Output is one of the main indicators for judging the performance of an extruder screw. However, simply emphasizing the percentage increase in output of an improved screw over the original screw is of little significance, because the basis for comparison is often unclear. From hydrodynamic theory, we know that replacing an already worn screw with one having a smaller flight clearance will also lead to a considerable increase in output. To accurately reflect this aspect of screw performance, comparisons can generally be made based on the following four criteria.
1. Specific throughput (Q/n), i.e., comparing the output per unit screw speed for different screws under the precondition of acceptable quality. Since the actual output Q (kg/h) and the screw speed n (rpm) can both be measured, the specific throughput Q/n is easy to calculate. Its unit is (kg/h)/rpm, meaning the output per hour per screw revolution.
If the Q/n value is too low, then other comparisons become meaningless, because it indicates that either the screw design is unreasonable or the process operating conditions are unreasonable. For example, for a Φ65 extruder, a Q/n value below 0.24 is probably too low; for a Φ90 extruder, it is desirable for Q/n to be above 2, where Q is the output when extruding polyethylene with a die. Of course, these reference figures only apply to the current situation, and they will likely be exceeded in the future.
2. Conveying efficiency (η), which is the ratio of the actual output Q to the theoretical output Q₁.
η = Q / Q₁
The actual output can be measured, while many methods and formulas exist for calculating the theoretical output Q₁. Currently, a simplified theoretical formula is generally used:
Q₁ = F · π · D · ρ · n = 0.06 (S – b) H₃ (D – H₃) π · ρ · n (7-2)
The physical meaning of Eq. (7-2) is that the screw conveys one annular ring of plastic per revolution (Fig. 7-1). The mean diameter of this ring is D, and the cross-sectional area F = (S – b) H₃, where S, b, H₃ and D are the screw pitch, axial flight width, channel depth in the metering section, and screw diameter, respectively, all in cm; n is the screw speed in rpm; the theoretical output is in kg/h; and ρ is the melt density. The densities of several thermoplastics are shown in Table 7-1.
When the screw parameters and density are known, the denominator in the ratio becomes a constant, so the specific throughput Q/n is linked to the conveying efficiency η, and they are clearly in direct proportion. That is, a larger specific throughput inevitably means a higher conveying efficiency. Therefore, by measuring the specific throughput, we can indirectly compare the conveying efficiency.
For screw design, the concept of conveying efficiency is very important, as it reflects the overall performance of the screw extrusion system. According to experiments, under normal conditions, the conveying efficiency of a smooth-bore barrel ranges from 0.30 to 0.50. A value higher than 0.50 is unlikely, and a value below 0.30 is uneconomical.
It must be pointed out that when longitudinal rectangular grooves are cut into the barrel of the feed section and intensive cooling is applied, both the specific throughput and the conveying efficiency will be greatly improved. The working principle of such a system (IKV system) is different from that of a smooth-bore barrel system. The latter calculates the theoretical output based on hydrodynamic theory and therefore bases the calculation on the metering section; whereas the output of the former is determined by the feed section.
3. Maximum output (Qmax). The main goal pursued by a screw designer is to achieve the highest possible output while ensuring quality. When comparing the maximum output Qmax of two screws, Eq. (7-4) can be used to calculate the maximum output for each screw.
Qmax = 0.85 n_max (Q/n) (7-4)
Considering that the normal operating speed of an extruder is typically about 85% of the designed maximum speed, a coefficient of 0.85 is multiplied in Eq. (7-4).
4. "Stiffness" of the screw characteristic. The so-called "stiffness" of the screw characteristic refers to how much the output decreases as the die pressure increases. From Fig. 7-2, it can be seen that the characteristic of screw a is better than that of screw b. This means that when the die pressure rises, the output of screw a drops less.
