6 Feed System Design
6.5 Practical Issues
6.5.1 Runner Cross-Sections
residence (1 turns) cycle
t n t (6.11)
This residence time is approximate since material flows through the hot runner system at various rates; the polymer melt near the walls and in dead spots of the hot runner can have much longer residence times than predicted by Eq. (6.11). Furthermore, the mold designer should remember that the material flowing into the hot runner system has already resided in the barrel of the molding machine for a significant amount of time. Accordingly, the mold designer should strive to minimize the number of turns to reduce the residence time and potential degradation of the polymer melt.
Example: Compute the number of turns and residence time of the hot runner designed in Section 6.4.5.
The hot runner design resulting from an allowed 50 MPa pressure drop had a volume of 21.3 cc. Since the volume of the bezel cavity is 27.5 cc, the number of turns is:
= =
turns
21.3 cc 27.5 cc 0.77 n
which is very low. New material will through the hot runner system and into the mold cavity with every cycle. In Section 3.4.3, the cycle time was estimated as 13.5 s. The residence time in the hot runner system is estimated as:
= + ⋅ =
residence
(1 0.77 cycles) 13.5 s 24 s cycle t
This residence time is very low compared to the allowable residence time of most polymers, which is typically greater than 15 minutes.
6.5 Practical Issues
While this chapter so far has discussed the purpose, types, and analysis of feed systems, there are some practical issues that the mold designer should consider before completing the feed system design.
6.5.1 Runner Cross-Sections
The provided analysis has been restricted to “full round” circular runners since these are extremely common in mold designs and provide for simple analysis. However, other runner
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cross sections are also fairly common in practice since they may be easier to machine. In particular, the trapezoidal, round-bottom trapezoid, and half-round runners are often machined into only the moving side of the mold as shown in Figure 6.20. This mold design strategy not only reduces the amount of machining, but also reduces the design time and potential for machining or misalignment mistakes associated with matching the two sides of a full round runner.
The primary drawback associated with these non-circular runners is that they give rise to non-uniform shear rates and shear stresses around the perimeter of the cross-section. For example, the trapezoidal runner is easy to machine, but the sections near the four corners conduct very little flow down the length of the runner. The performance of the trapezoidal runner can be improved by rounding the bottom surface to eliminate two of the corners.
However, all these non-circular types of runner will need to be slightly larger and consume additional material to provide the same pressure drop as a full round runner.
The previously described analysis can be adapted for use with non-circular runner sections.
While the results will not be as precise as for a full-round runner, the hydraulic diameter, Dh, for each runner type can be calculated as:
= ⋅ section
h
section
D 4 A
p (6.12)
where Asectionis the cross-sectional area of the runner and psectionis the perimeter of the cross-section of the runner. For reference, Table 6.3 provides equations relating the specified dimensions of the different sections in Figure 6.20 to the hydraulic diameter. It should be noted that the equations in Table 6.3 have been derived assuming a 5 degree taper angle to assist with the ejection of the runner from the mold. This assumption allows for a reduction in the number of design variables. The efficiencies listed in Table 6.3 are defined as:
2
152 6 Feed System Design
The results indicate that the full round runner is the most efficient section design, followed by the round bottom trapezoid, the trapezoid, and the half-round.
Example: The primary runner in the three-plate mold of Figure 6.7 has a trapezoidal section. Calculate the pressure drop through a 120 mm length of primary with a width of 6 mm, a depth of 8 mm, and a 5 degree taper angle. Assume the use of ABS with a flow rate of 44 cc/s.
First, the hydraulic diameter is calculated as:
⋅ ⋅ + ⋅
Then, the pressure drop is calculated using the power law model using the hydraulic diameter as if the trapezoidal runner were circular:
π
The dimensions of this trapezoidal design are too large, providing a low pressure drop but consuming excess material and cycle time. The depth and width of the runner should be reduced.
Table 6.3: Hydraulic diameter for different runner sections
Runner section
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There is one other runner section that is quite common in hot runner systems: the annulus.
Specifically, many hot runner systems incorporate valve pins down the length of the nozzles to physically shut-off the gate as discussed in Section 7.2.9. In this design, the polymer melt flows between a cylindrical drop and the cylindrical valve pin, forming an annulus as shown in Figure 6.21.
The polymer melt flow through an annular section may be closely approximated by adapting the equation for viscous flow in the strip. Specifically, the width of the strip can be replaced by the circumference of the mean diameter of the melt annulus while the thickness of the strip is replaced by the distance between the valve pin and the nozzle bore. Making these replacements in Eq. (5.17) results in the following relation between pressure drop and flow rate in an annular section:
where DPinis the diameter of the valve pin and DBoreis the diameter of the bore through the nozzle. The power-law model for an annulus can be similarly derived as:
π
bore pin bore pin bore pin
2 2 1
Example: Calculate the pressure drop through a valve gated nozzle having a length of 150 mm, a bore diameter of 10 mm, and a valve pin diameter of 5 mm. Assume a material with a viscosity of 100 Pa s flowing at a rate of 50 cc/s.
Substituting these values into Eq. (6.14), the estimated pressure drop is:
π
Figure 6.21: Annular section in valve gated hot-runner
6.5 Practical Issues
154 6 Feed System Design