Optimize Runner Diameters

Once the pressure drop through the feed system is analyzed, it is possible to adjust the feed system design to improve the performance. Multiple iterations of design and analysis may be conducted to obtain a design that provides a low pressure drop while consuming very little material. Multivariate optimization is a numerical technique that could be employed to simultaneously minimize the pressure drop while minimizing the runner volume. However, this approach requires time to implement and validate while hiding the details of the analysis from the designer.

The approach recommended here is to utilize constraint based method to directly solve the minimum runner system diameters given a specified constraint on the pressure drop. If the maximum pressure drop for a portion of the runner is specified asΔPmax, then for a Newtonian material the radius of the runner could be directly solved as:

6.4 Feed System Analysis

142 6 Feed System Design

A difficulty with this approach, however, is that the apparent viscosity, μ_melt, is a function of the shear rate and the runner radius. To avoid iterative estimation of the shear rate and viscosity, the power law model can be used to calculate the radius in a single step as:

π

An issue remains, however, as to what the maximum pressure drop should be in each segment of the feed system. Knowing the specification on the total pressure drop from the machine nozzle to the cavity, various schemes can be developed to allocate the pressure drop across each portion of the feed system. The simplest approach is to divide the maximum pressure drop for the entire feed system by the number of segments between the nozzle and the cavity. For instance, if the polymer melt flowed through a sprue, a primary runner, and a secondary runner and the maximum pressure drop for the feed system was 30 MPa, then the mold designer could choose to allocate a maximum pressure drop of 10 MPa for each of the segments of the feed system.

The problem with this approach, however, is that it does not account for the length of each portion of the feed system. A very short secondary runner, for instance, would be allocated the same pressure drop as a long primary runner. The resulting design would be suboptimal with the diameter being too small for the secondary runner and too large for the primary runner.

Another simple approach is to distribute the pressure drop across the feed system in proportion to the length of each runner segment:

=

whereΔPiis the maximum pressure drop allocated to runner segment i with length L_i, and m is the number of runner segments between the inlet and outlet of the feed system. As such, longer runner segments will be allowed a proportionally greater portion of the pressure drop through the feed system.

Example: Calculate the minimum diameters in the hot runner system design shown in Figure 6.18 so that the pressure drop through the feed system does not exceed 30 MPa.

Assume ABS is molded with the molding machine providing a volumetric flow rate of 125 cc/s.

143

The total length of the feed system from the inlet to the outlet is:

=

The maximum pressure drop through the sprue is allocated as:

Δ sprue = ⋅ =

90 mm

30 MPa 8.5 MPa

316 mm P

Given this pressure drop for the sprue, the sprue diameter can be calculated from Eq. (6.8) as:

Similarly, the maximum pressure drop through the manifold is allocated as:

Δ manifold = ⋅ =

118 mm

30 MPa 11.2 MPa

316 mm P

Given this pressure drop for the manifold, the primary runner diameter in the manifold can be calculated from Eq. (6.8) as:

π

Similarly, the maximum pressure drop through the nozzle is allocated as:

nozzle

108 mm

30 MPa 10.3 MPa

316 mm

ΔP = ⋅ =

Given this pressure drop for the nozzle, the nozzle bore diameter can be calculated from Eq. (6.8) as:

6.4 Feed System Analysis

144 6 Feed System Design

It should not be surprising that the diameter of the runner in the manifold and nozzle are the same since 1) the two runners have the same melt flow rate and 2) were purposefully assigned the same pressure drop per unit length according to Eq. (6.9). The resulting hot runner system design has a volume of 35 cc and a pressure drop of 30 MPa, both of which are about 5% less than the previous design (which had a volume of 37 cc and a pressure drop of 31.4 MPa). Furthermore, by maintaining the same runner diameter in the manifold and the nozzle, more uniform shear stresses are maintained with a lower likelihood for dead spots.

To further reduce the runner system volume, it is necessary to specify smaller feed system diameters. This action will result in a larger pressure drop through the feed system unless a higher melt temperature, lower viscosity material, or lower flow rate is assumed. If a 50 MPa pressure drop through the feed system was specified, then the above analysis can be applied to achieve the following results:

=

The mold designer may repeat the analysis to evaluate the volume of the feed system for different pressure drops. Figure 6.19 provides a plot of the volume of the feed system as a function of the maximum pressure drop. To achieve a low pressure drop, large runner diameters are necessary which results in a very high volume for the feed system. As the allowable pressure drop increases to 100 MPa, the volume of the feed system decreases substantially, though a runner volume of 10 cc remains necessary to convey the melt at a flow rate of 125 cc/s.

In optimizing the feed system design, the mold designer needs to know the flow rates during the filling stage and the expected pressured drop. Figure 6.19 indicates how the feed system designs will change with the volumetric flow rates during the filling stage. Lower flow rates will result in lower pressure drops, which in turn allow for a reduction in the radii and volume of the feed system. Since the actual flow rates are determined by the molder after the mold is designed and built, the molder should verify the expected fill time of the cavity with the molder and calculate the expected flow rates through the feed system. If the flow rates are uncertain, then the mold designer can estimate the linear melt velocity in the cavity per Eq. (5.23) and assume that the flow rate is constant throughout the filling stage.

145