Reinforc. Plast. Compos., 20, 1473 (2001).

7. B. Fan, D.O. Kazmer, W.C. Bushko, R.P. Theriault, and A.J. Poslinski, Polym. Eng. Sci., 43, 596 (2003).

8. F. Gao, W.I. Patterson, and M.R. Kamal, Polym. Eng. Sci., 36, 2467 (1996).

9. D. Kazmer, V. Kudchadkar, and R. Nageri, Plast. Rubber Compos., 33, 12 (2005).

10. D. Kazmer, V. Kudchadkar, and R. Nageri, Plast. Rubber Compos., 33, 20 (2005).

David Kazmer, Dheeraj Gupta, Mahesh Munavalli, Vijay Kudchadkar, Ranjan Nageri

Department of Plastics Engineering, University of Massachusetts Lowell, Lowell, Massachusetts 01854

Correspondence to: David Kazmer; e-mail: [e-mail]

Contract grant sponsor: National Science Foundation; contract grant number: 0245309; Contract grant sponsor: Mold-Masters Ltd.

TABLE 1. Design of experiments for analyses.

                    Pin       Outer   Inner
         Flow rate  position  radius  radius  Chamfer  Fillet
Run No.  (cc/sec)   (mm)      (mm)    (mm)    (mm)     (mm)

 1        1         2.5       2.5     1.25    0.5      0.5
 2        1         0.5       2.5     1.25    0.5      0.5
 3        1         0.1       2.5     1.25    0.5      0.5
 4        5         2.5       2.5     1.25    0.5      0.5
 5        5         0.5       2.5     1.25    0.5      0.5
 5-ne     5         0.5       2.5     1.25    0.5      0.5
 6        5         0.1       2.5     1.25    0.5      0.5
 7       25         2.5       2.5     1.25    0.5      0.5
 8       25         0.5       2.5     1.25    0.5      0.5
 9       25         0.1       2.5     1.25    0.5      0.5
10        5         0.5       2.5     1.25    0        0.5
11        5         0.5       2.5     1.25    0.5      0
12        5         0.5       2.5     1.25    0.5      0.5
13        5         0.5       5       1.25    0.5      0.5
14        5         0.5       2.5     0.625   0.5      0.5
15        5         0.5       2.5     1.875   0.5      0.5
16*       5         0.5       2.5     1.25    0.5      0.5
17*       5         0.5       2.5     1.25    0.5      0.5
18*       5         0.5       2.5     1.25    0.5      0.5

*Runs 16, 17, and 18 were replicates of run 5 respectively conducted for
PC, SAN and PA.

TABLE 2. Materials and properties.

Material          PP              PC

Run no.           1-15            15
Trade name        Hifax SP179     Lexan 141R
Melt temperature  239             295
  ([degrees]C)

                  Cross-WLF viscosity Model Data

n                 0.2961          0.5196
[tau]*(Pa)        26720           43300
D1 (Pa s)         8.44E + 12      5.66E + 09
D2 (K)            263.15          417.15
D3 (K/Pa)         0               0
A1                27.983          21.098
A2 (K)            51.6            51.6
Density (g/cc)    0.7299          1.0488

Material          SAN                PA

Run no.           16                 17
Trade name        Santoprene 121-62  Capron BU50i
Melt temperature  200                290
([degrees]C)

                  Cross-WLF viscosity Model Data

n                 0.2168             0.4877
[tau]*(Pa)        11317.6            21600
D1 (Pa s)         4.31E + 08         7.12E + 11
D2 (K)            323.15             323.1
D3 (K/Pa)         0                  0
A1                14.008             24.60
A2 (K)            51.6               51.6
Density (g/cc)    0.7874             0.8726

TABLE 3. Validation design of experiments.

     Inlet melt  Valve    Air
Run  pressure    voltage  pressure
no.  (MPa)       (%)      (MPa)

 1   25           25      0.34
 2   50           25      0.59
 3   25           50      0.34
 4   50           50      0.59
 5   25           75      0.34
 6   50           75      0.59
 7   25          100      0.34
 8   50          100      0.59
 9   25           25      0.34
10   50           25      0.59
11   25           50      0.34
12   50           50      0.59
13   25           75      0.34
14   50           75      0.59
15   25          100      0.34
16   50          100      0.59