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Pressure profile
The same conditions must be met for the calculation of the pressure profile as for the throughput or dosing time calculation. This applies to all input data (geometry, material data and processing parameters). Additionally, the point of calculation (just PSI) for which the pressure profile of the screw length shall be calculated has to be defined.
The pressure curve is calculated back to the location of the melt vortex formation (OSW).
The pressure curve calculation starts at the screw tip. The calculated throughput is used to determine the pressure loss within a calculation interval and added to the previous absolute pressure. The pressure in the screw vestibule (at the screw tip) results from the set back pressure.
The pressure curve is calculated isothermally at the melt temperature in each step and then multiplied by a correction factor. From a physical point of view, this correction factor ensures that the calculation is carried out at a temperature that allows the pressure and throughput behaviour to match. This is necessary because the flow rate must be calculated according to a mixed isothermal-non-isothermal approach, but the pressure curve must be calculated either isothermally or non-isothermally.
Pressure profile calculation for the barrier section
In order to calculate the barrier screw in the way described a constant pressure gradient has to be assumed. However, since every additional assumption increases inaccuracy, the so-called „Matrix model“ was implemented to eliminate this assumption. Its calculation method is similar to the FEM calculation method.
Here, single intervals are built for barrier flight, solid and melt channel and for each section between the individual balance points, the change in the flow is described by means of a linear equation. These equations form a linear system of equations. The equations only describe the development of the flow in the direction of the channel, which means that the mesh of the division of the geometry into the required intervals corresponds to constant conditions.
Before the resulting equation system can be solved with the familiar algorithms used to solve linear equation systems, it is first necessary to reduce the system. This reduction is achieved by allowing boundary conditions.
In the closed barrier section, the mass flow towards the first node, or away from the last node in the channel direction, can be taken as being equal to zero. If an open barrier section is calculated, by contrast, it is sufficient to alter the boundary condition in order to be able to calculate this design. Because of the lack of a geometrical separation, the pressure difference between the first and last nodes of the solids and melt channel is set at zero.
For a clear-cut solution of the system it is necessary to know about the mass flow. Here an iterative calculation helps, i.e. in the first step, the pressure-throughput behavior of the standard sections is calculated for a known pressure at the screw tip without considering the barrier section. In the second step, this throughput is taken to solve the equation system for the barrier section. Since the overall pressure requirement for the screw is equal to the sum of the pressure requirements of the individual screw sections, the calculated pressure requirement for the barrier section can be added to the pressure requirement of the remaining screw sections that was calculated in the first step.
Pressure curve calculation for wave screws
The calculation of the pressure curve in wave zones is similar to the calculation of the node point method in barrier zones. The node point method is an analogue model of network theory from electrical engineering. A network is formed from the geometry of the screw, which is made up of simple geometries (rectangular channels). A voltage source (drag flow) and a resistance (pressure flow) are defined for each of these simple geometries. A matrix is created and solved from the network of stress sources and resistances so that, for a given pressure difference in the zone, not only the flow rate but also the pressure is obtained for each of the simple geometries, so that the pressure curve over the zone is also known.