The gas trap in the previous example could have been avoided by moving the edge gate to the center of the 160 mm long side wall or by using a three-plate or hot runner mold to gate at the center of the mold cavity. Sometimes, however, the mold layout precludes these designs. As such, another alternative is to vary the thick- ness so that the melt purposefully flows faster in some portions of the mold [14, 15]. Such thicker sections used to control the flow velocity are generally known as “flow leaders.” It should be understood that thickness variations in molded parts are generally undesirable as discussed in Section 2.3.1. For the reasons discussed therein, the cavity thickness variation should be kept to a minimal amount. Newtonian flow analysis will now be used to redesign the wall thickness of the container to resolve the race-tracking issue. Equation 5.17 relates the pressure drop, velocity, and thickness. To eliminate the race-tracking, the pressure drop across the centerline should equal the pressure drop around the perimeter.
centerline side_walls
P P
136 5 Cavity Filling Analysis and Design
This condition will ensure that the flow traverses across the centerline at the same time that the flow reaches the far corners of the adjacent side walls to eliminate the race-tracking phenomenon. The flow lengths are provided in Fig. 5.18. From the geometry of the container, the lengths of flow across the centerline and around the side walls are calculated to be 280 mm and 210 mm, respectively.
Figure 5.18 Lay flat showing flow lengths
From Eq. 5.17, the pressure drops across the centerline and around the side walls can be evaluated and equated as
side_walls side_walls side_walls centerline centerline centerline
2 2 centerline side_walls 12 12 L v L v H H m m = (5.31)
The melt velocities in sections of different sections will not be equal. In fact, it is desired that the velocity of the perimeter be
side_walls side_walls centerline centerline L v v L = (5.32)
This condition will cause the melt to arrive at the far corner of the side wall at the same time it reaches the opposite side of the cavity along the centerline. Substituting this relation into Eq. 5.31 and solving for the thickness of the side walls, Hside_walls , as a function of the nominal thickness, H,
side_walls side_walls side_walls centerline centerline L H H L m m = (5.33)
The analysis indicates that the wall thickness will be largely proportional to the ratio of the flow lengths with a lesser dependence on the melt viscosities. Assum- ing the same viscosity throughout the cavity, the thickness of the side walls can be evaluated as
side_walls 2 mm210 mm280 mm 1.5 mm
H = = (5.34)
The lay flat analysis can also be used to predict the filling patterns for parts of varying wall thickness. When the wall thickness varies, it is necessary to increase the radii of the arcs to represent the distance that the melt traveled during the time step. For this case, the thickness of the side walls has been chosen such that the velocity of the melt in the side walls is:
side_walls
side_walls centerline centerline centerline centerline 210 mm 75% 280 mm L v v v v L = = = (5.35)
In the lay flat analysis, the radius of each arc in the thinner section should be in- cremented by 75 % of the arc in the thicker sections. Still using the same phantom gate, the resulting melt front progression in the redesigned container is shown in Fig. 5.19. The arrows along the edge of the side wall show the incremental position of the melt front in this section at various time steps. The analysis indicates that the melt does reach the end of the side walls before the melt reaches side of the cavity opposite the gate.
138 5 Cavity Filling Analysis and Design
To validate the lay flat approach, numerical simulations were performed for the container having a uniform thickness of 2 mm and a second container in which the thickness of the side walls was decreased to 1.5 mm. The results are shown in Fig. 5.20.
Uniform thickness Thinner side walls
Figure 5.20 Simulated melt front with and without flow leaders
As in the lay flat analyses, the simulation indicated that the container without the flow leader would exhibit race-tracking, a weld line, and a gas trap. Reducing the thickness of the side walls to 1.5 mm eliminated the problems. For reference, the reduction in the thickness of the side wall from 2 mm to 1.5 mm did increase the injection pressure by 10 % to fill out the thinner side walls but also decreased the part weight by a similar amount.
5.6Chapter Review
All mold engineering designs should consider the propagation of the viscous poly- mer melt throughout the mold cavity. Numerical simulations are preferred due to their ability to quickly and accurately consider non-Newtonian flows in complex geometries. However, analyses with Newtonian and power law viscosity models are not difficult to use and have been shown to provide reasonable results.
The single most important purpose of filling analyses is to ensure that the mold cavity can be completely filled by the selected molten plastic. If the wall thickness of the cavity is too thin and the melt pressure required to fill the cavity exceeds the capability of the machine, then incomplete moldings (known as “short shots”) will be produced. The molder will try to remedy the problem by attempting to increase the melt temperature or injection pressure or by using another resin. If these attempts are unsuccessful, then the mold will require design changes including
the addition of more gates, increasing the diameters of the feed system, increasing the wall thickness of the mold cavity, or other changes. Such physical alterations of the mold can be expensive and time-consuming.
Filling analyses can also be used to estimate the clamp tonnage, optimize the wall thickness, estimate the processing conditions, predict the advancement of the plastic melt throughout the cavity, and remedy filling problems by locating gates or designing flow leaders. While the governing equations for the Newtonian and power law provided in Eqs. 5.17 and 5.22 seem simple, careful application is re- quired to obtain useful solutions. It is recommended that filling analyses utilize mid-range melt temperatures when evaluating the viscosity, and the dependence of the viscosity on shear rate be verified when using the Newtonian model.
After reading this chapter, you should understand:
The relationship between shear stress, shear rate, and viscosity;
The relationship between cavity fill time, linear melt velocity, and volumetric flow rate;
The assumptions made in development of the Newtonian and power law models,
and potential issues associated with their use;
How to estimate the length of flow in a mold cavity from a gate to the end of flow;
How to calculate the shear rate, viscosity, filling pressure, and clamp tonnage for
melt flow in a rectangular mold cavity using either the Newtonian or power law model; and
How to estimate the minimum wall thickness in a molding application given the
material properties and maximum filling pressure.
The next chapter examines the design of the feed system for two-plate molds, three- plate molds, and hot runner molds. Flow analyses for the viscous melt in cylindri- cal and annular members is presented and used for feed system design. After- wards, the analysis and design of gates will be presented before addressing cooling and other elements of mold design.
5.7References
[1] Spencer, R. and R. Dillon, The viscous flow of molten polystyrene, J. Colloid. Sci. (1948) 3(2):
pp. 163–180
[2] Malkin, A. Y. and A. I. Isayev, Rheology: Concepts, Methods, and Applications, ChemTec Publishing
(2005)
[3] Tanner, R. I., Engineering rheology, Oxford University Press (2000)
[4] Bremner, T., A. Rudin, and D. Cook, Melt flow index values and molecular weight distributions of commercial thermoplastics, J. Appl. Polym. Sci. (1990) 41(7–8): pp. 1617–1627
140 5 Cavity Filling Analysis and Design
[5] Cross, M. M., Relation between viscoelasticity to shear-thinning behavior in liquids. Rheol. Acta (1979)
18: pp. 609–614
[6] O’Connell, P. A. and G. B. McKenna, Arrhenius-type temperature dependence of the segmental relaxa- tion below Tg, J. Chem. Phys. (1999) 110(22): pp. 11054–11060
[7] Williams, M. L., R. F. Landel, and J. D. Ferry, Temperature dependence of relaxation mechanisms in amorphous polymers and other glassforming liquids, J. Appl. Phys. (1953) 24: p. 911
[8] DiScipio, W. and D. Kazmer, Validation of molded part shrinkage predictions by CAE simulation, in Injection Molding Division of the SPE Annual Technical Conference, Detroit, MI (1992)
[9] Kazmer, D. O., et al., Validation of three on-line flow simulations for injection molding, Polym. Eng.
Sci. (2006) 46(3): pp. 274–288
[10] Lord, H. and G. Williams, Mold–filling studies for the injection molding of thermoplastic materials, Part II: The transient flow of plastic materials in the cavities of injection–molding dies, Polym. Eng.
Sci. (1975) 15(8): pp. 569–582
[11] Farshi, B., S. Gheshmi, and E. Miandoabchi, Optimization of injection molding process parameters using sequential simplex algorithm, Mater. Des. (2011) 32(1): pp. 414–423
[12] Orr, L. M. and D. J. Orr, When to Hire—or Not Hire—a Consultant: Getting Your Money’s Worth from Consulting Relationships, Apress (2013)
[13] Sommier, E., et al., Characterization of the injection molding process of passive vibration isolators,
J. Elastomers Plast. (2014) DOI: 1177/0095244314538439
[14] Seow, L. and Y. Lam, Optimizing flow in plastic injection molding, J. Mater. Process. Technol. (1997)
72(3): pp. 333–341
[15] Lam, Y. and L. Seow, Cavity balance for plastic injection molding, Polym. Eng. Sci. (2000) 40(6):
6
6.1Overview
The purpose of the feed system is to convey the polymer melt from the molding machine to the mold cavities. The design of feed systems can range from very simple to very complex. Increased investment in the feed system design will tend to provide for reduced cycle time and less material waste when using the mold. However, it is possible to overdesign the feed system, and the “best” feed system design is a function of the production volume, availability of molding pressure, and level of allowable investment.
The design of the feed system follows a four-step process. First, the type of feed system (two-plate cold runner, three-plate cold runner, or hot runner) is selected if not already known; these three types of feed systems are the most common, though a few other feed system technologies are discussed in Section 13.6. Second, the routing of the feed system through the mold is determined. Third, the diameters of each segment of the feed system are specified to balance pressure drops, shear rates, and material utilization. Finally, the design details for the feed system are embodied in the mold design. To assist the design process, a discussion of the objectives in feed system design is provided next.
6.2Objectives in Feed System Design
6.2.1Conveying the Polymer Melt from Machine to Cavities
The primary function of the feed system is to convey the polymer melt from the nozzle of the molding machine (where it is plasticized) to the mold cavities (where it will form a desired product). In most molding applications, the polymer melt must traverse portions of both the mold height and the mold width. The traversal