FINITE-ELEMENT ANALYSIS

To gain a better understanding of the fundamental phenomena occurring within an injection mold, ExpressTool began working with the FEA/Process Modelling and Optimization group at the National Research Council (NRC) (Boucherville, Quebec, Canada) under the direction of Georges Salloum.

The temperature distributions shown in this chapter were developed through a collaboration between the author and Michel Perrault of NRC. The calculations were based on the latest version of the NRC–FEA code. Starting from a CAD model of a specific part, Perrault developed the geometry of the mold, as well as the geometry of both the DCC and CCC cases. Finally, he used representative thermal and mechanical properties for H-13 steel, as well as those for electroformed nickel and electroformed copper where relevant.

This author believes that if one cannot understand a simple problem, the chance of understanding a more complicated problem is greatly dimin-ished. Thus, the part selected for the initial NRC–FEA thermal analysis is a simple circular disk, 3.00 in. in diameter and 0.100 in. thick. Although the part geometry is flat, it has a round shape typical of molded parts, and also has little intrinsic stiffness, with no supporting ribs or gussets.

Figure 7 is a top view of the two cases evaluated by FEA. The sections are split about a plane of symmetry to save computation time, so one is view-ing half of each part. The first case corresponds to an H-13 steel tool with DCC, shown on the left. The second case corresponds to an electroformed Ni–Cu tool with encapsulated CCC, shown on the right. For this case, the

Figure 7 A conventional H-13/DCC steel mold and a Ni–Cu/CCC mold.

CCC geometry looks something like a ‘‘keyhole’’ when viewed from above.

Although, in principle, the CCC could also have arbitrary cross-sectional shape, the channel cross sections were assumed to be circular for this study.

In future studies, we will evaluate the effects of noncircular channel cross sections.

Figure 8shows the model of the Ni–Cu tool developed at NRC by Mi-chel Perrault, which formed the basis of the ensuing FEA analysis. The follow-ing assumptions were made:

• The part was center gated.

• The nickel shell was 2 mm (0.080 in.) thick.

• The copper thermal management layer was 4 mm (0.160 in.) thick.

• The copper fully encapsulates the CCC.

• The tool was backed with aluminum-filled epoxy having a thermal conductivity of 2 W/m K.

Note that compared with a thermal conductivity of 88 W/m K for nickel and 390 W/m K for copper, a value of only 2 W/m K for the mold backing material effectively treats the latter as an insulator.

Figure 9is an FEA image of the distribution of temperature over a cross section through the center of the cooling channels on the core side for the conventional H-13 tool with DCC shown on the left and the Ni–Cu tool with CCC shown on the right.

Figure 8 Model of the Ni–Cu/CCC mold.

Figure 9 Core temperature distributions.

The difference in the two temperature distributions is dramatic! The H-13 tool with DCC shows a hot spot to the left of the cooling channel (near the sprue) and another to the right of the channel. Conversely, the Ni–Cu tool with CCC shows an almost isothermal temperature distribution. The value of

∆Tmaxfor the H-13/DCC case is 12.5°C. In contrast, the value of ∆Tmaxfor the nickel–copper tool with CCC is only 2°C. Obviously, the combination of high-thermal-conductivity materials and conformal cooling channels has significantly reduced mold temperature variations in this case.

Figure 10is another FEA image, this time of the temperature distribution on the active mold surface of the cavity side of the tool for the conventional H-13 tool with DCC on the left and the Ni–Cu tool with CCC on the right.

At the active mold surface the effect is even more dramatic. The value of∆Tmaxfor the H-13/DCC cavity is 18.6°C, and the corresponding value for the Ni–Cu/CCC cavity is only 1.9°C, or, essentially, an order of magnitude reduction in active mold surface temperature variance!

Figure 11shows the pseudo-color temperature distribution for the cavity surface of the H-13/DCC tool at 2-s intervals from 1 to 15 s after plastic injection. These images illustrate the cooling of the insert over time.Figure 12shows the same information for the Ni–Cu/CCC tool. It is clearly evident from inspection of these two figures that the cooling rates for the Ni–Cu/CCC tool are much faster than for the H-13/DCC tool. In fact, the temperatures

Figure 10 Cavity temperature distributions.

Figure 11 H-13/DCC temperature versus time.

Figure 12 Ni–Cu/CCC temperature versus time.

throughout the Ni–Cu/CCC tool only 3 s after injection are already lower than the corresponding temperatures for the H-13/DCC tool after 15 s!

These data begin to explain the reasons behind the extraordinary produc-tivity improvements noted in the two case studies presented in Sects. V and VI. The only reason the productivity gains are not even greater is that the cycle time includes not only the cooling time but also the times needed to (a) close the press, (b) inject the plastic, (c) pack the plastic, (d) open the mold, and, finally, (e) eject the part. However, neither the thermal conductivity of the mold nor the presence of CCC has any effect on these five time intervals.

Thus, the dramatic productivity gains documented for Ni–Cu/CCC inserts are purely the result of significantly reducing the mold cooling time.